From b3230b8828f461f5bedaf92fdef6ba9aebc9a138 Mon Sep 17 00:00:00 2001
From: eldridgejm-machine-user <jeldridge@ucsd.edu>
Date: Tue, 7 Jan 2025 18:05:30 -0800
Subject: [PATCH] automata commit

---
 practice/all.html                             | 456 +++++++++---------
 practice/midterm-01.html                      | 144 +++---
 practice/midterm-02.html                      | 280 +++++------
 practice/tags/Gaussians.html                  |  16 +-
 practice/tags/SVMs.html                       |   8 +-
 practice/tags/bayes classifier.html           | 104 ++--
 practice/tags/bayes error.html                |  72 +--
 practice/tags/computing loss.html             |  48 +-
 practice/tags/covariance.html                 |  32 +-
 practice/tags/density estimation.html         |   8 +-
 practice/tags/feature maps.html               |  16 +-
 practice/tags/gradient descent.html           |  16 +-
 practice/tags/gradients.html                  |  32 +-
 practice/tags/histogram estimators.html       |  88 ++--
 practice/tags/kernel ridge regression.html    |  32 +-
 practice/tags/least squares.html              |   8 +-
 .../tags/linear prediction functions.html     |  32 +-
 practice/tags/maximum likelihood.html         |  80 +--
 practice/tags/maxium likelihood.html          |  32 +-
 practice/tags/naive bayes.html                |   8 +-
 practice/tags/subgradients.html               |  32 +-
 21 files changed, 772 insertions(+), 772 deletions(-)

diff --git a/practice/all.html b/practice/all.html
index 58021287..1fe0b745 100644
--- a/practice/all.html
+++ b/practice/all.html
@@ -1007,13 +1007,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the (2,3) entry of the kernel matrix?</p>
 <p><span class="math">\(K_{23} = \)</span>
 <span class="inline-response-box">
-    <span id="answer-782e0112-6b0d-4ab5-aef0-b7947fa64bb3" style="display: none">1</span>
-    <span id="button-782e0112-6b0d-4ab5-aef0-b7947fa64bb3">
+    <span id="answer-96c704bc-d518-4d03-8cb7-d8ddd331381b" style="display: none">1</span>
+    <span id="button-96c704bc-d518-4d03-8cb7-d8ddd331381b">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-782e0112-6b0d-4ab5-aef0-b7947fa64bb3').style.display = 'inline-block';
-                document.getElementById('button-782e0112-6b0d-4ab5-aef0-b7947fa64bb3').style.display = 'none'
+                document.getElementById('answer-96c704bc-d518-4d03-8cb7-d8ddd331381b').style.display = 'inline-block';
+                document.getElementById('button-96c704bc-d518-4d03-8cb7-d8ddd331381b').style.display = 'none'
             "
         >
             Show Answer
@@ -1028,13 +1028,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>Let <span class="math">\(\vec x = (1, 1, 0)^T\)</span> be a new point. What is <span class="math">\(H(\vec x)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-026e1daa-0fca-4dd3-914b-453553fd580b" style="display: none">14</span>
-    <span id="button-026e1daa-0fca-4dd3-914b-453553fd580b">
+    <span id="answer-186da120-821f-4f7a-9edd-687d83b4c923" style="display: none">14</span>
+    <span id="button-186da120-821f-4f7a-9edd-687d83b4c923">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-026e1daa-0fca-4dd3-914b-453553fd580b').style.display = 'inline-block';
-                document.getElementById('button-026e1daa-0fca-4dd3-914b-453553fd580b').style.display = 'none'
+                document.getElementById('answer-186da120-821f-4f7a-9edd-687d83b4c923').style.display = 'inline-block';
+                document.getElementById('button-186da120-821f-4f7a-9edd-687d83b4c923').style.display = 'none'
             "
         >
             Show Answer
@@ -1127,13 +1127,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>Suppose <span class="math">\(\pr(Y = 1) = 0.5\)</span> and <span class="math">\(\pr(Y = 0) = 0.5\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-7a8a0477-da55-474f-ad2f-a052c353c993" style="display: none">0.25</span>
-    <span id="button-7a8a0477-da55-474f-ad2f-a052c353c993">
+    <span id="answer-60a32ee8-8006-4cd0-b555-73063d4594c0" style="display: none">0.25</span>
+    <span id="button-60a32ee8-8006-4cd0-b555-73063d4594c0">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-7a8a0477-da55-474f-ad2f-a052c353c993').style.display = 'inline-block';
-                document.getElementById('button-7a8a0477-da55-474f-ad2f-a052c353c993').style.display = 'none'
+                document.getElementById('answer-60a32ee8-8006-4cd0-b555-73063d4594c0').style.display = 'inline-block';
+                document.getElementById('button-60a32ee8-8006-4cd0-b555-73063d4594c0').style.display = 'none'
             "
         >
             Show Answer
@@ -1160,13 +1160,13 @@ <h3 class="subproblem-id">Part 4)</h3>
 <p>Now suppose <span class="math">\(\pr(Y = 1) = 0.7\)</span> and <span class="math">\(\pr(Y = 0) = 0.3\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-0fd1def3-06dd-4a32-8b98-740392c24784" style="display: none">0.29</span>
-    <span id="button-0fd1def3-06dd-4a32-8b98-740392c24784">
+    <span id="answer-502b9284-b61b-47a0-b061-29e27a78f64e" style="display: none">0.29</span>
+    <span id="button-502b9284-b61b-47a0-b061-29e27a78f64e">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-0fd1def3-06dd-4a32-8b98-740392c24784').style.display = 'inline-block';
-                document.getElementById('button-0fd1def3-06dd-4a32-8b98-740392c24784').style.display = 'none'
+                document.getElementById('answer-502b9284-b61b-47a0-b061-29e27a78f64e').style.display = 'inline-block';
+                document.getElementById('button-502b9284-b61b-47a0-b061-29e27a78f64e').style.display = 'none'
             "
         >
             Show Answer
@@ -1222,13 +1222,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is <span class="math">\(f(1.5)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-773bd204-8b13-458b-ab0e-2bacad5ed727" style="display: none">0.2</span>
-    <span id="button-773bd204-8b13-458b-ab0e-2bacad5ed727">
+    <span id="answer-11a3ee23-5382-4999-9402-6ea30c3d5c4c" style="display: none">0.2</span>
+    <span id="button-11a3ee23-5382-4999-9402-6ea30c3d5c4c">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-773bd204-8b13-458b-ab0e-2bacad5ed727').style.display = 'inline-block';
-                document.getElementById('button-773bd204-8b13-458b-ab0e-2bacad5ed727').style.display = 'none'
+                document.getElementById('answer-11a3ee23-5382-4999-9402-6ea30c3d5c4c').style.display = 'inline-block';
+                document.getElementById('button-11a3ee23-5382-4999-9402-6ea30c3d5c4c').style.display = 'none'
             "
         >
             Show Answer
@@ -1243,13 +1243,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is <span class="math">\(f(7)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-8edbe96e-966e-449d-bf86-6768eab2713d" style="display: none">.05</span>
-    <span id="button-8edbe96e-966e-449d-bf86-6768eab2713d">
+    <span id="answer-0e02e11e-7824-46b8-962f-d235b2e5d179" style="display: none">.05</span>
+    <span id="button-0e02e11e-7824-46b8-962f-d235b2e5d179">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-8edbe96e-966e-449d-bf86-6768eab2713d').style.display = 'inline-block';
-                document.getElementById('button-8edbe96e-966e-449d-bf86-6768eab2713d').style.display = 'none'
+                document.getElementById('answer-0e02e11e-7824-46b8-962f-d235b2e5d179').style.display = 'inline-block';
+                document.getElementById('button-0e02e11e-7824-46b8-962f-d235b2e5d179').style.display = 'none'
             "
         >
             Show Answer
@@ -1300,13 +1300,13 @@ <h2>Problem #036</h2>
 <p>What is the largest value that <span class="math">\(f(\vec x)\)</span> can possibly have?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-f9ae30ed-b4d9-48f8-8604-9e734314b972" style="display: none">1/6</span>
-    <span id="button-f9ae30ed-b4d9-48f8-8604-9e734314b972">
+    <span id="answer-da4bd1c7-8af0-445d-8f0e-00459afc9c54" style="display: none">1/6</span>
+    <span id="button-da4bd1c7-8af0-445d-8f0e-00459afc9c54">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-f9ae30ed-b4d9-48f8-8604-9e734314b972').style.display = 'inline-block';
-                document.getElementById('button-f9ae30ed-b4d9-48f8-8604-9e734314b972').style.display = 'none'
+                document.getElementById('answer-da4bd1c7-8af0-445d-8f0e-00459afc9c54').style.display = 'inline-block';
+                document.getElementById('button-da4bd1c7-8af0-445d-8f0e-00459afc9c54').style.display = 'none'
             "
         >
             Show Answer
@@ -1400,13 +1400,13 @@ <h2>Problem #040</h2>
 <p>Suppose a Gaussian with a diagonal covariance matrix is fit to 200 points in <span class="math">\(\mathbb R^4\)</span> using the maximum likelihood estimators. How many parameters are estimated? Count each entry of <span class="math">\(\mu\)</span> and the covariance matrix that must be estimated as its own parameter.</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-6b7f287e-f6a3-44e2-bfa5-83a984c19749" style="display: none">8</span>
-    <span id="button-6b7f287e-f6a3-44e2-bfa5-83a984c19749">
+    <span id="answer-e21f3161-3699-4a20-b0e7-5f24a5180dac" style="display: none">8</span>
+    <span id="button-e21f3161-3699-4a20-b0e7-5f24a5180dac">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-6b7f287e-f6a3-44e2-bfa5-83a984c19749').style.display = 'inline-block';
-                document.getElementById('button-6b7f287e-f6a3-44e2-bfa5-83a984c19749').style.display = 'none'
+                document.getElementById('answer-e21f3161-3699-4a20-b0e7-5f24a5180dac').style.display = 'inline-block';
+                document.getElementById('button-e21f3161-3699-4a20-b0e7-5f24a5180dac').style.display = 'none'
             "
         >
             Show Answer
@@ -1573,13 +1573,13 @@ <h2>Problem #045</h2>
 <p>If Gaussian Naive Bayes is trained on this data, how many univariate Gaussians will be fit?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-8e3d561b-1fbd-43cd-b7ed-e4ba424fda82" style="display: none">20</span>
-    <span id="button-8e3d561b-1fbd-43cd-b7ed-e4ba424fda82">
+    <span id="answer-165d2ba9-481e-4654-acc2-88b00acd4a60" style="display: none">20</span>
+    <span id="button-165d2ba9-481e-4654-acc2-88b00acd4a60">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-8e3d561b-1fbd-43cd-b7ed-e4ba424fda82').style.display = 'inline-block';
-                document.getElementById('button-8e3d561b-1fbd-43cd-b7ed-e4ba424fda82').style.display = 'none'
+                document.getElementById('answer-165d2ba9-481e-4654-acc2-88b00acd4a60').style.display = 'inline-block';
+                document.getElementById('button-165d2ba9-481e-4654-acc2-88b00acd4a60').style.display = 'none'
             "
         >
             Show Answer
@@ -1735,13 +1735,13 @@ <h2>Problem #049</h2>
 <p>The density estimate within a particular bin of the histogram is 0.1. How many data points from <span class="math">\(\mathcal D\)</span> fall within that histogram bin?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-f3fe737e-3a43-4f9d-9fa6-0cc3d0b0a602" style="display: none">80</span>
-    <span id="button-f3fe737e-3a43-4f9d-9fa6-0cc3d0b0a602">
+    <span id="answer-79ade3f8-8fde-4bb7-843a-8b77998e4c6e" style="display: none">80</span>
+    <span id="button-79ade3f8-8fde-4bb7-843a-8b77998e4c6e">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-f3fe737e-3a43-4f9d-9fa6-0cc3d0b0a602').style.display = 'inline-block';
-                document.getElementById('button-f3fe737e-3a43-4f9d-9fa6-0cc3d0b0a602').style.display = 'none'
+                document.getElementById('answer-79ade3f8-8fde-4bb7-843a-8b77998e4c6e').style.display = 'inline-block';
+                document.getElementById('button-79ade3f8-8fde-4bb7-843a-8b77998e4c6e').style.display = 'none'
             "
         >
             Show Answer
@@ -1835,13 +1835,13 @@ <h2>Problem #053</h2>
 <p>Suppose a Gaussian with a diagonal covariance matrix is fit to 200 points in <span class="math">\(\mathbb R^4\)</span> using the maximum likelihood estimators. How many parameters are estimated? Count each entry of <span class="math">\(\vec\mu\)</span> and the covariance matrix that must be estimated as its own parameter (the off-diagonal elements of the covariance are zero, and shouldn't be included in your count).</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-b56afb77-a3d7-4b47-99d3-7e229f8a16ef" style="display: none">8</span>
-    <span id="button-b56afb77-a3d7-4b47-99d3-7e229f8a16ef">
+    <span id="answer-ef799fd3-f23f-4426-826b-b9ba0d6679ec" style="display: none">8</span>
+    <span id="button-ef799fd3-f23f-4426-826b-b9ba0d6679ec">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-b56afb77-a3d7-4b47-99d3-7e229f8a16ef').style.display = 'inline-block';
-                document.getElementById('button-b56afb77-a3d7-4b47-99d3-7e229f8a16ef').style.display = 'none'
+                document.getElementById('answer-ef799fd3-f23f-4426-826b-b9ba0d6679ec').style.display = 'inline-block';
+                document.getElementById('button-ef799fd3-f23f-4426-826b-b9ba0d6679ec').style.display = 'none'
             "
         >
             Show Answer
@@ -2128,13 +2128,13 @@ <h2>Problem #061</h2>
 <p>Let <span class="math">\(\vec x = (1, 2)^T\)</span>. What is <span class="math">\(H(\vec x)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-22da90df-60fa-4b4f-9d6f-0a34dc7071d1" style="display: none">3</span>
-    <span id="button-22da90df-60fa-4b4f-9d6f-0a34dc7071d1">
+    <span id="answer-b38a1557-5b27-414b-8e2d-96ff9a8f6430" style="display: none">3</span>
+    <span id="button-b38a1557-5b27-414b-8e2d-96ff9a8f6430">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-22da90df-60fa-4b4f-9d6f-0a34dc7071d1').style.display = 'inline-block';
-                document.getElementById('button-22da90df-60fa-4b4f-9d6f-0a34dc7071d1').style.display = 'none'
+                document.getElementById('answer-b38a1557-5b27-414b-8e2d-96ff9a8f6430').style.display = 'inline-block';
+                document.getElementById('button-b38a1557-5b27-414b-8e2d-96ff9a8f6430').style.display = 'none'
             "
         >
             Show Answer
@@ -2206,13 +2206,13 @@ <h2>Problem #063</h2>
 <p>What is the value of <span class="math">\(H\)</span> at the point <span class="math">\(\nvec{x}{4} = (0, 1)^T\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-cdaca243-fc50-4d3f-922c-99629c874cf8" style="display: none">0</span>
-    <span id="button-cdaca243-fc50-4d3f-922c-99629c874cf8">
+    <span id="answer-4cecabf8-ee62-4a1e-a55b-91f5ce6f2141" style="display: none">0</span>
+    <span id="button-4cecabf8-ee62-4a1e-a55b-91f5ce6f2141">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-cdaca243-fc50-4d3f-922c-99629c874cf8').style.display = 'inline-block';
-                document.getElementById('button-cdaca243-fc50-4d3f-922c-99629c874cf8').style.display = 'none'
+                document.getElementById('answer-4cecabf8-ee62-4a1e-a55b-91f5ce6f2141').style.display = 'inline-block';
+                document.getElementById('button-4cecabf8-ee62-4a1e-a55b-91f5ce6f2141').style.display = 'none'
             "
         >
             Show Answer
@@ -2366,13 +2366,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the <b>total</b><i>square</i> loss of <span class="math">\(H\)</span> on this data set?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-86fb964b-a956-4917-8820-618d47744537" style="display: none">11.25</span>
-    <span id="button-86fb964b-a956-4917-8820-618d47744537">
+    <span id="answer-9da3d6c5-2ecc-4bdc-8db7-e2308e82a2c0" style="display: none">11.25</span>
+    <span id="button-9da3d6c5-2ecc-4bdc-8db7-e2308e82a2c0">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-86fb964b-a956-4917-8820-618d47744537').style.display = 'inline-block';
-                document.getElementById('button-86fb964b-a956-4917-8820-618d47744537').style.display = 'none'
+                document.getElementById('answer-9da3d6c5-2ecc-4bdc-8db7-e2308e82a2c0').style.display = 'inline-block';
+                document.getElementById('button-9da3d6c5-2ecc-4bdc-8db7-e2308e82a2c0').style.display = 'none'
             "
         >
             Show Answer
@@ -2387,13 +2387,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is the <b>total</b><i>perceptron</i> loss of <span class="math">\(H\)</span> on this data set?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-7f03751b-5b77-4cfb-86f5-d1ee507f76d6" style="display: none">1</span>
-    <span id="button-7f03751b-5b77-4cfb-86f5-d1ee507f76d6">
+    <span id="answer-bf18d374-6839-478d-ad70-12ea5843f438" style="display: none">1</span>
+    <span id="button-bf18d374-6839-478d-ad70-12ea5843f438">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-7f03751b-5b77-4cfb-86f5-d1ee507f76d6').style.display = 'inline-block';
-                document.getElementById('button-7f03751b-5b77-4cfb-86f5-d1ee507f76d6').style.display = 'none'
+                document.getElementById('answer-bf18d374-6839-478d-ad70-12ea5843f438').style.display = 'inline-block';
+                document.getElementById('button-bf18d374-6839-478d-ad70-12ea5843f438').style.display = 'none'
             "
         >
             Show Answer
@@ -2408,13 +2408,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>What is the <b>total</b><i>hinge</i> loss of <span class="math">\(H\)</span> on this data set?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-6d729397-b8db-4975-b7e7-86abc9376bd3" style="display: none">3.5</span>
-    <span id="button-6d729397-b8db-4975-b7e7-86abc9376bd3">
+    <span id="answer-df961876-206c-4954-8dc2-030a33a6f1aa" style="display: none">3.5</span>
+    <span id="button-df961876-206c-4954-8dc2-030a33a6f1aa">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-6d729397-b8db-4975-b7e7-86abc9376bd3').style.display = 'inline-block';
-                document.getElementById('button-6d729397-b8db-4975-b7e7-86abc9376bd3').style.display = 'none'
+                document.getElementById('answer-df961876-206c-4954-8dc2-030a33a6f1aa').style.display = 'inline-block';
+                document.getElementById('button-df961876-206c-4954-8dc2-030a33a6f1aa').style.display = 'none'
             "
         >
             Show Answer
@@ -2451,13 +2451,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the gradient of this function at the point <span class="math">\((0, 0)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-553f47d9-fe6b-4dab-a17a-59e59d275f9e" style="display: none"><span class="math">\((2, 1)^T\)</span></span>
-    <span id="button-553f47d9-fe6b-4dab-a17a-59e59d275f9e">
+    <span id="answer-c0a0413f-a869-42a2-8389-818fd0d97849" style="display: none"><span class="math">\((2, 1)^T\)</span></span>
+    <span id="button-c0a0413f-a869-42a2-8389-818fd0d97849">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-553f47d9-fe6b-4dab-a17a-59e59d275f9e').style.display = 'inline-block';
-                document.getElementById('button-553f47d9-fe6b-4dab-a17a-59e59d275f9e').style.display = 'none'
+                document.getElementById('answer-c0a0413f-a869-42a2-8389-818fd0d97849').style.display = 'inline-block';
+                document.getElementById('button-c0a0413f-a869-42a2-8389-818fd0d97849').style.display = 'none'
             "
         >
             Show Answer
@@ -2506,13 +2506,13 @@ <h2>Problem #068</h2>
 <p>Suppose that the initial weight vector is <span class="math">\(\vec w = (0, 0)^T\)</span> and that the learning rate <span class="math">\(\eta = 1\)</span>. What will be the weight vector after one iteration of subgradient descent?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-4065b4c3-f01f-40ee-a227-2f848d520639" style="display: none"><span class="math">\((1, 2)^T\)</span></span>
-    <span id="button-4065b4c3-f01f-40ee-a227-2f848d520639">
+    <span id="answer-9691969d-ee7e-4849-837c-0592e1750ee0" style="display: none"><span class="math">\((1, 2)^T\)</span></span>
+    <span id="button-9691969d-ee7e-4849-837c-0592e1750ee0">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-4065b4c3-f01f-40ee-a227-2f848d520639').style.display = 'inline-block';
-                document.getElementById('button-4065b4c3-f01f-40ee-a227-2f848d520639').style.display = 'none'
+                document.getElementById('answer-9691969d-ee7e-4849-837c-0592e1750ee0').style.display = 'inline-block';
+                document.getElementById('button-9691969d-ee7e-4849-837c-0592e1750ee0').style.display = 'none'
             "
         >
             Show Answer
@@ -2716,13 +2716,13 @@ <h2>Problem #073</h2>
 <p>What weight vector <i>is</i> the solution of the Hard SVM problem for this data set?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-adea6d92-ede3-4d97-96fe-552e0a962fa0" style="display: none"><span class="math">\((3, 0, \frac{1}{4})^T\)</span></span>
-    <span id="button-adea6d92-ede3-4d97-96fe-552e0a962fa0">
+    <span id="answer-6fe89a7c-de7a-402c-9cfc-9fa186cf1897" style="display: none"><span class="math">\((3, 0, \frac{1}{4})^T\)</span></span>
+    <span id="button-6fe89a7c-de7a-402c-9cfc-9fa186cf1897">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-adea6d92-ede3-4d97-96fe-552e0a962fa0').style.display = 'inline-block';
-                document.getElementById('button-adea6d92-ede3-4d97-96fe-552e0a962fa0').style.display = 'none'
+                document.getElementById('answer-6fe89a7c-de7a-402c-9cfc-9fa186cf1897').style.display = 'inline-block';
+                document.getElementById('button-6fe89a7c-de7a-402c-9cfc-9fa186cf1897').style.display = 'none'
             "
         >
             Show Answer
@@ -2756,13 +2756,13 @@ <h2>Problem #074</h2>
 <p>What is <span class="math">\(\frac{d}{d \vec w} f(\vec w)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-669c2ca7-463d-4926-ba65-fe7b0dc4f1a8" style="display: none"><span class="math">\(\sum_{i=1}^n \nvec{x}{i} + 2 \vec w\)</span></span>
-    <span id="button-669c2ca7-463d-4926-ba65-fe7b0dc4f1a8">
+    <span id="answer-6f2d7e9b-5d4b-4fc2-9d5c-32a0c04271cd" style="display: none"><span class="math">\(\sum_{i=1}^n \nvec{x}{i} + 2 \vec w\)</span></span>
+    <span id="button-6f2d7e9b-5d4b-4fc2-9d5c-32a0c04271cd">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-669c2ca7-463d-4926-ba65-fe7b0dc4f1a8').style.display = 'inline-block';
-                document.getElementById('button-669c2ca7-463d-4926-ba65-fe7b0dc4f1a8').style.display = 'none'
+                document.getElementById('answer-6f2d7e9b-5d4b-4fc2-9d5c-32a0c04271cd').style.display = 'inline-block';
+                document.getElementById('button-6f2d7e9b-5d4b-4fc2-9d5c-32a0c04271cd').style.display = 'none'
             "
         >
             Show Answer
@@ -2988,13 +2988,13 @@ <h2>Problem #079</h2>
 <p>Let <span class="math">\(\vec x = (1, 2, 1)^T\)</span>. What is <span class="math">\(H(\vec x)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-92c7c658-b347-45a8-88cf-c19875c01892" style="display: none"><span class="math">\(-3\)</span></span>
-    <span id="button-92c7c658-b347-45a8-88cf-c19875c01892">
+    <span id="answer-3206df7d-6b60-48a8-b29a-7d646be06c15" style="display: none"><span class="math">\(-3\)</span></span>
+    <span id="button-3206df7d-6b60-48a8-b29a-7d646be06c15">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-92c7c658-b347-45a8-88cf-c19875c01892').style.display = 'inline-block';
-                document.getElementById('button-92c7c658-b347-45a8-88cf-c19875c01892').style.display = 'none'
+                document.getElementById('answer-3206df7d-6b60-48a8-b29a-7d646be06c15').style.display = 'inline-block';
+                document.getElementById('button-3206df7d-6b60-48a8-b29a-7d646be06c15').style.display = 'none'
             "
         >
             Show Answer
@@ -3020,13 +3020,13 @@ <h2>Problem #080</h2>
 <p>What is the mean squared error of a least squares classifier trained on this data set (without regularization)? Your answer should be a number.</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-d46f2667-319f-4c48-84e6-e69ec24ea15b" style="display: none">0</span>
-    <span id="button-d46f2667-319f-4c48-84e6-e69ec24ea15b">
+    <span id="answer-331f3523-acd5-408f-92ad-f26289cee8c8" style="display: none">0</span>
+    <span id="button-331f3523-acd5-408f-92ad-f26289cee8c8">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-d46f2667-319f-4c48-84e6-e69ec24ea15b').style.display = 'inline-block';
-                document.getElementById('button-d46f2667-319f-4c48-84e6-e69ec24ea15b').style.display = 'none'
+                document.getElementById('answer-331f3523-acd5-408f-92ad-f26289cee8c8').style.display = 'inline-block';
+                document.getElementById('button-331f3523-acd5-408f-92ad-f26289cee8c8').style.display = 'none'
             "
         >
             Show Answer
@@ -3108,13 +3108,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the <b>total</b><i>square</i> loss of <span class="math">\(H\)</span> on this data set?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-4af8db9f-0ce8-45fb-8da8-4227c2820f1f" style="display: none">13.5</span>
-    <span id="button-4af8db9f-0ce8-45fb-8da8-4227c2820f1f">
+    <span id="answer-f60ec53f-452e-4079-83e5-93da6205ad12" style="display: none">13.5</span>
+    <span id="button-f60ec53f-452e-4079-83e5-93da6205ad12">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-4af8db9f-0ce8-45fb-8da8-4227c2820f1f').style.display = 'inline-block';
-                document.getElementById('button-4af8db9f-0ce8-45fb-8da8-4227c2820f1f').style.display = 'none'
+                document.getElementById('answer-f60ec53f-452e-4079-83e5-93da6205ad12').style.display = 'inline-block';
+                document.getElementById('button-f60ec53f-452e-4079-83e5-93da6205ad12').style.display = 'none'
             "
         >
             Show Answer
@@ -3129,13 +3129,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is the <b>total</b><i>perceptron</i> loss of <span class="math">\(H\)</span> on this data set?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-5bb6bc60-133a-4b9a-a9e0-25abf1965e1d" style="display: none">1.5</span>
-    <span id="button-5bb6bc60-133a-4b9a-a9e0-25abf1965e1d">
+    <span id="answer-405dcb60-c304-4d4b-8aaf-60a64dbddf6d" style="display: none">1.5</span>
+    <span id="button-405dcb60-c304-4d4b-8aaf-60a64dbddf6d">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-5bb6bc60-133a-4b9a-a9e0-25abf1965e1d').style.display = 'inline-block';
-                document.getElementById('button-5bb6bc60-133a-4b9a-a9e0-25abf1965e1d').style.display = 'none'
+                document.getElementById('answer-405dcb60-c304-4d4b-8aaf-60a64dbddf6d').style.display = 'inline-block';
+                document.getElementById('button-405dcb60-c304-4d4b-8aaf-60a64dbddf6d').style.display = 'none'
             "
         >
             Show Answer
@@ -3150,13 +3150,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>What is the <b>total</b><i>hinge</i> loss of <span class="math">\(H\)</span> on this data set?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-2ad43a7e-7358-44f5-b311-8c82220d1310" style="display: none">4</span>
-    <span id="button-2ad43a7e-7358-44f5-b311-8c82220d1310">
+    <span id="answer-358a68b7-e8d0-4bb9-96a6-a8c724e9e20f" style="display: none">4</span>
+    <span id="button-358a68b7-e8d0-4bb9-96a6-a8c724e9e20f">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-2ad43a7e-7358-44f5-b311-8c82220d1310').style.display = 'inline-block';
-                document.getElementById('button-2ad43a7e-7358-44f5-b311-8c82220d1310').style.display = 'none'
+                document.getElementById('answer-358a68b7-e8d0-4bb9-96a6-a8c724e9e20f').style.display = 'inline-block';
+                document.getElementById('button-358a68b7-e8d0-4bb9-96a6-a8c724e9e20f').style.display = 'none'
             "
         >
             Show Answer
@@ -3195,13 +3195,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the gradient of this function at the point <span class="math">\((1, 1)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-49b3ca93-e478-4a71-bc17-138f974bc1af" style="display: none"><span class="math">\((-1,3)^T\)</span></span>
-    <span id="button-49b3ca93-e478-4a71-bc17-138f974bc1af">
+    <span id="answer-73b60ad8-ac9e-45eb-8275-cffab7ff94b9" style="display: none"><span class="math">\((-1,3)^T\)</span></span>
+    <span id="button-73b60ad8-ac9e-45eb-8275-cffab7ff94b9">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-49b3ca93-e478-4a71-bc17-138f974bc1af').style.display = 'inline-block';
-                document.getElementById('button-49b3ca93-e478-4a71-bc17-138f974bc1af').style.display = 'none'
+                document.getElementById('answer-73b60ad8-ac9e-45eb-8275-cffab7ff94b9').style.display = 'inline-block';
+                document.getElementById('button-73b60ad8-ac9e-45eb-8275-cffab7ff94b9').style.display = 'none'
             "
         >
             Show Answer
@@ -3216,13 +3216,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is the gradient of this function at the point <span class="math">\((-1, -1)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-70ffc1c0-6d7a-4f24-988b-7b59c87d2048" style="display: none"><span class="math">\((-2,0)^T\)</span></span>
-    <span id="button-70ffc1c0-6d7a-4f24-988b-7b59c87d2048">
+    <span id="answer-e733c6ec-875b-46df-8b21-d1ab1caff7ac" style="display: none"><span class="math">\((-2,0)^T\)</span></span>
+    <span id="button-e733c6ec-875b-46df-8b21-d1ab1caff7ac">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-70ffc1c0-6d7a-4f24-988b-7b59c87d2048').style.display = 'inline-block';
-                document.getElementById('button-70ffc1c0-6d7a-4f24-988b-7b59c87d2048').style.display = 'none'
+                document.getElementById('answer-e733c6ec-875b-46df-8b21-d1ab1caff7ac').style.display = 'inline-block';
+                document.getElementById('button-e733c6ec-875b-46df-8b21-d1ab1caff7ac').style.display = 'none'
             "
         >
             Show Answer
@@ -3287,13 +3287,13 @@ <h2>Problem #085</h2>
 <p>Suppose that the initial weight vector is <span class="math">\(\vec w = (0, 0)^T\)</span> and that the learning rate is <span class="math">\(\eta = 1\)</span>. What will be the weight vector after one iteration of subgradient descent?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-ba644ebc-7075-459c-8993-774734b9fef2" style="display: none"><span class="math">\((1, 3)^T\)</span></span>
-    <span id="button-ba644ebc-7075-459c-8993-774734b9fef2">
+    <span id="answer-a5fe6df8-b223-41b1-8522-1b825402c82e" style="display: none"><span class="math">\((1, 3)^T\)</span></span>
+    <span id="button-a5fe6df8-b223-41b1-8522-1b825402c82e">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-ba644ebc-7075-459c-8993-774734b9fef2').style.display = 'inline-block';
-                document.getElementById('button-ba644ebc-7075-459c-8993-774734b9fef2').style.display = 'none'
+                document.getElementById('answer-a5fe6df8-b223-41b1-8522-1b825402c82e').style.display = 'inline-block';
+                document.getElementById('button-a5fe6df8-b223-41b1-8522-1b825402c82e').style.display = 'none'
             "
         >
             Show Answer
@@ -3439,13 +3439,13 @@ <h2>Problem #090</h2>
 <p>What is <span class="math">\(\frac{d}{d \vec x} f(\vec x)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-2ddbde35-010a-4da8-9539-fcbd8abc91b8" style="display: none"><span class="math">\(2 A \vec x + \vec b\)</span></span>
-    <span id="button-2ddbde35-010a-4da8-9539-fcbd8abc91b8">
+    <span id="answer-fcedde7f-575f-471a-9628-f00f0a313c40" style="display: none"><span class="math">\(2 A \vec x + \vec b\)</span></span>
+    <span id="button-fcedde7f-575f-471a-9628-f00f0a313c40">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-2ddbde35-010a-4da8-9539-fcbd8abc91b8').style.display = 'inline-block';
-                document.getElementById('button-2ddbde35-010a-4da8-9539-fcbd8abc91b8').style.display = 'none'
+                document.getElementById('answer-fcedde7f-575f-471a-9628-f00f0a313c40').style.display = 'inline-block';
+                document.getElementById('button-fcedde7f-575f-471a-9628-f00f0a313c40').style.display = 'none'
             "
         >
             Show Answer
@@ -3526,13 +3526,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is <span class="math">\(\pr(1 \leq X \leq 3 \given Y = 0)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-abe96449-fe58-43e4-8bd4-46c0260ab170" style="display: none">0.6</span>
-    <span id="button-abe96449-fe58-43e4-8bd4-46c0260ab170">
+    <span id="answer-2e18d865-898a-40ce-871d-6bb27456123d" style="display: none">0.6</span>
+    <span id="button-2e18d865-898a-40ce-871d-6bb27456123d">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-abe96449-fe58-43e4-8bd4-46c0260ab170').style.display = 'inline-block';
-                document.getElementById('button-abe96449-fe58-43e4-8bd4-46c0260ab170').style.display = 'none'
+                document.getElementById('answer-2e18d865-898a-40ce-871d-6bb27456123d').style.display = 'inline-block';
+                document.getElementById('button-2e18d865-898a-40ce-871d-6bb27456123d').style.display = 'none'
             "
         >
             Show Answer
@@ -3559,13 +3559,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>Suppose again that <span class="math">\(\pr(Y = 1) = \pr(Y = 0) = 0.5\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-4e00d2b9-c6d1-4971-808d-dead2a2eae93" style="display: none">0.30</span>
-    <span id="button-4e00d2b9-c6d1-4971-808d-dead2a2eae93">
+    <span id="answer-c92c2aa3-3460-40d2-ad16-a96db756c91f" style="display: none">0.30</span>
+    <span id="button-c92c2aa3-3460-40d2-ad16-a96db756c91f">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-4e00d2b9-c6d1-4971-808d-dead2a2eae93').style.display = 'inline-block';
-                document.getElementById('button-4e00d2b9-c6d1-4971-808d-dead2a2eae93').style.display = 'none'
+                document.getElementById('answer-c92c2aa3-3460-40d2-ad16-a96db756c91f').style.display = 'inline-block';
+                document.getElementById('button-c92c2aa3-3460-40d2-ad16-a96db756c91f').style.display = 'none'
             "
         >
             Show Answer
@@ -3592,13 +3592,13 @@ <h3 class="subproblem-id">Part 5)</h3>
 <p>Suppose again that <span class="math">\(\pr(Y = 1) = 0.7\)</span> and <span class="math">\(\pr(Y = 0) = 0.3\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-1894a6bf-c51a-45b9-993b-3279cc740ef3" style="display: none">0.27</span>
-    <span id="button-1894a6bf-c51a-45b9-993b-3279cc740ef3">
+    <span id="answer-af6ff066-6642-4eae-86f0-02c1c33e01da" style="display: none">0.27</span>
+    <span id="button-af6ff066-6642-4eae-86f0-02c1c33e01da">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-1894a6bf-c51a-45b9-993b-3279cc740ef3').style.display = 'inline-block';
-                document.getElementById('button-1894a6bf-c51a-45b9-993b-3279cc740ef3').style.display = 'none'
+                document.getElementById('answer-af6ff066-6642-4eae-86f0-02c1c33e01da').style.display = 'inline-block';
+                document.getElementById('button-af6ff066-6642-4eae-86f0-02c1c33e01da').style.display = 'none'
             "
         >
             Show Answer
@@ -3635,13 +3635,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the estimate of the Class 0 density at <span class="math">\(x = 3.5\)</span>? That is, what is the estimate for <span class="math">\(p(3.5 \given Y = 0)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-fdc39258-6533-4207-b557-f6310eaa9590" style="display: none">0.1</span>
-    <span id="button-fdc39258-6533-4207-b557-f6310eaa9590">
+    <span id="answer-ebac4df0-9a5b-4de3-ac04-0e8f97931bb4" style="display: none">0.1</span>
+    <span id="button-ebac4df0-9a5b-4de3-ac04-0e8f97931bb4">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-fdc39258-6533-4207-b557-f6310eaa9590').style.display = 'inline-block';
-                document.getElementById('button-fdc39258-6533-4207-b557-f6310eaa9590').style.display = 'none'
+                document.getElementById('answer-ebac4df0-9a5b-4de3-ac04-0e8f97931bb4').style.display = 'inline-block';
+                document.getElementById('button-ebac4df0-9a5b-4de3-ac04-0e8f97931bb4').style.display = 'none'
             "
         >
             Show Answer
@@ -3656,13 +3656,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>Using the same histogram estimator, what is the estimate of <span class="math">\(\pr(Y = 1 \given x = 3.5)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-3ecb9e36-13ff-4ea5-b683-cdab30330b84" style="display: none">0.5</span>
-    <span id="button-3ecb9e36-13ff-4ea5-b683-cdab30330b84">
+    <span id="answer-a3326f59-df06-4a30-a0b3-4f9e4afcaba8" style="display: none">0.5</span>
+    <span id="button-a3326f59-df06-4a30-a0b3-4f9e4afcaba8">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-3ecb9e36-13ff-4ea5-b683-cdab30330b84').style.display = 'inline-block';
-                document.getElementById('button-3ecb9e36-13ff-4ea5-b683-cdab30330b84').style.display = 'none'
+                document.getElementById('answer-a3326f59-df06-4a30-a0b3-4f9e4afcaba8').style.display = 'inline-block';
+                document.getElementById('button-a3326f59-df06-4a30-a0b3-4f9e4afcaba8').style.display = 'none'
             "
         >
             Show Answer
@@ -3695,13 +3695,13 @@ <h2>Problem #095</h2>
 <p>Consider a new point <span class="math">\(\vec x = (1, 1, 1)\)</span>. What is <span class="math">\(H(\vec x)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-1728e48a-b41e-4244-866a-f12555db0e38" style="display: none">50</span>
-    <span id="button-1728e48a-b41e-4244-866a-f12555db0e38">
+    <span id="answer-68bfbcfd-3d68-4965-9045-e050164f881b" style="display: none">50</span>
+    <span id="button-68bfbcfd-3d68-4965-9045-e050164f881b">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-1728e48a-b41e-4244-866a-f12555db0e38').style.display = 'inline-block';
-                document.getElementById('button-1728e48a-b41e-4244-866a-f12555db0e38').style.display = 'none'
+                document.getElementById('answer-68bfbcfd-3d68-4965-9045-e050164f881b').style.display = 'inline-block';
+                document.getElementById('button-68bfbcfd-3d68-4965-9045-e050164f881b').style.display = 'none'
             "
         >
             Show Answer
@@ -3963,13 +3963,13 @@ <h3 class="subproblem-id">Part 1)</h3>
             L(6, 5)\)</span>? Note that <span class="math">\(\mathcal L\)</span> is the likelihood, <i>not</i> the <i>log</i>-likelihood.</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-fc4bd2c9-43fe-4d1d-8d69-1cf1ae56fc5e" style="display: none"><span class="math">\(10^{-5}\)</span></span>
-    <span id="button-fc4bd2c9-43fe-4d1d-8d69-1cf1ae56fc5e">
+    <span id="answer-c7029729-e4bc-4128-a8f6-c4396e2cd129" style="display: none"><span class="math">\(10^{-5}\)</span></span>
+    <span id="button-c7029729-e4bc-4128-a8f6-c4396e2cd129">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-fc4bd2c9-43fe-4d1d-8d69-1cf1ae56fc5e').style.display = 'inline-block';
-                document.getElementById('button-fc4bd2c9-43fe-4d1d-8d69-1cf1ae56fc5e').style.display = 'none'
+                document.getElementById('answer-c7029729-e4bc-4128-a8f6-c4396e2cd129').style.display = 'inline-block';
+                document.getElementById('button-c7029729-e4bc-4128-a8f6-c4396e2cd129').style.display = 'none'
             "
         >
             Show Answer
@@ -3984,13 +3984,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is <span class="math">\(\mathcal L(3, 2)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-a5fb3577-d33c-406e-87b5-6128605e45ad" style="display: none">0</span>
-    <span id="button-a5fb3577-d33c-406e-87b5-6128605e45ad">
+    <span id="answer-cba6cdcf-cec5-4617-a413-43b24687f216" style="display: none">0</span>
+    <span id="button-cba6cdcf-cec5-4617-a413-43b24687f216">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-a5fb3577-d33c-406e-87b5-6128605e45ad').style.display = 'inline-block';
-                document.getElementById('button-a5fb3577-d33c-406e-87b5-6128605e45ad').style.display = 'none'
+                document.getElementById('answer-cba6cdcf-cec5-4617-a413-43b24687f216').style.display = 'inline-block';
+                document.getElementById('button-cba6cdcf-cec5-4617-a413-43b24687f216').style.display = 'none'
             "
         >
             Show Answer
@@ -4005,13 +4005,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>What are the maximum likelihood estimates of <span class="math">\(\alpha\)</span> and <span class="math">\(\beta\)</span>?</p>
 <p><span class="math">\(\alpha\)</span>: 
 <span class="inline-response-box">
-    <span id="answer-d528cab1-7dd4-4beb-89fc-56b1aba5ec51" style="display: none">5</span>
-    <span id="button-d528cab1-7dd4-4beb-89fc-56b1aba5ec51">
+    <span id="answer-2f9d3d7a-a669-443f-b275-31d53aac075f" style="display: none">5</span>
+    <span id="button-2f9d3d7a-a669-443f-b275-31d53aac075f">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-d528cab1-7dd4-4beb-89fc-56b1aba5ec51').style.display = 'inline-block';
-                document.getElementById('button-d528cab1-7dd4-4beb-89fc-56b1aba5ec51').style.display = 'none'
+                document.getElementById('answer-2f9d3d7a-a669-443f-b275-31d53aac075f').style.display = 'inline-block';
+                document.getElementById('button-2f9d3d7a-a669-443f-b275-31d53aac075f').style.display = 'none'
             "
         >
             Show Answer
@@ -4020,13 +4020,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 </span>
 <span class="math">\(\beta\)</span>: 
 <span class="inline-response-box">
-    <span id="answer-1508a176-9937-40d7-bddd-2a6fe687596e" style="display: none">4</span>
-    <span id="button-1508a176-9937-40d7-bddd-2a6fe687596e">
+    <span id="answer-7e1565cc-82ca-4228-b20e-16dbbcbc4983" style="display: none">4</span>
+    <span id="button-7e1565cc-82ca-4228-b20e-16dbbcbc4983">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-1508a176-9937-40d7-bddd-2a6fe687596e').style.display = 'inline-block';
-                document.getElementById('button-1508a176-9937-40d7-bddd-2a6fe687596e').style.display = 'none'
+                document.getElementById('answer-7e1565cc-82ca-4228-b20e-16dbbcbc4983').style.display = 'inline-block';
+                document.getElementById('button-7e1565cc-82ca-4228-b20e-16dbbcbc4983').style.display = 'none'
             "
         >
             Show Answer
@@ -4210,13 +4210,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the (1,2) entry of the sample covariance matrix?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-39f2ad2f-337d-4cf1-af05-6c17f95871ef" style="display: none">1</span>
-    <span id="button-39f2ad2f-337d-4cf1-af05-6c17f95871ef">
+    <span id="answer-8b1e3df3-c905-40a9-a9c4-a24254e14154" style="display: none">1</span>
+    <span id="button-8b1e3df3-c905-40a9-a9c4-a24254e14154">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-39f2ad2f-337d-4cf1-af05-6c17f95871ef').style.display = 'inline-block';
-                document.getElementById('button-39f2ad2f-337d-4cf1-af05-6c17f95871ef').style.display = 'none'
+                document.getElementById('answer-8b1e3df3-c905-40a9-a9c4-a24254e14154').style.display = 'inline-block';
+                document.getElementById('button-8b1e3df3-c905-40a9-a9c4-a24254e14154').style.display = 'none'
             "
         >
             Show Answer
@@ -4231,13 +4231,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is the (2,2) entry of the sample covariance matrix?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-b5406b26-5513-46f7-b0cf-90bc3ff02710" style="display: none">8/6</span>
-    <span id="button-b5406b26-5513-46f7-b0cf-90bc3ff02710">
+    <span id="answer-9787f66e-d16a-4139-84ac-d9a416b04e84" style="display: none">8/6</span>
+    <span id="button-9787f66e-d16a-4139-84ac-d9a416b04e84">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-b5406b26-5513-46f7-b0cf-90bc3ff02710').style.display = 'inline-block';
-                document.getElementById('button-b5406b26-5513-46f7-b0cf-90bc3ff02710').style.display = 'none'
+                document.getElementById('answer-9787f66e-d16a-4139-84ac-d9a416b04e84').style.display = 'inline-block';
+                document.getElementById('button-9787f66e-d16a-4139-84ac-d9a416b04e84').style.display = 'none'
             "
         >
             Show Answer
@@ -4351,13 +4351,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>Suppose that <span class="math">\(\pr(Y = 1) = \pr(Y = 0) = 0.5\)</span>. What is <span class="math">\(\pr(1 \leq X \leq 3)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-295a18b4-5e8a-4055-8241-ff3cea6de2f1" style="display: none">0.3</span>
-    <span id="button-295a18b4-5e8a-4055-8241-ff3cea6de2f1">
+    <span id="answer-028b74cc-c124-4f4b-bf48-dd906efe78b5" style="display: none">0.3</span>
+    <span id="button-028b74cc-c124-4f4b-bf48-dd906efe78b5">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-295a18b4-5e8a-4055-8241-ff3cea6de2f1').style.display = 'inline-block';
-                document.getElementById('button-295a18b4-5e8a-4055-8241-ff3cea6de2f1').style.display = 'none'
+                document.getElementById('answer-028b74cc-c124-4f4b-bf48-dd906efe78b5').style.display = 'inline-block';
+                document.getElementById('button-028b74cc-c124-4f4b-bf48-dd906efe78b5').style.display = 'none'
             "
         >
             Show Answer
@@ -4384,13 +4384,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>Suppose again that <span class="math">\(\pr(Y = 1) = \pr(Y = 0) = 0.5\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-f6cbfc4c-cf97-4aad-8bae-e2793cf4ebaf" style="display: none">0.25</span>
-    <span id="button-f6cbfc4c-cf97-4aad-8bae-e2793cf4ebaf">
+    <span id="answer-3d6e2b3f-19f6-48c7-b9cd-f9f621f24aa3" style="display: none">0.25</span>
+    <span id="button-3d6e2b3f-19f6-48c7-b9cd-f9f621f24aa3">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-f6cbfc4c-cf97-4aad-8bae-e2793cf4ebaf').style.display = 'inline-block';
-                document.getElementById('button-f6cbfc4c-cf97-4aad-8bae-e2793cf4ebaf').style.display = 'none'
+                document.getElementById('answer-3d6e2b3f-19f6-48c7-b9cd-f9f621f24aa3').style.display = 'inline-block';
+                document.getElementById('button-3d6e2b3f-19f6-48c7-b9cd-f9f621f24aa3').style.display = 'none'
             "
         >
             Show Answer
@@ -4405,13 +4405,13 @@ <h3 class="subproblem-id">Part 4)</h3>
 <p>Now suppose <span class="math">\(\pr(Y = 1) = 0.7\)</span> and <span class="math">\(\pr(Y = 0) = 0.3\)</span>. What is <span class="math">\(\pr(1 \leq X \leq 3)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-a97da2e1-1ac2-48b8-8425-3cfe68580a99" style="display: none">0.34</span>
-    <span id="button-a97da2e1-1ac2-48b8-8425-3cfe68580a99">
+    <span id="answer-3a7b5d28-9292-41e6-8f27-0cd0ab0f6ebb" style="display: none">0.34</span>
+    <span id="button-3a7b5d28-9292-41e6-8f27-0cd0ab0f6ebb">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-a97da2e1-1ac2-48b8-8425-3cfe68580a99').style.display = 'inline-block';
-                document.getElementById('button-a97da2e1-1ac2-48b8-8425-3cfe68580a99').style.display = 'none'
+                document.getElementById('answer-3a7b5d28-9292-41e6-8f27-0cd0ab0f6ebb').style.display = 'inline-block';
+                document.getElementById('button-3a7b5d28-9292-41e6-8f27-0cd0ab0f6ebb').style.display = 'none'
             "
         >
             Show Answer
@@ -4438,13 +4438,13 @@ <h3 class="subproblem-id">Part 6)</h3>
 <p>Suppose again that <span class="math">\(\pr(Y = 1) = 0.7\)</span> and <span class="math">\(\pr(Y = 0) = 0.3\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-33bd4610-377b-42b7-821a-90c87d442dff" style="display: none">0.28</span>
-    <span id="button-33bd4610-377b-42b7-821a-90c87d442dff">
+    <span id="answer-c50f2ee8-443f-4716-b4af-64bd2ba70dc8" style="display: none">0.28</span>
+    <span id="button-c50f2ee8-443f-4716-b4af-64bd2ba70dc8">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-33bd4610-377b-42b7-821a-90c87d442dff').style.display = 'inline-block';
-                document.getElementById('button-33bd4610-377b-42b7-821a-90c87d442dff').style.display = 'none'
+                document.getElementById('answer-c50f2ee8-443f-4716-b4af-64bd2ba70dc8').style.display = 'inline-block';
+                document.getElementById('button-c50f2ee8-443f-4716-b4af-64bd2ba70dc8').style.display = 'none'
             "
         >
             Show Answer
@@ -4476,13 +4476,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the estimate of the Class 0 density at <span class="math">\(x = 0.6\)</span>? That is, what is the estimate <span class="math">\(\hat p(0.6 \given Y = 0)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-bca0d4c6-8133-46fd-bb2c-167b0dae322e" style="display: none">5/3</span>
-    <span id="button-bca0d4c6-8133-46fd-bb2c-167b0dae322e">
+    <span id="answer-230f70cd-7224-48a8-8cc2-1519f6894710" style="display: none">5/3</span>
+    <span id="button-230f70cd-7224-48a8-8cc2-1519f6894710">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-bca0d4c6-8133-46fd-bb2c-167b0dae322e').style.display = 'inline-block';
-                document.getElementById('button-bca0d4c6-8133-46fd-bb2c-167b0dae322e').style.display = 'none'
+                document.getElementById('answer-230f70cd-7224-48a8-8cc2-1519f6894710').style.display = 'inline-block';
+                document.getElementById('button-230f70cd-7224-48a8-8cc2-1519f6894710').style.display = 'none'
             "
         >
             Show Answer
@@ -4497,13 +4497,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>Using the same histogram estimator, what is the estimate <span class="math">\(\hat\pr(Y = 1 \given x = 0.35)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-fa8d46f7-9d41-4bfe-8268-7fd467d573e1" style="display: none">3/5 = 0.6</span>
-    <span id="button-fa8d46f7-9d41-4bfe-8268-7fd467d573e1">
+    <span id="answer-961e785e-c471-4e43-9c43-1e05eb3087c4" style="display: none">3/5 = 0.6</span>
+    <span id="button-961e785e-c471-4e43-9c43-1e05eb3087c4">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-fa8d46f7-9d41-4bfe-8268-7fd467d573e1').style.display = 'inline-block';
-                document.getElementById('button-fa8d46f7-9d41-4bfe-8268-7fd467d573e1').style.display = 'none'
+                document.getElementById('answer-961e785e-c471-4e43-9c43-1e05eb3087c4').style.display = 'inline-block';
+                document.getElementById('button-961e785e-c471-4e43-9c43-1e05eb3087c4').style.display = 'none'
             "
         >
             Show Answer
@@ -4518,13 +4518,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>What is the estimate of the marginal density of <span class="math">\(x\)</span> at <span class="math">\(x = 0.1\)</span>? That is, what is <span class="math">\(\hat p(0.1)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-fd783ddd-2cc7-4249-8a95-0cd4c744c987" style="display: none">7/(19*0.25) = 1.47</span>
-    <span id="button-fd783ddd-2cc7-4249-8a95-0cd4c744c987">
+    <span id="answer-16395f16-38d4-41b7-9e48-20f1424eb59f" style="display: none">7/(19*0.25) = 1.47</span>
+    <span id="button-16395f16-38d4-41b7-9e48-20f1424eb59f">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-fd783ddd-2cc7-4249-8a95-0cd4c744c987').style.display = 'inline-block';
-                document.getElementById('button-fd783ddd-2cc7-4249-8a95-0cd4c744c987').style.display = 'none'
+                document.getElementById('answer-16395f16-38d4-41b7-9e48-20f1424eb59f').style.display = 'inline-block';
+                document.getElementById('button-16395f16-38d4-41b7-9e48-20f1424eb59f').style.display = 'none'
             "
         >
             Show Answer
@@ -4541,13 +4541,13 @@ <h3 class="subproblem-id">Part 4)</h3>
             \]</div>
 <p>
 <span class="inline-response-box">
-    <span id="answer-3f8e5eb1-2357-4e19-8acc-62d866ad515f" style="display: none">1</span>
-    <span id="button-3f8e5eb1-2357-4e19-8acc-62d866ad515f">
+    <span id="answer-b35e44a5-59f8-4288-b7bf-a1bd1c6dcfa7" style="display: none">1</span>
+    <span id="button-b35e44a5-59f8-4288-b7bf-a1bd1c6dcfa7">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-3f8e5eb1-2357-4e19-8acc-62d866ad515f').style.display = 'inline-block';
-                document.getElementById('button-3f8e5eb1-2357-4e19-8acc-62d866ad515f').style.display = 'none'
+                document.getElementById('answer-b35e44a5-59f8-4288-b7bf-a1bd1c6dcfa7').style.display = 'inline-block';
+                document.getElementById('button-b35e44a5-59f8-4288-b7bf-a1bd1c6dcfa7').style.display = 'none'
             "
         >
             Show Answer
@@ -4575,13 +4575,13 @@ <h2>Problem #112</h2>
 <p>Consider a new point <span class="math">\(\vec x = (2, 0, 1)^T\)</span>. What is <span class="math">\(H(\vec x)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-8e8a7476-aaf1-467a-99c9-a9f37dfacb2e" style="display: none">37</span>
-    <span id="button-8e8a7476-aaf1-467a-99c9-a9f37dfacb2e">
+    <span id="answer-09cd436a-3e73-4cbf-af0b-151d6fdfb1ee" style="display: none">37</span>
+    <span id="button-09cd436a-3e73-4cbf-af0b-151d6fdfb1ee">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-8e8a7476-aaf1-467a-99c9-a9f37dfacb2e').style.display = 'inline-block';
-                document.getElementById('button-8e8a7476-aaf1-467a-99c9-a9f37dfacb2e').style.display = 'none'
+                document.getElementById('answer-09cd436a-3e73-4cbf-af0b-151d6fdfb1ee').style.display = 'inline-block';
+                document.getElementById('button-09cd436a-3e73-4cbf-af0b-151d6fdfb1ee').style.display = 'none'
             "
         >
             Show Answer
@@ -4615,13 +4615,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the (1,3) entry of the sample covariance matrix?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-0c7f2ddc-337e-46a2-9ddd-87f9a07167db" style="display: none">9/4</span>
-    <span id="button-0c7f2ddc-337e-46a2-9ddd-87f9a07167db">
+    <span id="answer-73805621-60ca-4c41-b98f-f9406cfd7061" style="display: none">9/4</span>
+    <span id="button-73805621-60ca-4c41-b98f-f9406cfd7061">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-0c7f2ddc-337e-46a2-9ddd-87f9a07167db').style.display = 'inline-block';
-                document.getElementById('button-0c7f2ddc-337e-46a2-9ddd-87f9a07167db').style.display = 'none'
+                document.getElementById('answer-73805621-60ca-4c41-b98f-f9406cfd7061').style.display = 'inline-block';
+                document.getElementById('button-73805621-60ca-4c41-b98f-f9406cfd7061').style.display = 'none'
             "
         >
             Show Answer
@@ -4636,13 +4636,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is the (1,2) entry of the sample covariance matrix?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-f68a2d11-45c1-483d-b9cc-c6e542d66179" style="display: none">-3/4</span>
-    <span id="button-f68a2d11-45c1-483d-b9cc-c6e542d66179">
+    <span id="answer-1000e044-9a55-4446-a2f6-5c4384fbae99" style="display: none">-3/4</span>
+    <span id="button-1000e044-9a55-4446-a2f6-5c4384fbae99">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-f68a2d11-45c1-483d-b9cc-c6e542d66179').style.display = 'inline-block';
-                document.getElementById('button-f68a2d11-45c1-483d-b9cc-c6e542d66179').style.display = 'none'
+                document.getElementById('answer-1000e044-9a55-4446-a2f6-5c4384fbae99').style.display = 'inline-block';
+                document.getElementById('button-1000e044-9a55-4446-a2f6-5c4384fbae99').style.display = 'none'
             "
         >
             Show Answer
@@ -4770,13 +4770,13 @@ <h3 class="subproblem-id">Part 1)</h3>
             L(0, 2)\)</span>? Note that <span class="math">\(\mathcal L\)</span> is the likelihood, <i>not</i> the <i>log</i>-likelihood.</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-ca13ebee-208c-41bb-b41b-e7225c1c81c1" style="display: none">0</span>
-    <span id="button-ca13ebee-208c-41bb-b41b-e7225c1c81c1">
+    <span id="answer-9504160c-bc7b-4db3-8d14-097baa984a90" style="display: none">0</span>
+    <span id="button-9504160c-bc7b-4db3-8d14-097baa984a90">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-ca13ebee-208c-41bb-b41b-e7225c1c81c1').style.display = 'inline-block';
-                document.getElementById('button-ca13ebee-208c-41bb-b41b-e7225c1c81c1').style.display = 'none'
+                document.getElementById('answer-9504160c-bc7b-4db3-8d14-097baa984a90').style.display = 'inline-block';
+                document.getElementById('button-9504160c-bc7b-4db3-8d14-097baa984a90').style.display = 'none'
             "
         >
             Show Answer
@@ -4791,13 +4791,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>Let <span class="math">\(\mathcal X = \{0, 1, 2\}\)</span> be the same data set as in the previous part. What is <span class="math">\(\mathcal L(0, 4)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-b88306f5-1261-4d97-8ee1-67027a0beff8" style="display: none">3/64 = 0.0468</span>
-    <span id="button-b88306f5-1261-4d97-8ee1-67027a0beff8">
+    <span id="answer-53ad86c6-99e9-49ba-93a3-f5f7215c7dd1" style="display: none">3/64 = 0.0468</span>
+    <span id="button-53ad86c6-99e9-49ba-93a3-f5f7215c7dd1">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-b88306f5-1261-4d97-8ee1-67027a0beff8').style.display = 'inline-block';
-                document.getElementById('button-b88306f5-1261-4d97-8ee1-67027a0beff8').style.display = 'none'
+                document.getElementById('answer-53ad86c6-99e9-49ba-93a3-f5f7215c7dd1').style.display = 'inline-block';
+                document.getElementById('button-53ad86c6-99e9-49ba-93a3-f5f7215c7dd1').style.display = 'none'
             "
         >
             Show Answer
@@ -4812,13 +4812,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>Now let <span class="math">\(\mathcal X = \{6, 7\}\)</span> be a new data set of just two points. What are the maximum likelihood estimates of <span class="math">\(\alpha\)</span> and <span class="math">\(\beta\)</span> with respect to this data? Remember, <span class="math">\(\beta > 0\)</span>.</p>
 <p><span class="math">\(\alpha\)</span>: 
 <span class="inline-response-box">
-    <span id="answer-55514cf7-301e-4eac-8361-a2c1d8195e7f" style="display: none">6</span>
-    <span id="button-55514cf7-301e-4eac-8361-a2c1d8195e7f">
+    <span id="answer-7a10581e-fea5-4881-9748-d9dd9f8efb88" style="display: none">6</span>
+    <span id="button-7a10581e-fea5-4881-9748-d9dd9f8efb88">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-55514cf7-301e-4eac-8361-a2c1d8195e7f').style.display = 'inline-block';
-                document.getElementById('button-55514cf7-301e-4eac-8361-a2c1d8195e7f').style.display = 'none'
+                document.getElementById('answer-7a10581e-fea5-4881-9748-d9dd9f8efb88').style.display = 'inline-block';
+                document.getElementById('button-7a10581e-fea5-4881-9748-d9dd9f8efb88').style.display = 'none'
             "
         >
             Show Answer
@@ -4827,13 +4827,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 </span>
 <span class="math">\(\beta\)</span>: 
 <span class="inline-response-box">
-    <span id="answer-628a6cad-9c70-45dd-9bc1-101d65df6dd4" style="display: none">3</span>
-    <span id="button-628a6cad-9c70-45dd-9bc1-101d65df6dd4">
+    <span id="answer-63ac2bfd-6843-42a1-ba9d-1bc8b8a75a88" style="display: none">3</span>
+    <span id="button-63ac2bfd-6843-42a1-ba9d-1bc8b8a75a88">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-628a6cad-9c70-45dd-9bc1-101d65df6dd4').style.display = 'inline-block';
-                document.getElementById('button-628a6cad-9c70-45dd-9bc1-101d65df6dd4').style.display = 'none'
+                document.getElementById('answer-63ac2bfd-6843-42a1-ba9d-1bc8b8a75a88').style.display = 'inline-block';
+                document.getElementById('button-63ac2bfd-6843-42a1-ba9d-1bc8b8a75a88').style.display = 'none'
             "
         >
             Show Answer
@@ -4946,13 +4946,13 @@ <h2>Problem #119</h2>
 <p>If these estimates are used in place of the true class-conditional densities in the Bayes classifier, what will be the training error of the classifier? That is, what percentage of the data above will be misclassified? You may leave your answer as a fraction or a decimal.</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-c957b83c-6386-40e4-b9d5-903c21846f70" style="display: none">4/14 = .2857</span>
-    <span id="button-c957b83c-6386-40e4-b9d5-903c21846f70">
+    <span id="answer-dc1aa701-d468-43e9-ac62-ce141b32e0b6" style="display: none">4/14 = .2857</span>
+    <span id="button-dc1aa701-d468-43e9-ac62-ce141b32e0b6">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-c957b83c-6386-40e4-b9d5-903c21846f70').style.display = 'inline-block';
-                document.getElementById('button-c957b83c-6386-40e4-b9d5-903c21846f70').style.display = 'none'
+                document.getElementById('answer-dc1aa701-d468-43e9-ac62-ce141b32e0b6').style.display = 'inline-block';
+                document.getElementById('button-dc1aa701-d468-43e9-ac62-ce141b32e0b6').style.display = 'none'
             "
         >
             Show Answer
diff --git a/practice/midterm-01.html b/practice/midterm-01.html
index 3edfff42..6c6b9d61 100644
--- a/practice/midterm-01.html
+++ b/practice/midterm-01.html
@@ -984,13 +984,13 @@ <h2>Problem #061</h2>
 <p>Let <span class="math">\(\vec x = (1, 2)^T\)</span>. What is <span class="math">\(H(\vec x)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-06ebac2c-a207-43c2-bca6-f0439c2f226f" style="display: none">3</span>
-    <span id="button-06ebac2c-a207-43c2-bca6-f0439c2f226f">
+    <span id="answer-02f3dd8e-aa64-47c6-a1d8-d79c3c88542b" style="display: none">3</span>
+    <span id="button-02f3dd8e-aa64-47c6-a1d8-d79c3c88542b">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-06ebac2c-a207-43c2-bca6-f0439c2f226f').style.display = 'inline-block';
-                document.getElementById('button-06ebac2c-a207-43c2-bca6-f0439c2f226f').style.display = 'none'
+                document.getElementById('answer-02f3dd8e-aa64-47c6-a1d8-d79c3c88542b').style.display = 'inline-block';
+                document.getElementById('button-02f3dd8e-aa64-47c6-a1d8-d79c3c88542b').style.display = 'none'
             "
         >
             Show Answer
@@ -1062,13 +1062,13 @@ <h2>Problem #063</h2>
 <p>What is the value of <span class="math">\(H\)</span> at the point <span class="math">\(\nvec{x}{4} = (0, 1)^T\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-28eb33cd-57d2-43fb-b4ab-29ca24ae00d2" style="display: none">0</span>
-    <span id="button-28eb33cd-57d2-43fb-b4ab-29ca24ae00d2">
+    <span id="answer-3c791f67-9c0d-4319-ba78-d0686b3bc757" style="display: none">0</span>
+    <span id="button-3c791f67-9c0d-4319-ba78-d0686b3bc757">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-28eb33cd-57d2-43fb-b4ab-29ca24ae00d2').style.display = 'inline-block';
-                document.getElementById('button-28eb33cd-57d2-43fb-b4ab-29ca24ae00d2').style.display = 'none'
+                document.getElementById('answer-3c791f67-9c0d-4319-ba78-d0686b3bc757').style.display = 'inline-block';
+                document.getElementById('button-3c791f67-9c0d-4319-ba78-d0686b3bc757').style.display = 'none'
             "
         >
             Show Answer
@@ -1222,13 +1222,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the <b>total</b><i>square</i> loss of <span class="math">\(H\)</span> on this data set?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-0bb66a75-f0b7-4deb-bb64-e4255965f8b4" style="display: none">11.25</span>
-    <span id="button-0bb66a75-f0b7-4deb-bb64-e4255965f8b4">
+    <span id="answer-d2576366-7987-4b7f-8596-93d15ed37f4d" style="display: none">11.25</span>
+    <span id="button-d2576366-7987-4b7f-8596-93d15ed37f4d">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-0bb66a75-f0b7-4deb-bb64-e4255965f8b4').style.display = 'inline-block';
-                document.getElementById('button-0bb66a75-f0b7-4deb-bb64-e4255965f8b4').style.display = 'none'
+                document.getElementById('answer-d2576366-7987-4b7f-8596-93d15ed37f4d').style.display = 'inline-block';
+                document.getElementById('button-d2576366-7987-4b7f-8596-93d15ed37f4d').style.display = 'none'
             "
         >
             Show Answer
@@ -1243,13 +1243,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is the <b>total</b><i>perceptron</i> loss of <span class="math">\(H\)</span> on this data set?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-297d1762-2ddd-4957-af90-eacd2bfa0c14" style="display: none">1</span>
-    <span id="button-297d1762-2ddd-4957-af90-eacd2bfa0c14">
+    <span id="answer-63932fa4-6c0c-4d02-ae04-991ee3f54b6f" style="display: none">1</span>
+    <span id="button-63932fa4-6c0c-4d02-ae04-991ee3f54b6f">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-297d1762-2ddd-4957-af90-eacd2bfa0c14').style.display = 'inline-block';
-                document.getElementById('button-297d1762-2ddd-4957-af90-eacd2bfa0c14').style.display = 'none'
+                document.getElementById('answer-63932fa4-6c0c-4d02-ae04-991ee3f54b6f').style.display = 'inline-block';
+                document.getElementById('button-63932fa4-6c0c-4d02-ae04-991ee3f54b6f').style.display = 'none'
             "
         >
             Show Answer
@@ -1264,13 +1264,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>What is the <b>total</b><i>hinge</i> loss of <span class="math">\(H\)</span> on this data set?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-10451c49-bcb9-4b87-87e0-77a9453e1b0e" style="display: none">3.5</span>
-    <span id="button-10451c49-bcb9-4b87-87e0-77a9453e1b0e">
+    <span id="answer-72a39ad4-84ce-4d3b-a6de-55b21c634ce2" style="display: none">3.5</span>
+    <span id="button-72a39ad4-84ce-4d3b-a6de-55b21c634ce2">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-10451c49-bcb9-4b87-87e0-77a9453e1b0e').style.display = 'inline-block';
-                document.getElementById('button-10451c49-bcb9-4b87-87e0-77a9453e1b0e').style.display = 'none'
+                document.getElementById('answer-72a39ad4-84ce-4d3b-a6de-55b21c634ce2').style.display = 'inline-block';
+                document.getElementById('button-72a39ad4-84ce-4d3b-a6de-55b21c634ce2').style.display = 'none'
             "
         >
             Show Answer
@@ -1307,13 +1307,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the gradient of this function at the point <span class="math">\((0, 0)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-17cece7c-c9ce-4fe2-b02f-84b634d75f6c" style="display: none"><span class="math">\((2, 1)^T\)</span></span>
-    <span id="button-17cece7c-c9ce-4fe2-b02f-84b634d75f6c">
+    <span id="answer-1f164a0a-dd8a-4b19-ad96-d3585e7d572b" style="display: none"><span class="math">\((2, 1)^T\)</span></span>
+    <span id="button-1f164a0a-dd8a-4b19-ad96-d3585e7d572b">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-17cece7c-c9ce-4fe2-b02f-84b634d75f6c').style.display = 'inline-block';
-                document.getElementById('button-17cece7c-c9ce-4fe2-b02f-84b634d75f6c').style.display = 'none'
+                document.getElementById('answer-1f164a0a-dd8a-4b19-ad96-d3585e7d572b').style.display = 'inline-block';
+                document.getElementById('button-1f164a0a-dd8a-4b19-ad96-d3585e7d572b').style.display = 'none'
             "
         >
             Show Answer
@@ -1362,13 +1362,13 @@ <h2>Problem #068</h2>
 <p>Suppose that the initial weight vector is <span class="math">\(\vec w = (0, 0)^T\)</span> and that the learning rate <span class="math">\(\eta = 1\)</span>. What will be the weight vector after one iteration of subgradient descent?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-3918d6b2-14f8-4347-941e-3055960e52b6" style="display: none"><span class="math">\((1, 2)^T\)</span></span>
-    <span id="button-3918d6b2-14f8-4347-941e-3055960e52b6">
+    <span id="answer-21973d24-0e8c-4fb7-b4d7-5a8e6f82a0d7" style="display: none"><span class="math">\((1, 2)^T\)</span></span>
+    <span id="button-21973d24-0e8c-4fb7-b4d7-5a8e6f82a0d7">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-3918d6b2-14f8-4347-941e-3055960e52b6').style.display = 'inline-block';
-                document.getElementById('button-3918d6b2-14f8-4347-941e-3055960e52b6').style.display = 'none'
+                document.getElementById('answer-21973d24-0e8c-4fb7-b4d7-5a8e6f82a0d7').style.display = 'inline-block';
+                document.getElementById('button-21973d24-0e8c-4fb7-b4d7-5a8e6f82a0d7').style.display = 'none'
             "
         >
             Show Answer
@@ -1533,13 +1533,13 @@ <h2>Problem #073</h2>
 <p>What weight vector <i>is</i> the solution of the Hard SVM problem for this data set?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-459d22f8-75e4-43e0-b012-fdc427bd1ee7" style="display: none"><span class="math">\((3, 0, \frac{1}{4})^T\)</span></span>
-    <span id="button-459d22f8-75e4-43e0-b012-fdc427bd1ee7">
+    <span id="answer-856ded84-a02e-4aa4-9eb1-e460911ad10f" style="display: none"><span class="math">\((3, 0, \frac{1}{4})^T\)</span></span>
+    <span id="button-856ded84-a02e-4aa4-9eb1-e460911ad10f">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-459d22f8-75e4-43e0-b012-fdc427bd1ee7').style.display = 'inline-block';
-                document.getElementById('button-459d22f8-75e4-43e0-b012-fdc427bd1ee7').style.display = 'none'
+                document.getElementById('answer-856ded84-a02e-4aa4-9eb1-e460911ad10f').style.display = 'inline-block';
+                document.getElementById('button-856ded84-a02e-4aa4-9eb1-e460911ad10f').style.display = 'none'
             "
         >
             Show Answer
@@ -1573,13 +1573,13 @@ <h2>Problem #074</h2>
 <p>What is <span class="math">\(\frac{d}{d \vec w} f(\vec w)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-40afe31f-6901-4a6b-809a-22cf950f8296" style="display: none"><span class="math">\(\sum_{i=1}^n \nvec{x}{i} + 2 \vec w\)</span></span>
-    <span id="button-40afe31f-6901-4a6b-809a-22cf950f8296">
+    <span id="answer-e6eed497-f4d0-47a2-8c00-050d9fcf4667" style="display: none"><span class="math">\(\sum_{i=1}^n \nvec{x}{i} + 2 \vec w\)</span></span>
+    <span id="button-e6eed497-f4d0-47a2-8c00-050d9fcf4667">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-40afe31f-6901-4a6b-809a-22cf950f8296').style.display = 'inline-block';
-                document.getElementById('button-40afe31f-6901-4a6b-809a-22cf950f8296').style.display = 'none'
+                document.getElementById('answer-e6eed497-f4d0-47a2-8c00-050d9fcf4667').style.display = 'inline-block';
+                document.getElementById('button-e6eed497-f4d0-47a2-8c00-050d9fcf4667').style.display = 'none'
             "
         >
             Show Answer
@@ -1774,13 +1774,13 @@ <h2>Problem #079</h2>
 <p>Let <span class="math">\(\vec x = (1, 2, 1)^T\)</span>. What is <span class="math">\(H(\vec x)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-d3aced5a-1214-41c3-acec-a8192f4e58d9" style="display: none"><span class="math">\(-3\)</span></span>
-    <span id="button-d3aced5a-1214-41c3-acec-a8192f4e58d9">
+    <span id="answer-91b9741a-8578-4d8e-88bf-a1b4804b6c79" style="display: none"><span class="math">\(-3\)</span></span>
+    <span id="button-91b9741a-8578-4d8e-88bf-a1b4804b6c79">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-d3aced5a-1214-41c3-acec-a8192f4e58d9').style.display = 'inline-block';
-                document.getElementById('button-d3aced5a-1214-41c3-acec-a8192f4e58d9').style.display = 'none'
+                document.getElementById('answer-91b9741a-8578-4d8e-88bf-a1b4804b6c79').style.display = 'inline-block';
+                document.getElementById('button-91b9741a-8578-4d8e-88bf-a1b4804b6c79').style.display = 'none'
             "
         >
             Show Answer
@@ -1806,13 +1806,13 @@ <h2>Problem #080</h2>
 <p>What is the mean squared error of a least squares classifier trained on this data set (without regularization)? Your answer should be a number.</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-a55097f3-10ae-4df6-9076-3cadef6f0cdd" style="display: none">0</span>
-    <span id="button-a55097f3-10ae-4df6-9076-3cadef6f0cdd">
+    <span id="answer-c10163ae-7d53-4075-9ae3-e4fc81ebb489" style="display: none">0</span>
+    <span id="button-c10163ae-7d53-4075-9ae3-e4fc81ebb489">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-a55097f3-10ae-4df6-9076-3cadef6f0cdd').style.display = 'inline-block';
-                document.getElementById('button-a55097f3-10ae-4df6-9076-3cadef6f0cdd').style.display = 'none'
+                document.getElementById('answer-c10163ae-7d53-4075-9ae3-e4fc81ebb489').style.display = 'inline-block';
+                document.getElementById('button-c10163ae-7d53-4075-9ae3-e4fc81ebb489').style.display = 'none'
             "
         >
             Show Answer
@@ -1894,13 +1894,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the <b>total</b><i>square</i> loss of <span class="math">\(H\)</span> on this data set?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-e29c102e-2a57-49f8-9efc-2bf341c7f088" style="display: none">13.5</span>
-    <span id="button-e29c102e-2a57-49f8-9efc-2bf341c7f088">
+    <span id="answer-70d230e2-c2ba-4004-a54c-47e6b99e0e5a" style="display: none">13.5</span>
+    <span id="button-70d230e2-c2ba-4004-a54c-47e6b99e0e5a">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-e29c102e-2a57-49f8-9efc-2bf341c7f088').style.display = 'inline-block';
-                document.getElementById('button-e29c102e-2a57-49f8-9efc-2bf341c7f088').style.display = 'none'
+                document.getElementById('answer-70d230e2-c2ba-4004-a54c-47e6b99e0e5a').style.display = 'inline-block';
+                document.getElementById('button-70d230e2-c2ba-4004-a54c-47e6b99e0e5a').style.display = 'none'
             "
         >
             Show Answer
@@ -1915,13 +1915,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is the <b>total</b><i>perceptron</i> loss of <span class="math">\(H\)</span> on this data set?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-b8062ea3-dd7a-46b3-bf49-ba76d3744353" style="display: none">1.5</span>
-    <span id="button-b8062ea3-dd7a-46b3-bf49-ba76d3744353">
+    <span id="answer-df1b2410-c1fd-4b2d-8b74-067987f4aae8" style="display: none">1.5</span>
+    <span id="button-df1b2410-c1fd-4b2d-8b74-067987f4aae8">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-b8062ea3-dd7a-46b3-bf49-ba76d3744353').style.display = 'inline-block';
-                document.getElementById('button-b8062ea3-dd7a-46b3-bf49-ba76d3744353').style.display = 'none'
+                document.getElementById('answer-df1b2410-c1fd-4b2d-8b74-067987f4aae8').style.display = 'inline-block';
+                document.getElementById('button-df1b2410-c1fd-4b2d-8b74-067987f4aae8').style.display = 'none'
             "
         >
             Show Answer
@@ -1936,13 +1936,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>What is the <b>total</b><i>hinge</i> loss of <span class="math">\(H\)</span> on this data set?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-9e74d8bc-bc06-436a-ae4a-8180663edca1" style="display: none">4</span>
-    <span id="button-9e74d8bc-bc06-436a-ae4a-8180663edca1">
+    <span id="answer-9889ed17-26a9-483e-ada6-701b19fdca82" style="display: none">4</span>
+    <span id="button-9889ed17-26a9-483e-ada6-701b19fdca82">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-9e74d8bc-bc06-436a-ae4a-8180663edca1').style.display = 'inline-block';
-                document.getElementById('button-9e74d8bc-bc06-436a-ae4a-8180663edca1').style.display = 'none'
+                document.getElementById('answer-9889ed17-26a9-483e-ada6-701b19fdca82').style.display = 'inline-block';
+                document.getElementById('button-9889ed17-26a9-483e-ada6-701b19fdca82').style.display = 'none'
             "
         >
             Show Answer
@@ -1981,13 +1981,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the gradient of this function at the point <span class="math">\((1, 1)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-1e5856db-0566-4fb2-9e1f-3f932847d7f6" style="display: none"><span class="math">\((-1,3)^T\)</span></span>
-    <span id="button-1e5856db-0566-4fb2-9e1f-3f932847d7f6">
+    <span id="answer-c97f1088-80c8-4f60-a960-b3cc0b0f37ee" style="display: none"><span class="math">\((-1,3)^T\)</span></span>
+    <span id="button-c97f1088-80c8-4f60-a960-b3cc0b0f37ee">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-1e5856db-0566-4fb2-9e1f-3f932847d7f6').style.display = 'inline-block';
-                document.getElementById('button-1e5856db-0566-4fb2-9e1f-3f932847d7f6').style.display = 'none'
+                document.getElementById('answer-c97f1088-80c8-4f60-a960-b3cc0b0f37ee').style.display = 'inline-block';
+                document.getElementById('button-c97f1088-80c8-4f60-a960-b3cc0b0f37ee').style.display = 'none'
             "
         >
             Show Answer
@@ -2002,13 +2002,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is the gradient of this function at the point <span class="math">\((-1, -1)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-19773e5f-e425-468e-bbd1-a39aa7bb74be" style="display: none"><span class="math">\((-2,0)^T\)</span></span>
-    <span id="button-19773e5f-e425-468e-bbd1-a39aa7bb74be">
+    <span id="answer-20c09026-04a8-4b3e-8db5-a33547c5c580" style="display: none"><span class="math">\((-2,0)^T\)</span></span>
+    <span id="button-20c09026-04a8-4b3e-8db5-a33547c5c580">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-19773e5f-e425-468e-bbd1-a39aa7bb74be').style.display = 'inline-block';
-                document.getElementById('button-19773e5f-e425-468e-bbd1-a39aa7bb74be').style.display = 'none'
+                document.getElementById('answer-20c09026-04a8-4b3e-8db5-a33547c5c580').style.display = 'inline-block';
+                document.getElementById('button-20c09026-04a8-4b3e-8db5-a33547c5c580').style.display = 'none'
             "
         >
             Show Answer
@@ -2073,13 +2073,13 @@ <h2>Problem #085</h2>
 <p>Suppose that the initial weight vector is <span class="math">\(\vec w = (0, 0)^T\)</span> and that the learning rate is <span class="math">\(\eta = 1\)</span>. What will be the weight vector after one iteration of subgradient descent?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-5439ff11-da05-4dca-a22b-64c766d1b89e" style="display: none"><span class="math">\((1, 3)^T\)</span></span>
-    <span id="button-5439ff11-da05-4dca-a22b-64c766d1b89e">
+    <span id="answer-24cf6821-d30a-4c1f-abee-61857a807903" style="display: none"><span class="math">\((1, 3)^T\)</span></span>
+    <span id="button-24cf6821-d30a-4c1f-abee-61857a807903">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-5439ff11-da05-4dca-a22b-64c766d1b89e').style.display = 'inline-block';
-                document.getElementById('button-5439ff11-da05-4dca-a22b-64c766d1b89e').style.display = 'none'
+                document.getElementById('answer-24cf6821-d30a-4c1f-abee-61857a807903').style.display = 'inline-block';
+                document.getElementById('button-24cf6821-d30a-4c1f-abee-61857a807903').style.display = 'none'
             "
         >
             Show Answer
@@ -2194,13 +2194,13 @@ <h2>Problem #090</h2>
 <p>What is <span class="math">\(\frac{d}{d \vec x} f(\vec x)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-195c6e84-1a64-44dc-818f-11eff66c393e" style="display: none"><span class="math">\(2 A \vec x + \vec b\)</span></span>
-    <span id="button-195c6e84-1a64-44dc-818f-11eff66c393e">
+    <span id="answer-613ac34c-ecca-43e0-b0b5-eb3bd0f4a455" style="display: none"><span class="math">\(2 A \vec x + \vec b\)</span></span>
+    <span id="button-613ac34c-ecca-43e0-b0b5-eb3bd0f4a455">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-195c6e84-1a64-44dc-818f-11eff66c393e').style.display = 'inline-block';
-                document.getElementById('button-195c6e84-1a64-44dc-818f-11eff66c393e').style.display = 'none'
+                document.getElementById('answer-613ac34c-ecca-43e0-b0b5-eb3bd0f4a455').style.display = 'inline-block';
+                document.getElementById('button-613ac34c-ecca-43e0-b0b5-eb3bd0f4a455').style.display = 'none'
             "
         >
             Show Answer
diff --git a/practice/midterm-02.html b/practice/midterm-02.html
index 2270fc15..c4f60f97 100644
--- a/practice/midterm-02.html
+++ b/practice/midterm-02.html
@@ -225,13 +225,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the (2,3) entry of the kernel matrix?</p>
 <p><span class="math">\(K_{23} = \)</span>
 <span class="inline-response-box">
-    <span id="answer-8fd6ea78-722a-4424-9f8e-2618bf45e586" style="display: none">1</span>
-    <span id="button-8fd6ea78-722a-4424-9f8e-2618bf45e586">
+    <span id="answer-e9429973-1ef3-4cc0-8a57-b8ce497a8c4a" style="display: none">1</span>
+    <span id="button-e9429973-1ef3-4cc0-8a57-b8ce497a8c4a">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-8fd6ea78-722a-4424-9f8e-2618bf45e586').style.display = 'inline-block';
-                document.getElementById('button-8fd6ea78-722a-4424-9f8e-2618bf45e586').style.display = 'none'
+                document.getElementById('answer-e9429973-1ef3-4cc0-8a57-b8ce497a8c4a').style.display = 'inline-block';
+                document.getElementById('button-e9429973-1ef3-4cc0-8a57-b8ce497a8c4a').style.display = 'none'
             "
         >
             Show Answer
@@ -246,13 +246,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>Let <span class="math">\(\vec x = (1, 1, 0)^T\)</span> be a new point. What is <span class="math">\(H(\vec x)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-e53845ea-ade4-4651-b18f-e8a26838d96d" style="display: none">14</span>
-    <span id="button-e53845ea-ade4-4651-b18f-e8a26838d96d">
+    <span id="answer-b376ebd1-f320-4fc3-80f9-c27e0da2149d" style="display: none">14</span>
+    <span id="button-b376ebd1-f320-4fc3-80f9-c27e0da2149d">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-e53845ea-ade4-4651-b18f-e8a26838d96d').style.display = 'inline-block';
-                document.getElementById('button-e53845ea-ade4-4651-b18f-e8a26838d96d').style.display = 'none'
+                document.getElementById('answer-b376ebd1-f320-4fc3-80f9-c27e0da2149d').style.display = 'inline-block';
+                document.getElementById('button-b376ebd1-f320-4fc3-80f9-c27e0da2149d').style.display = 'none'
             "
         >
             Show Answer
@@ -345,13 +345,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>Suppose <span class="math">\(\pr(Y = 1) = 0.5\)</span> and <span class="math">\(\pr(Y = 0) = 0.5\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-3cad5539-ee5a-4a02-aae3-588f3fb816d9" style="display: none">0.25</span>
-    <span id="button-3cad5539-ee5a-4a02-aae3-588f3fb816d9">
+    <span id="answer-4a48c20e-37ca-4e48-91ad-4865e7091bf3" style="display: none">0.25</span>
+    <span id="button-4a48c20e-37ca-4e48-91ad-4865e7091bf3">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-3cad5539-ee5a-4a02-aae3-588f3fb816d9').style.display = 'inline-block';
-                document.getElementById('button-3cad5539-ee5a-4a02-aae3-588f3fb816d9').style.display = 'none'
+                document.getElementById('answer-4a48c20e-37ca-4e48-91ad-4865e7091bf3').style.display = 'inline-block';
+                document.getElementById('button-4a48c20e-37ca-4e48-91ad-4865e7091bf3').style.display = 'none'
             "
         >
             Show Answer
@@ -378,13 +378,13 @@ <h3 class="subproblem-id">Part 4)</h3>
 <p>Now suppose <span class="math">\(\pr(Y = 1) = 0.7\)</span> and <span class="math">\(\pr(Y = 0) = 0.3\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-bd20fe62-2b4e-4323-a482-8f9dcf0cd2bd" style="display: none">0.29</span>
-    <span id="button-bd20fe62-2b4e-4323-a482-8f9dcf0cd2bd">
+    <span id="answer-3fb023d4-913c-470f-a3b1-cd9e85fd9e1d" style="display: none">0.29</span>
+    <span id="button-3fb023d4-913c-470f-a3b1-cd9e85fd9e1d">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-bd20fe62-2b4e-4323-a482-8f9dcf0cd2bd').style.display = 'inline-block';
-                document.getElementById('button-bd20fe62-2b4e-4323-a482-8f9dcf0cd2bd').style.display = 'none'
+                document.getElementById('answer-3fb023d4-913c-470f-a3b1-cd9e85fd9e1d').style.display = 'inline-block';
+                document.getElementById('button-3fb023d4-913c-470f-a3b1-cd9e85fd9e1d').style.display = 'none'
             "
         >
             Show Answer
@@ -440,13 +440,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is <span class="math">\(f(1.5)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-57a2eb8b-5a3f-475f-ab42-5c35913ce5a4" style="display: none">0.2</span>
-    <span id="button-57a2eb8b-5a3f-475f-ab42-5c35913ce5a4">
+    <span id="answer-1fcedd11-b225-4dfd-b43d-6525688d9234" style="display: none">0.2</span>
+    <span id="button-1fcedd11-b225-4dfd-b43d-6525688d9234">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-57a2eb8b-5a3f-475f-ab42-5c35913ce5a4').style.display = 'inline-block';
-                document.getElementById('button-57a2eb8b-5a3f-475f-ab42-5c35913ce5a4').style.display = 'none'
+                document.getElementById('answer-1fcedd11-b225-4dfd-b43d-6525688d9234').style.display = 'inline-block';
+                document.getElementById('button-1fcedd11-b225-4dfd-b43d-6525688d9234').style.display = 'none'
             "
         >
             Show Answer
@@ -461,13 +461,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is <span class="math">\(f(7)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-fe8f5a50-dd3a-45b7-884d-513d7ad62508" style="display: none">.05</span>
-    <span id="button-fe8f5a50-dd3a-45b7-884d-513d7ad62508">
+    <span id="answer-d964db37-70c0-437c-985e-0406c8240475" style="display: none">.05</span>
+    <span id="button-d964db37-70c0-437c-985e-0406c8240475">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-fe8f5a50-dd3a-45b7-884d-513d7ad62508').style.display = 'inline-block';
-                document.getElementById('button-fe8f5a50-dd3a-45b7-884d-513d7ad62508').style.display = 'none'
+                document.getElementById('answer-d964db37-70c0-437c-985e-0406c8240475').style.display = 'inline-block';
+                document.getElementById('button-d964db37-70c0-437c-985e-0406c8240475').style.display = 'none'
             "
         >
             Show Answer
@@ -518,13 +518,13 @@ <h2>Problem #036</h2>
 <p>What is the largest value that <span class="math">\(f(\vec x)\)</span> can possibly have?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-5fd85d26-bf8f-4257-b4bd-279fa630fd7e" style="display: none">1/6</span>
-    <span id="button-5fd85d26-bf8f-4257-b4bd-279fa630fd7e">
+    <span id="answer-7d281bfa-56b1-4ebf-b921-a40faf4aae90" style="display: none">1/6</span>
+    <span id="button-7d281bfa-56b1-4ebf-b921-a40faf4aae90">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-5fd85d26-bf8f-4257-b4bd-279fa630fd7e').style.display = 'inline-block';
-                document.getElementById('button-5fd85d26-bf8f-4257-b4bd-279fa630fd7e').style.display = 'none'
+                document.getElementById('answer-7d281bfa-56b1-4ebf-b921-a40faf4aae90').style.display = 'inline-block';
+                document.getElementById('button-7d281bfa-56b1-4ebf-b921-a40faf4aae90').style.display = 'none'
             "
         >
             Show Answer
@@ -618,13 +618,13 @@ <h2>Problem #040</h2>
 <p>Suppose a Gaussian with a diagonal covariance matrix is fit to 200 points in <span class="math">\(\mathbb R^4\)</span> using the maximum likelihood estimators. How many parameters are estimated? Count each entry of <span class="math">\(\mu\)</span> and the covariance matrix that must be estimated as its own parameter.</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-5d8b34a4-9513-4e4b-b4c8-03bee4b73c09" style="display: none">8</span>
-    <span id="button-5d8b34a4-9513-4e4b-b4c8-03bee4b73c09">
+    <span id="answer-ce1e3801-054a-4e35-befa-5397be79f185" style="display: none">8</span>
+    <span id="button-ce1e3801-054a-4e35-befa-5397be79f185">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-5d8b34a4-9513-4e4b-b4c8-03bee4b73c09').style.display = 'inline-block';
-                document.getElementById('button-5d8b34a4-9513-4e4b-b4c8-03bee4b73c09').style.display = 'none'
+                document.getElementById('answer-ce1e3801-054a-4e35-befa-5397be79f185').style.display = 'inline-block';
+                document.getElementById('button-ce1e3801-054a-4e35-befa-5397be79f185').style.display = 'none'
             "
         >
             Show Answer
@@ -791,13 +791,13 @@ <h2>Problem #045</h2>
 <p>If Gaussian Naive Bayes is trained on this data, how many univariate Gaussians will be fit?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-886c1dd2-08ed-43fd-b1ce-fdd5556ec67f" style="display: none">20</span>
-    <span id="button-886c1dd2-08ed-43fd-b1ce-fdd5556ec67f">
+    <span id="answer-5f92efaf-1e7f-4edc-a491-6c7710c6480f" style="display: none">20</span>
+    <span id="button-5f92efaf-1e7f-4edc-a491-6c7710c6480f">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-886c1dd2-08ed-43fd-b1ce-fdd5556ec67f').style.display = 'inline-block';
-                document.getElementById('button-886c1dd2-08ed-43fd-b1ce-fdd5556ec67f').style.display = 'none'
+                document.getElementById('answer-5f92efaf-1e7f-4edc-a491-6c7710c6480f').style.display = 'inline-block';
+                document.getElementById('button-5f92efaf-1e7f-4edc-a491-6c7710c6480f').style.display = 'none'
             "
         >
             Show Answer
@@ -953,13 +953,13 @@ <h2>Problem #049</h2>
 <p>The density estimate within a particular bin of the histogram is 0.1. How many data points from <span class="math">\(\mathcal D\)</span> fall within that histogram bin?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-57d8a360-c57b-4361-8947-95a1c4845518" style="display: none">80</span>
-    <span id="button-57d8a360-c57b-4361-8947-95a1c4845518">
+    <span id="answer-a072eaa0-1d02-4e72-9469-d86dbb1dcca5" style="display: none">80</span>
+    <span id="button-a072eaa0-1d02-4e72-9469-d86dbb1dcca5">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-57d8a360-c57b-4361-8947-95a1c4845518').style.display = 'inline-block';
-                document.getElementById('button-57d8a360-c57b-4361-8947-95a1c4845518').style.display = 'none'
+                document.getElementById('answer-a072eaa0-1d02-4e72-9469-d86dbb1dcca5').style.display = 'inline-block';
+                document.getElementById('button-a072eaa0-1d02-4e72-9469-d86dbb1dcca5').style.display = 'none'
             "
         >
             Show Answer
@@ -1053,13 +1053,13 @@ <h2>Problem #053</h2>
 <p>Suppose a Gaussian with a diagonal covariance matrix is fit to 200 points in <span class="math">\(\mathbb R^4\)</span> using the maximum likelihood estimators. How many parameters are estimated? Count each entry of <span class="math">\(\vec\mu\)</span> and the covariance matrix that must be estimated as its own parameter (the off-diagonal elements of the covariance are zero, and shouldn't be included in your count).</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-ff814df8-ff00-4acb-9ced-80077eb51335" style="display: none">8</span>
-    <span id="button-ff814df8-ff00-4acb-9ced-80077eb51335">
+    <span id="answer-a7d7375b-c117-4b9b-a6d8-09713e7ae720" style="display: none">8</span>
+    <span id="button-a7d7375b-c117-4b9b-a6d8-09713e7ae720">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-ff814df8-ff00-4acb-9ced-80077eb51335').style.display = 'inline-block';
-                document.getElementById('button-ff814df8-ff00-4acb-9ced-80077eb51335').style.display = 'none'
+                document.getElementById('answer-a7d7375b-c117-4b9b-a6d8-09713e7ae720').style.display = 'inline-block';
+                document.getElementById('button-a7d7375b-c117-4b9b-a6d8-09713e7ae720').style.display = 'none'
             "
         >
             Show Answer
@@ -1411,13 +1411,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is <span class="math">\(\pr(1 \leq X \leq 3 \given Y = 0)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-659389fd-cc4c-4885-a94b-869b8b220042" style="display: none">0.6</span>
-    <span id="button-659389fd-cc4c-4885-a94b-869b8b220042">
+    <span id="answer-57d03282-f47d-4ddc-8b7f-2b9a8181f7da" style="display: none">0.6</span>
+    <span id="button-57d03282-f47d-4ddc-8b7f-2b9a8181f7da">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-659389fd-cc4c-4885-a94b-869b8b220042').style.display = 'inline-block';
-                document.getElementById('button-659389fd-cc4c-4885-a94b-869b8b220042').style.display = 'none'
+                document.getElementById('answer-57d03282-f47d-4ddc-8b7f-2b9a8181f7da').style.display = 'inline-block';
+                document.getElementById('button-57d03282-f47d-4ddc-8b7f-2b9a8181f7da').style.display = 'none'
             "
         >
             Show Answer
@@ -1444,13 +1444,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>Suppose again that <span class="math">\(\pr(Y = 1) = \pr(Y = 0) = 0.5\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-b52ebb53-2b1b-4fb4-9401-30f12e846e64" style="display: none">0.30</span>
-    <span id="button-b52ebb53-2b1b-4fb4-9401-30f12e846e64">
+    <span id="answer-b15422d2-ac73-4f7a-b04d-ad71763076aa" style="display: none">0.30</span>
+    <span id="button-b15422d2-ac73-4f7a-b04d-ad71763076aa">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-b52ebb53-2b1b-4fb4-9401-30f12e846e64').style.display = 'inline-block';
-                document.getElementById('button-b52ebb53-2b1b-4fb4-9401-30f12e846e64').style.display = 'none'
+                document.getElementById('answer-b15422d2-ac73-4f7a-b04d-ad71763076aa').style.display = 'inline-block';
+                document.getElementById('button-b15422d2-ac73-4f7a-b04d-ad71763076aa').style.display = 'none'
             "
         >
             Show Answer
@@ -1477,13 +1477,13 @@ <h3 class="subproblem-id">Part 5)</h3>
 <p>Suppose again that <span class="math">\(\pr(Y = 1) = 0.7\)</span> and <span class="math">\(\pr(Y = 0) = 0.3\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-8df1762b-70ac-46bc-b380-aa7683f857f8" style="display: none">0.27</span>
-    <span id="button-8df1762b-70ac-46bc-b380-aa7683f857f8">
+    <span id="answer-1a4c11ec-b396-4dba-973b-06f25e7a8f85" style="display: none">0.27</span>
+    <span id="button-1a4c11ec-b396-4dba-973b-06f25e7a8f85">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-8df1762b-70ac-46bc-b380-aa7683f857f8').style.display = 'inline-block';
-                document.getElementById('button-8df1762b-70ac-46bc-b380-aa7683f857f8').style.display = 'none'
+                document.getElementById('answer-1a4c11ec-b396-4dba-973b-06f25e7a8f85').style.display = 'inline-block';
+                document.getElementById('button-1a4c11ec-b396-4dba-973b-06f25e7a8f85').style.display = 'none'
             "
         >
             Show Answer
@@ -1520,13 +1520,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the estimate of the Class 0 density at <span class="math">\(x = 3.5\)</span>? That is, what is the estimate for <span class="math">\(p(3.5 \given Y = 0)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-6523d228-1425-426a-a7f6-8f27978f17bb" style="display: none">0.1</span>
-    <span id="button-6523d228-1425-426a-a7f6-8f27978f17bb">
+    <span id="answer-1499db12-bd58-472e-83d1-05e8ec8f2ee9" style="display: none">0.1</span>
+    <span id="button-1499db12-bd58-472e-83d1-05e8ec8f2ee9">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-6523d228-1425-426a-a7f6-8f27978f17bb').style.display = 'inline-block';
-                document.getElementById('button-6523d228-1425-426a-a7f6-8f27978f17bb').style.display = 'none'
+                document.getElementById('answer-1499db12-bd58-472e-83d1-05e8ec8f2ee9').style.display = 'inline-block';
+                document.getElementById('button-1499db12-bd58-472e-83d1-05e8ec8f2ee9').style.display = 'none'
             "
         >
             Show Answer
@@ -1541,13 +1541,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>Using the same histogram estimator, what is the estimate of <span class="math">\(\pr(Y = 1 \given x = 3.5)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-e34d44e4-626b-4635-9628-75053dc49bfe" style="display: none">0.5</span>
-    <span id="button-e34d44e4-626b-4635-9628-75053dc49bfe">
+    <span id="answer-76b67353-2f9f-474a-9c06-3a37748f7466" style="display: none">0.5</span>
+    <span id="button-76b67353-2f9f-474a-9c06-3a37748f7466">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-e34d44e4-626b-4635-9628-75053dc49bfe').style.display = 'inline-block';
-                document.getElementById('button-e34d44e4-626b-4635-9628-75053dc49bfe').style.display = 'none'
+                document.getElementById('answer-76b67353-2f9f-474a-9c06-3a37748f7466').style.display = 'inline-block';
+                document.getElementById('button-76b67353-2f9f-474a-9c06-3a37748f7466').style.display = 'none'
             "
         >
             Show Answer
@@ -1580,13 +1580,13 @@ <h2>Problem #095</h2>
 <p>Consider a new point <span class="math">\(\vec x = (1, 1, 1)\)</span>. What is <span class="math">\(H(\vec x)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-ef5359a7-8711-4cc1-a5b7-0a0784334cfb" style="display: none">50</span>
-    <span id="button-ef5359a7-8711-4cc1-a5b7-0a0784334cfb">
+    <span id="answer-2006b025-3b51-47ca-a409-25e1eccb97a3" style="display: none">50</span>
+    <span id="button-2006b025-3b51-47ca-a409-25e1eccb97a3">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-ef5359a7-8711-4cc1-a5b7-0a0784334cfb').style.display = 'inline-block';
-                document.getElementById('button-ef5359a7-8711-4cc1-a5b7-0a0784334cfb').style.display = 'none'
+                document.getElementById('answer-2006b025-3b51-47ca-a409-25e1eccb97a3').style.display = 'inline-block';
+                document.getElementById('button-2006b025-3b51-47ca-a409-25e1eccb97a3').style.display = 'none'
             "
         >
             Show Answer
@@ -1848,13 +1848,13 @@ <h3 class="subproblem-id">Part 1)</h3>
             L(6, 5)\)</span>? Note that <span class="math">\(\mathcal L\)</span> is the likelihood, <i>not</i> the <i>log</i>-likelihood.</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-58ff6deb-d67b-4c7e-949a-58a5a7a9f61c" style="display: none"><span class="math">\(10^{-5}\)</span></span>
-    <span id="button-58ff6deb-d67b-4c7e-949a-58a5a7a9f61c">
+    <span id="answer-c19ef901-d357-49b6-8fbf-6e685245113c" style="display: none"><span class="math">\(10^{-5}\)</span></span>
+    <span id="button-c19ef901-d357-49b6-8fbf-6e685245113c">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-58ff6deb-d67b-4c7e-949a-58a5a7a9f61c').style.display = 'inline-block';
-                document.getElementById('button-58ff6deb-d67b-4c7e-949a-58a5a7a9f61c').style.display = 'none'
+                document.getElementById('answer-c19ef901-d357-49b6-8fbf-6e685245113c').style.display = 'inline-block';
+                document.getElementById('button-c19ef901-d357-49b6-8fbf-6e685245113c').style.display = 'none'
             "
         >
             Show Answer
@@ -1869,13 +1869,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is <span class="math">\(\mathcal L(3, 2)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-4fd9d94d-2e06-48cc-9eeb-c119c3bb838e" style="display: none">0</span>
-    <span id="button-4fd9d94d-2e06-48cc-9eeb-c119c3bb838e">
+    <span id="answer-3e2584eb-b99b-4a42-8033-ddda183b6e2d" style="display: none">0</span>
+    <span id="button-3e2584eb-b99b-4a42-8033-ddda183b6e2d">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-4fd9d94d-2e06-48cc-9eeb-c119c3bb838e').style.display = 'inline-block';
-                document.getElementById('button-4fd9d94d-2e06-48cc-9eeb-c119c3bb838e').style.display = 'none'
+                document.getElementById('answer-3e2584eb-b99b-4a42-8033-ddda183b6e2d').style.display = 'inline-block';
+                document.getElementById('button-3e2584eb-b99b-4a42-8033-ddda183b6e2d').style.display = 'none'
             "
         >
             Show Answer
@@ -1890,13 +1890,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>What are the maximum likelihood estimates of <span class="math">\(\alpha\)</span> and <span class="math">\(\beta\)</span>?</p>
 <p><span class="math">\(\alpha\)</span>: 
 <span class="inline-response-box">
-    <span id="answer-fefc947c-227a-4635-8059-a5bdb5bd4c13" style="display: none">5</span>
-    <span id="button-fefc947c-227a-4635-8059-a5bdb5bd4c13">
+    <span id="answer-0cb2053a-3caa-49ea-b18e-60c02e57a578" style="display: none">5</span>
+    <span id="button-0cb2053a-3caa-49ea-b18e-60c02e57a578">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-fefc947c-227a-4635-8059-a5bdb5bd4c13').style.display = 'inline-block';
-                document.getElementById('button-fefc947c-227a-4635-8059-a5bdb5bd4c13').style.display = 'none'
+                document.getElementById('answer-0cb2053a-3caa-49ea-b18e-60c02e57a578').style.display = 'inline-block';
+                document.getElementById('button-0cb2053a-3caa-49ea-b18e-60c02e57a578').style.display = 'none'
             "
         >
             Show Answer
@@ -1905,13 +1905,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 </span>
 <span class="math">\(\beta\)</span>: 
 <span class="inline-response-box">
-    <span id="answer-fea83bf6-aabe-462e-a8dc-60a43c2ebee4" style="display: none">4</span>
-    <span id="button-fea83bf6-aabe-462e-a8dc-60a43c2ebee4">
+    <span id="answer-e7e67c66-8831-4b18-ae99-b34fcd70081f" style="display: none">4</span>
+    <span id="button-e7e67c66-8831-4b18-ae99-b34fcd70081f">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-fea83bf6-aabe-462e-a8dc-60a43c2ebee4').style.display = 'inline-block';
-                document.getElementById('button-fea83bf6-aabe-462e-a8dc-60a43c2ebee4').style.display = 'none'
+                document.getElementById('answer-e7e67c66-8831-4b18-ae99-b34fcd70081f').style.display = 'inline-block';
+                document.getElementById('button-e7e67c66-8831-4b18-ae99-b34fcd70081f').style.display = 'none'
             "
         >
             Show Answer
@@ -2095,13 +2095,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the (1,2) entry of the sample covariance matrix?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-09015b9a-1a68-4693-bed4-73cf1f2cd2ef" style="display: none">1</span>
-    <span id="button-09015b9a-1a68-4693-bed4-73cf1f2cd2ef">
+    <span id="answer-c1cbe8b2-9fe3-4161-9e36-ad1e1ce5b99f" style="display: none">1</span>
+    <span id="button-c1cbe8b2-9fe3-4161-9e36-ad1e1ce5b99f">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-09015b9a-1a68-4693-bed4-73cf1f2cd2ef').style.display = 'inline-block';
-                document.getElementById('button-09015b9a-1a68-4693-bed4-73cf1f2cd2ef').style.display = 'none'
+                document.getElementById('answer-c1cbe8b2-9fe3-4161-9e36-ad1e1ce5b99f').style.display = 'inline-block';
+                document.getElementById('button-c1cbe8b2-9fe3-4161-9e36-ad1e1ce5b99f').style.display = 'none'
             "
         >
             Show Answer
@@ -2116,13 +2116,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is the (2,2) entry of the sample covariance matrix?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-45c0806e-1c03-42a8-854d-7dd75d2b0edc" style="display: none">8/6</span>
-    <span id="button-45c0806e-1c03-42a8-854d-7dd75d2b0edc">
+    <span id="answer-a596efac-ae05-4be7-8a9f-1e90f7922a7d" style="display: none">8/6</span>
+    <span id="button-a596efac-ae05-4be7-8a9f-1e90f7922a7d">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-45c0806e-1c03-42a8-854d-7dd75d2b0edc').style.display = 'inline-block';
-                document.getElementById('button-45c0806e-1c03-42a8-854d-7dd75d2b0edc').style.display = 'none'
+                document.getElementById('answer-a596efac-ae05-4be7-8a9f-1e90f7922a7d').style.display = 'inline-block';
+                document.getElementById('button-a596efac-ae05-4be7-8a9f-1e90f7922a7d').style.display = 'none'
             "
         >
             Show Answer
@@ -2236,13 +2236,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>Suppose that <span class="math">\(\pr(Y = 1) = \pr(Y = 0) = 0.5\)</span>. What is <span class="math">\(\pr(1 \leq X \leq 3)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-13c3f5de-eabd-44e4-81e4-0b25861919e9" style="display: none">0.3</span>
-    <span id="button-13c3f5de-eabd-44e4-81e4-0b25861919e9">
+    <span id="answer-5da42dd8-cf24-48e7-a19e-7ab35c919b71" style="display: none">0.3</span>
+    <span id="button-5da42dd8-cf24-48e7-a19e-7ab35c919b71">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-13c3f5de-eabd-44e4-81e4-0b25861919e9').style.display = 'inline-block';
-                document.getElementById('button-13c3f5de-eabd-44e4-81e4-0b25861919e9').style.display = 'none'
+                document.getElementById('answer-5da42dd8-cf24-48e7-a19e-7ab35c919b71').style.display = 'inline-block';
+                document.getElementById('button-5da42dd8-cf24-48e7-a19e-7ab35c919b71').style.display = 'none'
             "
         >
             Show Answer
@@ -2269,13 +2269,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>Suppose again that <span class="math">\(\pr(Y = 1) = \pr(Y = 0) = 0.5\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-882c2c36-9fbd-45d4-8ee3-636fd79937cd" style="display: none">0.25</span>
-    <span id="button-882c2c36-9fbd-45d4-8ee3-636fd79937cd">
+    <span id="answer-64bd3f3c-e9b7-42ec-be8d-3a7e398ef1ee" style="display: none">0.25</span>
+    <span id="button-64bd3f3c-e9b7-42ec-be8d-3a7e398ef1ee">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-882c2c36-9fbd-45d4-8ee3-636fd79937cd').style.display = 'inline-block';
-                document.getElementById('button-882c2c36-9fbd-45d4-8ee3-636fd79937cd').style.display = 'none'
+                document.getElementById('answer-64bd3f3c-e9b7-42ec-be8d-3a7e398ef1ee').style.display = 'inline-block';
+                document.getElementById('button-64bd3f3c-e9b7-42ec-be8d-3a7e398ef1ee').style.display = 'none'
             "
         >
             Show Answer
@@ -2290,13 +2290,13 @@ <h3 class="subproblem-id">Part 4)</h3>
 <p>Now suppose <span class="math">\(\pr(Y = 1) = 0.7\)</span> and <span class="math">\(\pr(Y = 0) = 0.3\)</span>. What is <span class="math">\(\pr(1 \leq X \leq 3)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-2a8c0ded-d435-439c-af25-f2a1037ffc63" style="display: none">0.34</span>
-    <span id="button-2a8c0ded-d435-439c-af25-f2a1037ffc63">
+    <span id="answer-f5d1bcff-7787-4c2e-9312-9951eae00549" style="display: none">0.34</span>
+    <span id="button-f5d1bcff-7787-4c2e-9312-9951eae00549">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-2a8c0ded-d435-439c-af25-f2a1037ffc63').style.display = 'inline-block';
-                document.getElementById('button-2a8c0ded-d435-439c-af25-f2a1037ffc63').style.display = 'none'
+                document.getElementById('answer-f5d1bcff-7787-4c2e-9312-9951eae00549').style.display = 'inline-block';
+                document.getElementById('button-f5d1bcff-7787-4c2e-9312-9951eae00549').style.display = 'none'
             "
         >
             Show Answer
@@ -2323,13 +2323,13 @@ <h3 class="subproblem-id">Part 6)</h3>
 <p>Suppose again that <span class="math">\(\pr(Y = 1) = 0.7\)</span> and <span class="math">\(\pr(Y = 0) = 0.3\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-ad57ba82-9eb0-4769-a228-1f6db55a6f76" style="display: none">0.28</span>
-    <span id="button-ad57ba82-9eb0-4769-a228-1f6db55a6f76">
+    <span id="answer-798aaa65-9475-4738-9cc4-934f13857744" style="display: none">0.28</span>
+    <span id="button-798aaa65-9475-4738-9cc4-934f13857744">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-ad57ba82-9eb0-4769-a228-1f6db55a6f76').style.display = 'inline-block';
-                document.getElementById('button-ad57ba82-9eb0-4769-a228-1f6db55a6f76').style.display = 'none'
+                document.getElementById('answer-798aaa65-9475-4738-9cc4-934f13857744').style.display = 'inline-block';
+                document.getElementById('button-798aaa65-9475-4738-9cc4-934f13857744').style.display = 'none'
             "
         >
             Show Answer
@@ -2361,13 +2361,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the estimate of the Class 0 density at <span class="math">\(x = 0.6\)</span>? That is, what is the estimate <span class="math">\(\hat p(0.6 \given Y = 0)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-e427fbe7-8230-4d6d-ac80-abe4c3876e01" style="display: none">5/3</span>
-    <span id="button-e427fbe7-8230-4d6d-ac80-abe4c3876e01">
+    <span id="answer-7f3ee03e-5437-4a21-a5e1-03f0f77c9459" style="display: none">5/3</span>
+    <span id="button-7f3ee03e-5437-4a21-a5e1-03f0f77c9459">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-e427fbe7-8230-4d6d-ac80-abe4c3876e01').style.display = 'inline-block';
-                document.getElementById('button-e427fbe7-8230-4d6d-ac80-abe4c3876e01').style.display = 'none'
+                document.getElementById('answer-7f3ee03e-5437-4a21-a5e1-03f0f77c9459').style.display = 'inline-block';
+                document.getElementById('button-7f3ee03e-5437-4a21-a5e1-03f0f77c9459').style.display = 'none'
             "
         >
             Show Answer
@@ -2382,13 +2382,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>Using the same histogram estimator, what is the estimate <span class="math">\(\hat\pr(Y = 1 \given x = 0.35)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-62f5804f-c581-46c1-be43-162ed7b23375" style="display: none">3/5 = 0.6</span>
-    <span id="button-62f5804f-c581-46c1-be43-162ed7b23375">
+    <span id="answer-d9e5ab81-99bb-4d07-8f92-77263a949b54" style="display: none">3/5 = 0.6</span>
+    <span id="button-d9e5ab81-99bb-4d07-8f92-77263a949b54">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-62f5804f-c581-46c1-be43-162ed7b23375').style.display = 'inline-block';
-                document.getElementById('button-62f5804f-c581-46c1-be43-162ed7b23375').style.display = 'none'
+                document.getElementById('answer-d9e5ab81-99bb-4d07-8f92-77263a949b54').style.display = 'inline-block';
+                document.getElementById('button-d9e5ab81-99bb-4d07-8f92-77263a949b54').style.display = 'none'
             "
         >
             Show Answer
@@ -2403,13 +2403,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>What is the estimate of the marginal density of <span class="math">\(x\)</span> at <span class="math">\(x = 0.1\)</span>? That is, what is <span class="math">\(\hat p(0.1)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-0baa5dbd-d5a8-46e4-928c-123ecac28c4d" style="display: none">7/(19*0.25) = 1.47</span>
-    <span id="button-0baa5dbd-d5a8-46e4-928c-123ecac28c4d">
+    <span id="answer-4a2e0a54-f955-426c-abb9-462725832307" style="display: none">7/(19*0.25) = 1.47</span>
+    <span id="button-4a2e0a54-f955-426c-abb9-462725832307">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-0baa5dbd-d5a8-46e4-928c-123ecac28c4d').style.display = 'inline-block';
-                document.getElementById('button-0baa5dbd-d5a8-46e4-928c-123ecac28c4d').style.display = 'none'
+                document.getElementById('answer-4a2e0a54-f955-426c-abb9-462725832307').style.display = 'inline-block';
+                document.getElementById('button-4a2e0a54-f955-426c-abb9-462725832307').style.display = 'none'
             "
         >
             Show Answer
@@ -2426,13 +2426,13 @@ <h3 class="subproblem-id">Part 4)</h3>
             \]</div>
 <p>
 <span class="inline-response-box">
-    <span id="answer-a2dbb1a7-5671-42b0-9bbd-046ec66d82f6" style="display: none">1</span>
-    <span id="button-a2dbb1a7-5671-42b0-9bbd-046ec66d82f6">
+    <span id="answer-9d9cd74b-0000-451b-b0d5-f64d4783edf4" style="display: none">1</span>
+    <span id="button-9d9cd74b-0000-451b-b0d5-f64d4783edf4">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-a2dbb1a7-5671-42b0-9bbd-046ec66d82f6').style.display = 'inline-block';
-                document.getElementById('button-a2dbb1a7-5671-42b0-9bbd-046ec66d82f6').style.display = 'none'
+                document.getElementById('answer-9d9cd74b-0000-451b-b0d5-f64d4783edf4').style.display = 'inline-block';
+                document.getElementById('button-9d9cd74b-0000-451b-b0d5-f64d4783edf4').style.display = 'none'
             "
         >
             Show Answer
@@ -2460,13 +2460,13 @@ <h2>Problem #112</h2>
 <p>Consider a new point <span class="math">\(\vec x = (2, 0, 1)^T\)</span>. What is <span class="math">\(H(\vec x)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-9857ea02-6806-46cf-a6ca-47d84faa30f8" style="display: none">37</span>
-    <span id="button-9857ea02-6806-46cf-a6ca-47d84faa30f8">
+    <span id="answer-e07f159d-da5c-49ae-89b7-b5bf3575e1ba" style="display: none">37</span>
+    <span id="button-e07f159d-da5c-49ae-89b7-b5bf3575e1ba">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-9857ea02-6806-46cf-a6ca-47d84faa30f8').style.display = 'inline-block';
-                document.getElementById('button-9857ea02-6806-46cf-a6ca-47d84faa30f8').style.display = 'none'
+                document.getElementById('answer-e07f159d-da5c-49ae-89b7-b5bf3575e1ba').style.display = 'inline-block';
+                document.getElementById('button-e07f159d-da5c-49ae-89b7-b5bf3575e1ba').style.display = 'none'
             "
         >
             Show Answer
@@ -2500,13 +2500,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the (1,3) entry of the sample covariance matrix?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-e7e199bf-4acd-4296-9faf-455b2ea37ef0" style="display: none">9/4</span>
-    <span id="button-e7e199bf-4acd-4296-9faf-455b2ea37ef0">
+    <span id="answer-5cd3c674-6875-4d7a-8051-9a0f82ffb39c" style="display: none">9/4</span>
+    <span id="button-5cd3c674-6875-4d7a-8051-9a0f82ffb39c">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-e7e199bf-4acd-4296-9faf-455b2ea37ef0').style.display = 'inline-block';
-                document.getElementById('button-e7e199bf-4acd-4296-9faf-455b2ea37ef0').style.display = 'none'
+                document.getElementById('answer-5cd3c674-6875-4d7a-8051-9a0f82ffb39c').style.display = 'inline-block';
+                document.getElementById('button-5cd3c674-6875-4d7a-8051-9a0f82ffb39c').style.display = 'none'
             "
         >
             Show Answer
@@ -2521,13 +2521,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is the (1,2) entry of the sample covariance matrix?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-70d32f5a-6f4f-404b-9328-5a0b70c405d5" style="display: none">-3/4</span>
-    <span id="button-70d32f5a-6f4f-404b-9328-5a0b70c405d5">
+    <span id="answer-22286e15-2947-4ffd-b3b3-77533bf9c426" style="display: none">-3/4</span>
+    <span id="button-22286e15-2947-4ffd-b3b3-77533bf9c426">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-70d32f5a-6f4f-404b-9328-5a0b70c405d5').style.display = 'inline-block';
-                document.getElementById('button-70d32f5a-6f4f-404b-9328-5a0b70c405d5').style.display = 'none'
+                document.getElementById('answer-22286e15-2947-4ffd-b3b3-77533bf9c426').style.display = 'inline-block';
+                document.getElementById('button-22286e15-2947-4ffd-b3b3-77533bf9c426').style.display = 'none'
             "
         >
             Show Answer
@@ -2641,13 +2641,13 @@ <h2>Problem #119</h2>
 <p>If these estimates are used in place of the true class-conditional densities in the Bayes classifier, what will be the training error of the classifier? That is, what percentage of the data above will be misclassified? You may leave your answer as a fraction or a decimal.</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-e0398068-7fa0-4bba-9ae7-d970d7c6a369" style="display: none">4/14 = .2857</span>
-    <span id="button-e0398068-7fa0-4bba-9ae7-d970d7c6a369">
+    <span id="answer-acfe60e2-5728-4210-8791-939bb0e812af" style="display: none">4/14 = .2857</span>
+    <span id="button-acfe60e2-5728-4210-8791-939bb0e812af">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-e0398068-7fa0-4bba-9ae7-d970d7c6a369').style.display = 'inline-block';
-                document.getElementById('button-e0398068-7fa0-4bba-9ae7-d970d7c6a369').style.display = 'none'
+                document.getElementById('answer-acfe60e2-5728-4210-8791-939bb0e812af').style.display = 'inline-block';
+                document.getElementById('button-acfe60e2-5728-4210-8791-939bb0e812af').style.display = 'none'
             "
         >
             Show Answer
diff --git a/practice/tags/Gaussians.html b/practice/tags/Gaussians.html
index 9e93f5af..6356fc81 100644
--- a/practice/tags/Gaussians.html
+++ b/practice/tags/Gaussians.html
@@ -123,13 +123,13 @@ <h2>Problem #040</h2>
 <p>Suppose a Gaussian with a diagonal covariance matrix is fit to 200 points in <span class="math">\(\mathbb R^4\)</span> using the maximum likelihood estimators. How many parameters are estimated? Count each entry of <span class="math">\(\mu\)</span> and the covariance matrix that must be estimated as its own parameter.</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-b3b2563e-19b8-4910-9d86-9c7347bfdf32" style="display: none">8</span>
-    <span id="button-b3b2563e-19b8-4910-9d86-9c7347bfdf32">
+    <span id="answer-03a05001-f579-440a-a17c-a3b5d065d5d7" style="display: none">8</span>
+    <span id="button-03a05001-f579-440a-a17c-a3b5d065d5d7">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-b3b2563e-19b8-4910-9d86-9c7347bfdf32').style.display = 'inline-block';
-                document.getElementById('button-b3b2563e-19b8-4910-9d86-9c7347bfdf32').style.display = 'none'
+                document.getElementById('answer-03a05001-f579-440a-a17c-a3b5d065d5d7').style.display = 'inline-block';
+                document.getElementById('button-03a05001-f579-440a-a17c-a3b5d065d5d7').style.display = 'none'
             "
         >
             Show Answer
@@ -179,13 +179,13 @@ <h2>Problem #053</h2>
 <p>Suppose a Gaussian with a diagonal covariance matrix is fit to 200 points in <span class="math">\(\mathbb R^4\)</span> using the maximum likelihood estimators. How many parameters are estimated? Count each entry of <span class="math">\(\vec\mu\)</span> and the covariance matrix that must be estimated as its own parameter (the off-diagonal elements of the covariance are zero, and shouldn't be included in your count).</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-e91d5f5d-a9e8-4c4d-bd76-7d92c3d6cb5c" style="display: none">8</span>
-    <span id="button-e91d5f5d-a9e8-4c4d-bd76-7d92c3d6cb5c">
+    <span id="answer-c2549aff-d001-4fa2-8746-0ac0e2c96643" style="display: none">8</span>
+    <span id="button-c2549aff-d001-4fa2-8746-0ac0e2c96643">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-e91d5f5d-a9e8-4c4d-bd76-7d92c3d6cb5c').style.display = 'inline-block';
-                document.getElementById('button-e91d5f5d-a9e8-4c4d-bd76-7d92c3d6cb5c').style.display = 'none'
+                document.getElementById('answer-c2549aff-d001-4fa2-8746-0ac0e2c96643').style.display = 'inline-block';
+                document.getElementById('button-c2549aff-d001-4fa2-8746-0ac0e2c96643').style.display = 'none'
             "
         >
             Show Answer
diff --git a/practice/tags/SVMs.html b/practice/tags/SVMs.html
index fabed4d3..395f7922 100644
--- a/practice/tags/SVMs.html
+++ b/practice/tags/SVMs.html
@@ -298,13 +298,13 @@ <h2>Problem #073</h2>
 <p>What weight vector <i>is</i> the solution of the Hard SVM problem for this data set?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-7bbba19b-9c18-4274-bd74-b388af91e4a3" style="display: none"><span class="math">\((3, 0, \frac{1}{4})^T\)</span></span>
-    <span id="button-7bbba19b-9c18-4274-bd74-b388af91e4a3">
+    <span id="answer-bd1de0c0-0467-46e8-b96e-29d3b026d287" style="display: none"><span class="math">\((3, 0, \frac{1}{4})^T\)</span></span>
+    <span id="button-bd1de0c0-0467-46e8-b96e-29d3b026d287">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-7bbba19b-9c18-4274-bd74-b388af91e4a3').style.display = 'inline-block';
-                document.getElementById('button-7bbba19b-9c18-4274-bd74-b388af91e4a3').style.display = 'none'
+                document.getElementById('answer-bd1de0c0-0467-46e8-b96e-29d3b026d287').style.display = 'inline-block';
+                document.getElementById('button-bd1de0c0-0467-46e8-b96e-29d3b026d287').style.display = 'none'
             "
         >
             Show Answer
diff --git a/practice/tags/bayes classifier.html b/practice/tags/bayes classifier.html
index e2b8b19e..4aa61b43 100644
--- a/practice/tags/bayes classifier.html	
+++ b/practice/tags/bayes classifier.html	
@@ -139,13 +139,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>Suppose <span class="math">\(\pr(Y = 1) = 0.5\)</span> and <span class="math">\(\pr(Y = 0) = 0.5\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-06006f87-33eb-4c8e-83ed-19a281352b80" style="display: none">0.25</span>
-    <span id="button-06006f87-33eb-4c8e-83ed-19a281352b80">
+    <span id="answer-0c84258b-2897-4343-b529-2cf388ecbabd" style="display: none">0.25</span>
+    <span id="button-0c84258b-2897-4343-b529-2cf388ecbabd">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-06006f87-33eb-4c8e-83ed-19a281352b80').style.display = 'inline-block';
-                document.getElementById('button-06006f87-33eb-4c8e-83ed-19a281352b80').style.display = 'none'
+                document.getElementById('answer-0c84258b-2897-4343-b529-2cf388ecbabd').style.display = 'inline-block';
+                document.getElementById('button-0c84258b-2897-4343-b529-2cf388ecbabd').style.display = 'none'
             "
         >
             Show Answer
@@ -172,13 +172,13 @@ <h3 class="subproblem-id">Part 4)</h3>
 <p>Now suppose <span class="math">\(\pr(Y = 1) = 0.7\)</span> and <span class="math">\(\pr(Y = 0) = 0.3\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-80147019-9041-46eb-b21f-bc6ac20d7164" style="display: none">0.29</span>
-    <span id="button-80147019-9041-46eb-b21f-bc6ac20d7164">
+    <span id="answer-a7a6ede2-4c23-4016-ba85-58c3688dd24b" style="display: none">0.29</span>
+    <span id="button-a7a6ede2-4c23-4016-ba85-58c3688dd24b">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-80147019-9041-46eb-b21f-bc6ac20d7164').style.display = 'inline-block';
-                document.getElementById('button-80147019-9041-46eb-b21f-bc6ac20d7164').style.display = 'none'
+                document.getElementById('answer-a7a6ede2-4c23-4016-ba85-58c3688dd24b').style.display = 'inline-block';
+                document.getElementById('button-a7a6ede2-4c23-4016-ba85-58c3688dd24b').style.display = 'none'
             "
         >
             Show Answer
@@ -278,13 +278,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is <span class="math">\(\pr(1 \leq X \leq 3 \given Y = 0)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-68dd6822-203a-4202-9b65-39b503e115fe" style="display: none">0.6</span>
-    <span id="button-68dd6822-203a-4202-9b65-39b503e115fe">
+    <span id="answer-eb56582a-443c-4104-bb88-242a73b239fc" style="display: none">0.6</span>
+    <span id="button-eb56582a-443c-4104-bb88-242a73b239fc">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-68dd6822-203a-4202-9b65-39b503e115fe').style.display = 'inline-block';
-                document.getElementById('button-68dd6822-203a-4202-9b65-39b503e115fe').style.display = 'none'
+                document.getElementById('answer-eb56582a-443c-4104-bb88-242a73b239fc').style.display = 'inline-block';
+                document.getElementById('button-eb56582a-443c-4104-bb88-242a73b239fc').style.display = 'none'
             "
         >
             Show Answer
@@ -311,13 +311,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>Suppose again that <span class="math">\(\pr(Y = 1) = \pr(Y = 0) = 0.5\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-cb5655aa-b703-41e0-8ab1-88cf7f4a6cb9" style="display: none">0.30</span>
-    <span id="button-cb5655aa-b703-41e0-8ab1-88cf7f4a6cb9">
+    <span id="answer-4f75bef5-eb2f-475f-9c87-7bfa0aee525d" style="display: none">0.30</span>
+    <span id="button-4f75bef5-eb2f-475f-9c87-7bfa0aee525d">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-cb5655aa-b703-41e0-8ab1-88cf7f4a6cb9').style.display = 'inline-block';
-                document.getElementById('button-cb5655aa-b703-41e0-8ab1-88cf7f4a6cb9').style.display = 'none'
+                document.getElementById('answer-4f75bef5-eb2f-475f-9c87-7bfa0aee525d').style.display = 'inline-block';
+                document.getElementById('button-4f75bef5-eb2f-475f-9c87-7bfa0aee525d').style.display = 'none'
             "
         >
             Show Answer
@@ -344,13 +344,13 @@ <h3 class="subproblem-id">Part 5)</h3>
 <p>Suppose again that <span class="math">\(\pr(Y = 1) = 0.7\)</span> and <span class="math">\(\pr(Y = 0) = 0.3\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-4af37001-8a0c-4f4e-9261-d67b39468075" style="display: none">0.27</span>
-    <span id="button-4af37001-8a0c-4f4e-9261-d67b39468075">
+    <span id="answer-7143ffab-e63c-4b89-87b2-bc7657d3e7ea" style="display: none">0.27</span>
+    <span id="button-7143ffab-e63c-4b89-87b2-bc7657d3e7ea">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-4af37001-8a0c-4f4e-9261-d67b39468075').style.display = 'inline-block';
-                document.getElementById('button-4af37001-8a0c-4f4e-9261-d67b39468075').style.display = 'none'
+                document.getElementById('answer-7143ffab-e63c-4b89-87b2-bc7657d3e7ea').style.display = 'inline-block';
+                document.getElementById('button-7143ffab-e63c-4b89-87b2-bc7657d3e7ea').style.display = 'none'
             "
         >
             Show Answer
@@ -385,13 +385,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>Suppose that <span class="math">\(\pr(Y = 1) = \pr(Y = 0) = 0.5\)</span>. What is <span class="math">\(\pr(1 \leq X \leq 3)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-312d152b-befd-495c-b805-9160ba69d069" style="display: none">0.3</span>
-    <span id="button-312d152b-befd-495c-b805-9160ba69d069">
+    <span id="answer-364fd8a4-9ffc-433c-a88b-bb43782529d6" style="display: none">0.3</span>
+    <span id="button-364fd8a4-9ffc-433c-a88b-bb43782529d6">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-312d152b-befd-495c-b805-9160ba69d069').style.display = 'inline-block';
-                document.getElementById('button-312d152b-befd-495c-b805-9160ba69d069').style.display = 'none'
+                document.getElementById('answer-364fd8a4-9ffc-433c-a88b-bb43782529d6').style.display = 'inline-block';
+                document.getElementById('button-364fd8a4-9ffc-433c-a88b-bb43782529d6').style.display = 'none'
             "
         >
             Show Answer
@@ -418,13 +418,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>Suppose again that <span class="math">\(\pr(Y = 1) = \pr(Y = 0) = 0.5\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-1b86b119-fec0-44a1-b023-c88c43c15069" style="display: none">0.25</span>
-    <span id="button-1b86b119-fec0-44a1-b023-c88c43c15069">
+    <span id="answer-1a793f60-d507-4cce-95ba-9ebb513695e1" style="display: none">0.25</span>
+    <span id="button-1a793f60-d507-4cce-95ba-9ebb513695e1">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-1b86b119-fec0-44a1-b023-c88c43c15069').style.display = 'inline-block';
-                document.getElementById('button-1b86b119-fec0-44a1-b023-c88c43c15069').style.display = 'none'
+                document.getElementById('answer-1a793f60-d507-4cce-95ba-9ebb513695e1').style.display = 'inline-block';
+                document.getElementById('button-1a793f60-d507-4cce-95ba-9ebb513695e1').style.display = 'none'
             "
         >
             Show Answer
@@ -439,13 +439,13 @@ <h3 class="subproblem-id">Part 4)</h3>
 <p>Now suppose <span class="math">\(\pr(Y = 1) = 0.7\)</span> and <span class="math">\(\pr(Y = 0) = 0.3\)</span>. What is <span class="math">\(\pr(1 \leq X \leq 3)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-c98f772b-4760-4a30-be7a-51b487b1d01a" style="display: none">0.34</span>
-    <span id="button-c98f772b-4760-4a30-be7a-51b487b1d01a">
+    <span id="answer-9a1bf012-d3bc-4ff8-abd0-30dca9fba1f5" style="display: none">0.34</span>
+    <span id="button-9a1bf012-d3bc-4ff8-abd0-30dca9fba1f5">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-c98f772b-4760-4a30-be7a-51b487b1d01a').style.display = 'inline-block';
-                document.getElementById('button-c98f772b-4760-4a30-be7a-51b487b1d01a').style.display = 'none'
+                document.getElementById('answer-9a1bf012-d3bc-4ff8-abd0-30dca9fba1f5').style.display = 'inline-block';
+                document.getElementById('button-9a1bf012-d3bc-4ff8-abd0-30dca9fba1f5').style.display = 'none'
             "
         >
             Show Answer
@@ -472,13 +472,13 @@ <h3 class="subproblem-id">Part 6)</h3>
 <p>Suppose again that <span class="math">\(\pr(Y = 1) = 0.7\)</span> and <span class="math">\(\pr(Y = 0) = 0.3\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-7e683842-2994-4b97-ab53-d5d629e69028" style="display: none">0.28</span>
-    <span id="button-7e683842-2994-4b97-ab53-d5d629e69028">
+    <span id="answer-a3b61af5-738a-4d73-a4c4-3857da14ab2b" style="display: none">0.28</span>
+    <span id="button-a3b61af5-738a-4d73-a4c4-3857da14ab2b">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-7e683842-2994-4b97-ab53-d5d629e69028').style.display = 'inline-block';
-                document.getElementById('button-7e683842-2994-4b97-ab53-d5d629e69028').style.display = 'none'
+                document.getElementById('answer-a3b61af5-738a-4d73-a4c4-3857da14ab2b').style.display = 'inline-block';
+                document.getElementById('button-a3b61af5-738a-4d73-a4c4-3857da14ab2b').style.display = 'none'
             "
         >
             Show Answer
@@ -510,13 +510,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the estimate of the Class 0 density at <span class="math">\(x = 0.6\)</span>? That is, what is the estimate <span class="math">\(\hat p(0.6 \given Y = 0)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-2f7429f2-3e42-446f-8578-467a33baa934" style="display: none">5/3</span>
-    <span id="button-2f7429f2-3e42-446f-8578-467a33baa934">
+    <span id="answer-34ef9c50-7fe8-4f33-8550-ed2ae0d2a36d" style="display: none">5/3</span>
+    <span id="button-34ef9c50-7fe8-4f33-8550-ed2ae0d2a36d">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-2f7429f2-3e42-446f-8578-467a33baa934').style.display = 'inline-block';
-                document.getElementById('button-2f7429f2-3e42-446f-8578-467a33baa934').style.display = 'none'
+                document.getElementById('answer-34ef9c50-7fe8-4f33-8550-ed2ae0d2a36d').style.display = 'inline-block';
+                document.getElementById('button-34ef9c50-7fe8-4f33-8550-ed2ae0d2a36d').style.display = 'none'
             "
         >
             Show Answer
@@ -531,13 +531,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>Using the same histogram estimator, what is the estimate <span class="math">\(\hat\pr(Y = 1 \given x = 0.35)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-386c56af-efed-4de5-9fba-e9afcfec79ae" style="display: none">3/5 = 0.6</span>
-    <span id="button-386c56af-efed-4de5-9fba-e9afcfec79ae">
+    <span id="answer-b8276926-ceda-488a-8687-0710d5605d49" style="display: none">3/5 = 0.6</span>
+    <span id="button-b8276926-ceda-488a-8687-0710d5605d49">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-386c56af-efed-4de5-9fba-e9afcfec79ae').style.display = 'inline-block';
-                document.getElementById('button-386c56af-efed-4de5-9fba-e9afcfec79ae').style.display = 'none'
+                document.getElementById('answer-b8276926-ceda-488a-8687-0710d5605d49').style.display = 'inline-block';
+                document.getElementById('button-b8276926-ceda-488a-8687-0710d5605d49').style.display = 'none'
             "
         >
             Show Answer
@@ -552,13 +552,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>What is the estimate of the marginal density of <span class="math">\(x\)</span> at <span class="math">\(x = 0.1\)</span>? That is, what is <span class="math">\(\hat p(0.1)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-de7f8e16-870f-47b7-ab2c-cd36495254ce" style="display: none">7/(19*0.25) = 1.47</span>
-    <span id="button-de7f8e16-870f-47b7-ab2c-cd36495254ce">
+    <span id="answer-bf2f0035-6f29-45f0-ae45-4b292b281924" style="display: none">7/(19*0.25) = 1.47</span>
+    <span id="button-bf2f0035-6f29-45f0-ae45-4b292b281924">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-de7f8e16-870f-47b7-ab2c-cd36495254ce').style.display = 'inline-block';
-                document.getElementById('button-de7f8e16-870f-47b7-ab2c-cd36495254ce').style.display = 'none'
+                document.getElementById('answer-bf2f0035-6f29-45f0-ae45-4b292b281924').style.display = 'inline-block';
+                document.getElementById('button-bf2f0035-6f29-45f0-ae45-4b292b281924').style.display = 'none'
             "
         >
             Show Answer
@@ -575,13 +575,13 @@ <h3 class="subproblem-id">Part 4)</h3>
             \]</div>
 <p>
 <span class="inline-response-box">
-    <span id="answer-93e85867-e81b-4ab0-8929-6dce8d354c9e" style="display: none">1</span>
-    <span id="button-93e85867-e81b-4ab0-8929-6dce8d354c9e">
+    <span id="answer-e975a472-67ce-4557-a0b5-7cbac35a5db6" style="display: none">1</span>
+    <span id="button-e975a472-67ce-4557-a0b5-7cbac35a5db6">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-93e85867-e81b-4ab0-8929-6dce8d354c9e').style.display = 'inline-block';
-                document.getElementById('button-93e85867-e81b-4ab0-8929-6dce8d354c9e').style.display = 'none'
+                document.getElementById('answer-e975a472-67ce-4557-a0b5-7cbac35a5db6').style.display = 'inline-block';
+                document.getElementById('button-e975a472-67ce-4557-a0b5-7cbac35a5db6').style.display = 'none'
             "
         >
             Show Answer
diff --git a/practice/tags/bayes error.html b/practice/tags/bayes error.html
index cfbb99e2..cb8f8ea3 100644
--- a/practice/tags/bayes error.html	
+++ b/practice/tags/bayes error.html	
@@ -139,13 +139,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>Suppose <span class="math">\(\pr(Y = 1) = 0.5\)</span> and <span class="math">\(\pr(Y = 0) = 0.5\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-f792298b-b390-4f3f-b326-4a06b7286fd3" style="display: none">0.25</span>
-    <span id="button-f792298b-b390-4f3f-b326-4a06b7286fd3">
+    <span id="answer-9eb535d9-1fef-4c95-8c9c-6d967ec8fae3" style="display: none">0.25</span>
+    <span id="button-9eb535d9-1fef-4c95-8c9c-6d967ec8fae3">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-f792298b-b390-4f3f-b326-4a06b7286fd3').style.display = 'inline-block';
-                document.getElementById('button-f792298b-b390-4f3f-b326-4a06b7286fd3').style.display = 'none'
+                document.getElementById('answer-9eb535d9-1fef-4c95-8c9c-6d967ec8fae3').style.display = 'inline-block';
+                document.getElementById('button-9eb535d9-1fef-4c95-8c9c-6d967ec8fae3').style.display = 'none'
             "
         >
             Show Answer
@@ -172,13 +172,13 @@ <h3 class="subproblem-id">Part 4)</h3>
 <p>Now suppose <span class="math">\(\pr(Y = 1) = 0.7\)</span> and <span class="math">\(\pr(Y = 0) = 0.3\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-f076b442-2c8e-48fc-8a32-47f1b7f33926" style="display: none">0.29</span>
-    <span id="button-f076b442-2c8e-48fc-8a32-47f1b7f33926">
+    <span id="answer-8484b84d-6db6-4916-ba99-3563ba75836e" style="display: none">0.29</span>
+    <span id="button-8484b84d-6db6-4916-ba99-3563ba75836e">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-f076b442-2c8e-48fc-8a32-47f1b7f33926').style.display = 'inline-block';
-                document.getElementById('button-f076b442-2c8e-48fc-8a32-47f1b7f33926').style.display = 'none'
+                document.getElementById('answer-8484b84d-6db6-4916-ba99-3563ba75836e').style.display = 'inline-block';
+                document.getElementById('button-8484b84d-6db6-4916-ba99-3563ba75836e').style.display = 'none'
             "
         >
             Show Answer
@@ -253,13 +253,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is <span class="math">\(\pr(1 \leq X \leq 3 \given Y = 0)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-5f34c346-403b-4143-91dd-1d7399ef0720" style="display: none">0.6</span>
-    <span id="button-5f34c346-403b-4143-91dd-1d7399ef0720">
+    <span id="answer-02a8be23-bf04-47ea-854a-edbb1b118c74" style="display: none">0.6</span>
+    <span id="button-02a8be23-bf04-47ea-854a-edbb1b118c74">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-5f34c346-403b-4143-91dd-1d7399ef0720').style.display = 'inline-block';
-                document.getElementById('button-5f34c346-403b-4143-91dd-1d7399ef0720').style.display = 'none'
+                document.getElementById('answer-02a8be23-bf04-47ea-854a-edbb1b118c74').style.display = 'inline-block';
+                document.getElementById('button-02a8be23-bf04-47ea-854a-edbb1b118c74').style.display = 'none'
             "
         >
             Show Answer
@@ -286,13 +286,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>Suppose again that <span class="math">\(\pr(Y = 1) = \pr(Y = 0) = 0.5\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-2a945a04-fca0-448e-8d4a-58cb4eec1cab" style="display: none">0.30</span>
-    <span id="button-2a945a04-fca0-448e-8d4a-58cb4eec1cab">
+    <span id="answer-1719dcf8-6a32-4941-90a4-7581128af702" style="display: none">0.30</span>
+    <span id="button-1719dcf8-6a32-4941-90a4-7581128af702">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-2a945a04-fca0-448e-8d4a-58cb4eec1cab').style.display = 'inline-block';
-                document.getElementById('button-2a945a04-fca0-448e-8d4a-58cb4eec1cab').style.display = 'none'
+                document.getElementById('answer-1719dcf8-6a32-4941-90a4-7581128af702').style.display = 'inline-block';
+                document.getElementById('button-1719dcf8-6a32-4941-90a4-7581128af702').style.display = 'none'
             "
         >
             Show Answer
@@ -319,13 +319,13 @@ <h3 class="subproblem-id">Part 5)</h3>
 <p>Suppose again that <span class="math">\(\pr(Y = 1) = 0.7\)</span> and <span class="math">\(\pr(Y = 0) = 0.3\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-f20cd689-48b5-4d9a-ba3c-4aa0b90642bf" style="display: none">0.27</span>
-    <span id="button-f20cd689-48b5-4d9a-ba3c-4aa0b90642bf">
+    <span id="answer-4e60bcfc-807b-4065-9ca8-ad815c7669aa" style="display: none">0.27</span>
+    <span id="button-4e60bcfc-807b-4065-9ca8-ad815c7669aa">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-f20cd689-48b5-4d9a-ba3c-4aa0b90642bf').style.display = 'inline-block';
-                document.getElementById('button-f20cd689-48b5-4d9a-ba3c-4aa0b90642bf').style.display = 'none'
+                document.getElementById('answer-4e60bcfc-807b-4065-9ca8-ad815c7669aa').style.display = 'inline-block';
+                document.getElementById('button-4e60bcfc-807b-4065-9ca8-ad815c7669aa').style.display = 'none'
             "
         >
             Show Answer
@@ -360,13 +360,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>Suppose that <span class="math">\(\pr(Y = 1) = \pr(Y = 0) = 0.5\)</span>. What is <span class="math">\(\pr(1 \leq X \leq 3)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-936516fa-1b93-4989-86d6-4f185baef77d" style="display: none">0.3</span>
-    <span id="button-936516fa-1b93-4989-86d6-4f185baef77d">
+    <span id="answer-59a51232-6158-439e-bfec-13069a424c85" style="display: none">0.3</span>
+    <span id="button-59a51232-6158-439e-bfec-13069a424c85">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-936516fa-1b93-4989-86d6-4f185baef77d').style.display = 'inline-block';
-                document.getElementById('button-936516fa-1b93-4989-86d6-4f185baef77d').style.display = 'none'
+                document.getElementById('answer-59a51232-6158-439e-bfec-13069a424c85').style.display = 'inline-block';
+                document.getElementById('button-59a51232-6158-439e-bfec-13069a424c85').style.display = 'none'
             "
         >
             Show Answer
@@ -393,13 +393,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>Suppose again that <span class="math">\(\pr(Y = 1) = \pr(Y = 0) = 0.5\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-0ef51ad7-0447-4160-a75a-03c86b1c212d" style="display: none">0.25</span>
-    <span id="button-0ef51ad7-0447-4160-a75a-03c86b1c212d">
+    <span id="answer-fbfc4fd5-7895-4c0c-bec5-25f1c87308fc" style="display: none">0.25</span>
+    <span id="button-fbfc4fd5-7895-4c0c-bec5-25f1c87308fc">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-0ef51ad7-0447-4160-a75a-03c86b1c212d').style.display = 'inline-block';
-                document.getElementById('button-0ef51ad7-0447-4160-a75a-03c86b1c212d').style.display = 'none'
+                document.getElementById('answer-fbfc4fd5-7895-4c0c-bec5-25f1c87308fc').style.display = 'inline-block';
+                document.getElementById('button-fbfc4fd5-7895-4c0c-bec5-25f1c87308fc').style.display = 'none'
             "
         >
             Show Answer
@@ -414,13 +414,13 @@ <h3 class="subproblem-id">Part 4)</h3>
 <p>Now suppose <span class="math">\(\pr(Y = 1) = 0.7\)</span> and <span class="math">\(\pr(Y = 0) = 0.3\)</span>. What is <span class="math">\(\pr(1 \leq X \leq 3)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-33381f95-8af1-4625-b329-b1d347b48c6a" style="display: none">0.34</span>
-    <span id="button-33381f95-8af1-4625-b329-b1d347b48c6a">
+    <span id="answer-23c38ef0-cf5a-4fbb-adf5-5d70c5759369" style="display: none">0.34</span>
+    <span id="button-23c38ef0-cf5a-4fbb-adf5-5d70c5759369">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-33381f95-8af1-4625-b329-b1d347b48c6a').style.display = 'inline-block';
-                document.getElementById('button-33381f95-8af1-4625-b329-b1d347b48c6a').style.display = 'none'
+                document.getElementById('answer-23c38ef0-cf5a-4fbb-adf5-5d70c5759369').style.display = 'inline-block';
+                document.getElementById('button-23c38ef0-cf5a-4fbb-adf5-5d70c5759369').style.display = 'none'
             "
         >
             Show Answer
@@ -447,13 +447,13 @@ <h3 class="subproblem-id">Part 6)</h3>
 <p>Suppose again that <span class="math">\(\pr(Y = 1) = 0.7\)</span> and <span class="math">\(\pr(Y = 0) = 0.3\)</span>. What is the Bayes error with respect to this distribution?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-1a0914db-ae03-4597-abaf-ab47390175b4" style="display: none">0.28</span>
-    <span id="button-1a0914db-ae03-4597-abaf-ab47390175b4">
+    <span id="answer-3f704c01-96c4-476f-9bf1-3393aa599a86" style="display: none">0.28</span>
+    <span id="button-3f704c01-96c4-476f-9bf1-3393aa599a86">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-1a0914db-ae03-4597-abaf-ab47390175b4').style.display = 'inline-block';
-                document.getElementById('button-1a0914db-ae03-4597-abaf-ab47390175b4').style.display = 'none'
+                document.getElementById('answer-3f704c01-96c4-476f-9bf1-3393aa599a86').style.display = 'inline-block';
+                document.getElementById('button-3f704c01-96c4-476f-9bf1-3393aa599a86').style.display = 'none'
             "
         >
             Show Answer
diff --git a/practice/tags/computing loss.html b/practice/tags/computing loss.html
index e72ad7dc..71ea2075 100644
--- a/practice/tags/computing loss.html	
+++ b/practice/tags/computing loss.html	
@@ -220,13 +220,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the <b>total</b><i>square</i> loss of <span class="math">\(H\)</span> on this data set?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-aa2b93d8-dfcb-4d75-b06e-a0a14a5e94a7" style="display: none">11.25</span>
-    <span id="button-aa2b93d8-dfcb-4d75-b06e-a0a14a5e94a7">
+    <span id="answer-1dc9ea73-2b94-4f3c-88b5-89974ca4c7c2" style="display: none">11.25</span>
+    <span id="button-1dc9ea73-2b94-4f3c-88b5-89974ca4c7c2">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-aa2b93d8-dfcb-4d75-b06e-a0a14a5e94a7').style.display = 'inline-block';
-                document.getElementById('button-aa2b93d8-dfcb-4d75-b06e-a0a14a5e94a7').style.display = 'none'
+                document.getElementById('answer-1dc9ea73-2b94-4f3c-88b5-89974ca4c7c2').style.display = 'inline-block';
+                document.getElementById('button-1dc9ea73-2b94-4f3c-88b5-89974ca4c7c2').style.display = 'none'
             "
         >
             Show Answer
@@ -241,13 +241,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is the <b>total</b><i>perceptron</i> loss of <span class="math">\(H\)</span> on this data set?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-9b935a1e-d360-4607-b8a3-60995999b3fa" style="display: none">1</span>
-    <span id="button-9b935a1e-d360-4607-b8a3-60995999b3fa">
+    <span id="answer-8f94ca4b-c335-4f7d-a206-b79e55617d60" style="display: none">1</span>
+    <span id="button-8f94ca4b-c335-4f7d-a206-b79e55617d60">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-9b935a1e-d360-4607-b8a3-60995999b3fa').style.display = 'inline-block';
-                document.getElementById('button-9b935a1e-d360-4607-b8a3-60995999b3fa').style.display = 'none'
+                document.getElementById('answer-8f94ca4b-c335-4f7d-a206-b79e55617d60').style.display = 'inline-block';
+                document.getElementById('button-8f94ca4b-c335-4f7d-a206-b79e55617d60').style.display = 'none'
             "
         >
             Show Answer
@@ -262,13 +262,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>What is the <b>total</b><i>hinge</i> loss of <span class="math">\(H\)</span> on this data set?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-50a63be7-e17d-4fbe-961f-2ff3af6c1333" style="display: none">3.5</span>
-    <span id="button-50a63be7-e17d-4fbe-961f-2ff3af6c1333">
+    <span id="answer-ef4c8f9e-1c76-40c7-a663-b30c69e7d1b4" style="display: none">3.5</span>
+    <span id="button-ef4c8f9e-1c76-40c7-a663-b30c69e7d1b4">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-50a63be7-e17d-4fbe-961f-2ff3af6c1333').style.display = 'inline-block';
-                document.getElementById('button-50a63be7-e17d-4fbe-961f-2ff3af6c1333').style.display = 'none'
+                document.getElementById('answer-ef4c8f9e-1c76-40c7-a663-b30c69e7d1b4').style.display = 'inline-block';
+                document.getElementById('button-ef4c8f9e-1c76-40c7-a663-b30c69e7d1b4').style.display = 'none'
             "
         >
             Show Answer
@@ -300,13 +300,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the <b>total</b><i>square</i> loss of <span class="math">\(H\)</span> on this data set?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-95cc5e11-3ceb-42f2-9e82-311e488ab8ef" style="display: none">13.5</span>
-    <span id="button-95cc5e11-3ceb-42f2-9e82-311e488ab8ef">
+    <span id="answer-c3e1c43a-2b9b-4994-a7dd-695112155539" style="display: none">13.5</span>
+    <span id="button-c3e1c43a-2b9b-4994-a7dd-695112155539">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-95cc5e11-3ceb-42f2-9e82-311e488ab8ef').style.display = 'inline-block';
-                document.getElementById('button-95cc5e11-3ceb-42f2-9e82-311e488ab8ef').style.display = 'none'
+                document.getElementById('answer-c3e1c43a-2b9b-4994-a7dd-695112155539').style.display = 'inline-block';
+                document.getElementById('button-c3e1c43a-2b9b-4994-a7dd-695112155539').style.display = 'none'
             "
         >
             Show Answer
@@ -321,13 +321,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is the <b>total</b><i>perceptron</i> loss of <span class="math">\(H\)</span> on this data set?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-e4225af8-e86f-490d-aec4-c36bf6c44f14" style="display: none">1.5</span>
-    <span id="button-e4225af8-e86f-490d-aec4-c36bf6c44f14">
+    <span id="answer-23587366-0629-40ee-b4c6-4518ee88afaa" style="display: none">1.5</span>
+    <span id="button-23587366-0629-40ee-b4c6-4518ee88afaa">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-e4225af8-e86f-490d-aec4-c36bf6c44f14').style.display = 'inline-block';
-                document.getElementById('button-e4225af8-e86f-490d-aec4-c36bf6c44f14').style.display = 'none'
+                document.getElementById('answer-23587366-0629-40ee-b4c6-4518ee88afaa').style.display = 'inline-block';
+                document.getElementById('button-23587366-0629-40ee-b4c6-4518ee88afaa').style.display = 'none'
             "
         >
             Show Answer
@@ -342,13 +342,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>What is the <b>total</b><i>hinge</i> loss of <span class="math">\(H\)</span> on this data set?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-46a70218-08a1-4b41-a3c7-3b21762b3ab7" style="display: none">4</span>
-    <span id="button-46a70218-08a1-4b41-a3c7-3b21762b3ab7">
+    <span id="answer-bee99748-1cee-41c9-919e-4c77a7cee440" style="display: none">4</span>
+    <span id="button-bee99748-1cee-41c9-919e-4c77a7cee440">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-46a70218-08a1-4b41-a3c7-3b21762b3ab7').style.display = 'inline-block';
-                document.getElementById('button-46a70218-08a1-4b41-a3c7-3b21762b3ab7').style.display = 'none'
+                document.getElementById('answer-bee99748-1cee-41c9-919e-4c77a7cee440').style.display = 'inline-block';
+                document.getElementById('button-bee99748-1cee-41c9-919e-4c77a7cee440').style.display = 'none'
             "
         >
             Show Answer
diff --git a/practice/tags/covariance.html b/practice/tags/covariance.html
index 7dfefecf..f0f1d854 100644
--- a/practice/tags/covariance.html
+++ b/practice/tags/covariance.html
@@ -415,13 +415,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the (1,2) entry of the sample covariance matrix?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-16d57125-0e31-4d85-a1ab-2d02af4984ef" style="display: none">1</span>
-    <span id="button-16d57125-0e31-4d85-a1ab-2d02af4984ef">
+    <span id="answer-811eae43-ace2-4d25-9277-adddbb91eab9" style="display: none">1</span>
+    <span id="button-811eae43-ace2-4d25-9277-adddbb91eab9">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-16d57125-0e31-4d85-a1ab-2d02af4984ef').style.display = 'inline-block';
-                document.getElementById('button-16d57125-0e31-4d85-a1ab-2d02af4984ef').style.display = 'none'
+                document.getElementById('answer-811eae43-ace2-4d25-9277-adddbb91eab9').style.display = 'inline-block';
+                document.getElementById('button-811eae43-ace2-4d25-9277-adddbb91eab9').style.display = 'none'
             "
         >
             Show Answer
@@ -436,13 +436,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is the (2,2) entry of the sample covariance matrix?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-89d28255-fa27-4240-84d3-dac8567d4d6f" style="display: none">8/6</span>
-    <span id="button-89d28255-fa27-4240-84d3-dac8567d4d6f">
+    <span id="answer-90437a8c-bbfe-48dc-9cce-a1987482cee2" style="display: none">8/6</span>
+    <span id="button-90437a8c-bbfe-48dc-9cce-a1987482cee2">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-89d28255-fa27-4240-84d3-dac8567d4d6f').style.display = 'inline-block';
-                document.getElementById('button-89d28255-fa27-4240-84d3-dac8567d4d6f').style.display = 'none'
+                document.getElementById('answer-90437a8c-bbfe-48dc-9cce-a1987482cee2').style.display = 'inline-block';
+                document.getElementById('button-90437a8c-bbfe-48dc-9cce-a1987482cee2').style.display = 'none'
             "
         >
             Show Answer
@@ -508,13 +508,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the (1,3) entry of the sample covariance matrix?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-9deeb730-9504-499a-8000-e11557174890" style="display: none">9/4</span>
-    <span id="button-9deeb730-9504-499a-8000-e11557174890">
+    <span id="answer-4ffbc839-78ca-4888-a0d3-808163973ecc" style="display: none">9/4</span>
+    <span id="button-4ffbc839-78ca-4888-a0d3-808163973ecc">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-9deeb730-9504-499a-8000-e11557174890').style.display = 'inline-block';
-                document.getElementById('button-9deeb730-9504-499a-8000-e11557174890').style.display = 'none'
+                document.getElementById('answer-4ffbc839-78ca-4888-a0d3-808163973ecc').style.display = 'inline-block';
+                document.getElementById('button-4ffbc839-78ca-4888-a0d3-808163973ecc').style.display = 'none'
             "
         >
             Show Answer
@@ -529,13 +529,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is the (1,2) entry of the sample covariance matrix?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-fef5b8c1-4eb6-467e-9de5-c82bb681b5be" style="display: none">-3/4</span>
-    <span id="button-fef5b8c1-4eb6-467e-9de5-c82bb681b5be">
+    <span id="answer-f548b66e-f7d8-4684-bf9c-29a7021755e7" style="display: none">-3/4</span>
+    <span id="button-f548b66e-f7d8-4684-bf9c-29a7021755e7">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-fef5b8c1-4eb6-467e-9de5-c82bb681b5be').style.display = 'inline-block';
-                document.getElementById('button-fef5b8c1-4eb6-467e-9de5-c82bb681b5be').style.display = 'none'
+                document.getElementById('answer-f548b66e-f7d8-4684-bf9c-29a7021755e7').style.display = 'inline-block';
+                document.getElementById('button-f548b66e-f7d8-4684-bf9c-29a7021755e7').style.display = 'none'
             "
         >
             Show Answer
diff --git a/practice/tags/density estimation.html b/practice/tags/density estimation.html
index c2a4fae2..7fa39c36 100644
--- a/practice/tags/density estimation.html	
+++ b/practice/tags/density estimation.html	
@@ -124,13 +124,13 @@ <h2>Problem #036</h2>
 <p>What is the largest value that <span class="math">\(f(\vec x)\)</span> can possibly have?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-34face13-022f-4b0f-8ac5-6c4d97f6f3e0" style="display: none">1/6</span>
-    <span id="button-34face13-022f-4b0f-8ac5-6c4d97f6f3e0">
+    <span id="answer-2532f6a2-e1a3-4854-8fcd-b2d8baa0bd9c" style="display: none">1/6</span>
+    <span id="button-2532f6a2-e1a3-4854-8fcd-b2d8baa0bd9c">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-34face13-022f-4b0f-8ac5-6c4d97f6f3e0').style.display = 'inline-block';
-                document.getElementById('button-34face13-022f-4b0f-8ac5-6c4d97f6f3e0').style.display = 'none'
+                document.getElementById('answer-2532f6a2-e1a3-4854-8fcd-b2d8baa0bd9c').style.display = 'inline-block';
+                document.getElementById('button-2532f6a2-e1a3-4854-8fcd-b2d8baa0bd9c').style.display = 'none'
             "
         >
             Show Answer
diff --git a/practice/tags/feature maps.html b/practice/tags/feature maps.html
index efeb41c0..0a59448b 100644
--- a/practice/tags/feature maps.html	
+++ b/practice/tags/feature maps.html	
@@ -128,13 +128,13 @@ <h2>Problem #061</h2>
 <p>Let <span class="math">\(\vec x = (1, 2)^T\)</span>. What is <span class="math">\(H(\vec x)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-386b66bc-9c46-4e5a-9a57-71e9833854f1" style="display: none">3</span>
-    <span id="button-386b66bc-9c46-4e5a-9a57-71e9833854f1">
+    <span id="answer-cba90933-f146-4ab6-b336-104015470946" style="display: none">3</span>
+    <span id="button-cba90933-f146-4ab6-b336-104015470946">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-386b66bc-9c46-4e5a-9a57-71e9833854f1').style.display = 'inline-block';
-                document.getElementById('button-386b66bc-9c46-4e5a-9a57-71e9833854f1').style.display = 'none'
+                document.getElementById('answer-cba90933-f146-4ab6-b336-104015470946').style.display = 'inline-block';
+                document.getElementById('button-cba90933-f146-4ab6-b336-104015470946').style.display = 'none'
             "
         >
             Show Answer
@@ -174,13 +174,13 @@ <h2>Problem #079</h2>
 <p>Let <span class="math">\(\vec x = (1, 2, 1)^T\)</span>. What is <span class="math">\(H(\vec x)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-9094cb28-2dd1-4bb0-a84c-ae539ab29940" style="display: none"><span class="math">\(-3\)</span></span>
-    <span id="button-9094cb28-2dd1-4bb0-a84c-ae539ab29940">
+    <span id="answer-1ce45f98-c56b-4cde-887a-8285a01bba73" style="display: none"><span class="math">\(-3\)</span></span>
+    <span id="button-1ce45f98-c56b-4cde-887a-8285a01bba73">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-9094cb28-2dd1-4bb0-a84c-ae539ab29940').style.display = 'inline-block';
-                document.getElementById('button-9094cb28-2dd1-4bb0-a84c-ae539ab29940').style.display = 'none'
+                document.getElementById('answer-1ce45f98-c56b-4cde-887a-8285a01bba73').style.display = 'inline-block';
+                document.getElementById('button-1ce45f98-c56b-4cde-887a-8285a01bba73').style.display = 'none'
             "
         >
             Show Answer
diff --git a/practice/tags/gradient descent.html b/practice/tags/gradient descent.html
index 5e582c9f..4f564a52 100644
--- a/practice/tags/gradient descent.html	
+++ b/practice/tags/gradient descent.html	
@@ -176,13 +176,13 @@ <h2>Problem #068</h2>
 <p>Suppose that the initial weight vector is <span class="math">\(\vec w = (0, 0)^T\)</span> and that the learning rate <span class="math">\(\eta = 1\)</span>. What will be the weight vector after one iteration of subgradient descent?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-5c744ec0-5a37-4e49-8aa4-ccf075374de6" style="display: none"><span class="math">\((1, 2)^T\)</span></span>
-    <span id="button-5c744ec0-5a37-4e49-8aa4-ccf075374de6">
+    <span id="answer-5e82383e-3216-404c-92f0-cdaaf9ac999d" style="display: none"><span class="math">\((1, 2)^T\)</span></span>
+    <span id="button-5e82383e-3216-404c-92f0-cdaaf9ac999d">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-5c744ec0-5a37-4e49-8aa4-ccf075374de6').style.display = 'inline-block';
-                document.getElementById('button-5c744ec0-5a37-4e49-8aa4-ccf075374de6').style.display = 'none'
+                document.getElementById('answer-5e82383e-3216-404c-92f0-cdaaf9ac999d').style.display = 'inline-block';
+                document.getElementById('button-5e82383e-3216-404c-92f0-cdaaf9ac999d').style.display = 'none'
             "
         >
             Show Answer
@@ -228,13 +228,13 @@ <h2>Problem #085</h2>
 <p>Suppose that the initial weight vector is <span class="math">\(\vec w = (0, 0)^T\)</span> and that the learning rate is <span class="math">\(\eta = 1\)</span>. What will be the weight vector after one iteration of subgradient descent?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-2650589b-6f6d-448c-afb5-97d2acf6e96f" style="display: none"><span class="math">\((1, 3)^T\)</span></span>
-    <span id="button-2650589b-6f6d-448c-afb5-97d2acf6e96f">
+    <span id="answer-42d28be0-d2e2-4d4f-8c2e-bfc75765b1c8" style="display: none"><span class="math">\((1, 3)^T\)</span></span>
+    <span id="button-42d28be0-d2e2-4d4f-8c2e-bfc75765b1c8">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-2650589b-6f6d-448c-afb5-97d2acf6e96f').style.display = 'inline-block';
-                document.getElementById('button-2650589b-6f6d-448c-afb5-97d2acf6e96f').style.display = 'none'
+                document.getElementById('answer-42d28be0-d2e2-4d4f-8c2e-bfc75765b1c8').style.display = 'inline-block';
+                document.getElementById('button-42d28be0-d2e2-4d4f-8c2e-bfc75765b1c8').style.display = 'none'
             "
         >
             Show Answer
diff --git a/practice/tags/gradients.html b/practice/tags/gradients.html
index 546779d4..cf68e03c 100644
--- a/practice/tags/gradients.html
+++ b/practice/tags/gradients.html
@@ -201,13 +201,13 @@ <h2>Problem #074</h2>
 <p>What is <span class="math">\(\frac{d}{d \vec w} f(\vec w)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-16ec0901-6cd4-4680-8121-ced103b17afa" style="display: none"><span class="math">\(\sum_{i=1}^n \nvec{x}{i} + 2 \vec w\)</span></span>
-    <span id="button-16ec0901-6cd4-4680-8121-ced103b17afa">
+    <span id="answer-56150042-91d6-498a-b713-03c031adc669" style="display: none"><span class="math">\(\sum_{i=1}^n \nvec{x}{i} + 2 \vec w\)</span></span>
+    <span id="button-56150042-91d6-498a-b713-03c031adc669">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-16ec0901-6cd4-4680-8121-ced103b17afa').style.display = 'inline-block';
-                document.getElementById('button-16ec0901-6cd4-4680-8121-ced103b17afa').style.display = 'none'
+                document.getElementById('answer-56150042-91d6-498a-b713-03c031adc669').style.display = 'inline-block';
+                document.getElementById('button-56150042-91d6-498a-b713-03c031adc669').style.display = 'none'
             "
         >
             Show Answer
@@ -279,13 +279,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the gradient of this function at the point <span class="math">\((1, 1)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-c275c304-be5a-4e3a-b1f5-2af98d8d93c3" style="display: none"><span class="math">\((-1,3)^T\)</span></span>
-    <span id="button-c275c304-be5a-4e3a-b1f5-2af98d8d93c3">
+    <span id="answer-83a11de7-7de9-4d5c-8f28-872ce487fd6d" style="display: none"><span class="math">\((-1,3)^T\)</span></span>
+    <span id="button-83a11de7-7de9-4d5c-8f28-872ce487fd6d">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-c275c304-be5a-4e3a-b1f5-2af98d8d93c3').style.display = 'inline-block';
-                document.getElementById('button-c275c304-be5a-4e3a-b1f5-2af98d8d93c3').style.display = 'none'
+                document.getElementById('answer-83a11de7-7de9-4d5c-8f28-872ce487fd6d').style.display = 'inline-block';
+                document.getElementById('button-83a11de7-7de9-4d5c-8f28-872ce487fd6d').style.display = 'none'
             "
         >
             Show Answer
@@ -300,13 +300,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is the gradient of this function at the point <span class="math">\((-1, -1)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-8b10aff3-61e9-485b-a987-c6b6d9ef8a65" style="display: none"><span class="math">\((-2,0)^T\)</span></span>
-    <span id="button-8b10aff3-61e9-485b-a987-c6b6d9ef8a65">
+    <span id="answer-f1a9a918-4c99-4700-98c7-d265eed5c825" style="display: none"><span class="math">\((-2,0)^T\)</span></span>
+    <span id="button-f1a9a918-4c99-4700-98c7-d265eed5c825">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-8b10aff3-61e9-485b-a987-c6b6d9ef8a65').style.display = 'inline-block';
-                document.getElementById('button-8b10aff3-61e9-485b-a987-c6b6d9ef8a65').style.display = 'none'
+                document.getElementById('answer-f1a9a918-4c99-4700-98c7-d265eed5c825').style.display = 'inline-block';
+                document.getElementById('button-f1a9a918-4c99-4700-98c7-d265eed5c825').style.display = 'none'
             "
         >
             Show Answer
@@ -394,13 +394,13 @@ <h2>Problem #090</h2>
 <p>What is <span class="math">\(\frac{d}{d \vec x} f(\vec x)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-e60fe3fa-48c5-40ab-b25d-20c82fe4e842" style="display: none"><span class="math">\(2 A \vec x + \vec b\)</span></span>
-    <span id="button-e60fe3fa-48c5-40ab-b25d-20c82fe4e842">
+    <span id="answer-91cca2f2-b4df-46f1-8626-7e11172f5bf4" style="display: none"><span class="math">\(2 A \vec x + \vec b\)</span></span>
+    <span id="button-91cca2f2-b4df-46f1-8626-7e11172f5bf4">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-e60fe3fa-48c5-40ab-b25d-20c82fe4e842').style.display = 'inline-block';
-                document.getElementById('button-e60fe3fa-48c5-40ab-b25d-20c82fe4e842').style.display = 'none'
+                document.getElementById('answer-91cca2f2-b4df-46f1-8626-7e11172f5bf4').style.display = 'inline-block';
+                document.getElementById('button-91cca2f2-b4df-46f1-8626-7e11172f5bf4').style.display = 'none'
             "
         >
             Show Answer
diff --git a/practice/tags/histogram estimators.html b/practice/tags/histogram estimators.html
index 6547f227..3ab573c7 100644
--- a/practice/tags/histogram estimators.html	
+++ b/practice/tags/histogram estimators.html	
@@ -128,13 +128,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is <span class="math">\(f(1.5)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-7825d6cd-51c9-4604-9519-748bba2d3933" style="display: none">0.2</span>
-    <span id="button-7825d6cd-51c9-4604-9519-748bba2d3933">
+    <span id="answer-5ba491a4-a87a-457d-b476-c9c86692f95e" style="display: none">0.2</span>
+    <span id="button-5ba491a4-a87a-457d-b476-c9c86692f95e">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-7825d6cd-51c9-4604-9519-748bba2d3933').style.display = 'inline-block';
-                document.getElementById('button-7825d6cd-51c9-4604-9519-748bba2d3933').style.display = 'none'
+                document.getElementById('answer-5ba491a4-a87a-457d-b476-c9c86692f95e').style.display = 'inline-block';
+                document.getElementById('button-5ba491a4-a87a-457d-b476-c9c86692f95e').style.display = 'none'
             "
         >
             Show Answer
@@ -149,13 +149,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is <span class="math">\(f(7)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-286858bc-53b4-4e12-9e2f-ddb31072916a" style="display: none">.05</span>
-    <span id="button-286858bc-53b4-4e12-9e2f-ddb31072916a">
+    <span id="answer-f2d328b8-93a6-433f-8f56-385f971fd8b7" style="display: none">.05</span>
+    <span id="button-f2d328b8-93a6-433f-8f56-385f971fd8b7">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-286858bc-53b4-4e12-9e2f-ddb31072916a').style.display = 'inline-block';
-                document.getElementById('button-286858bc-53b4-4e12-9e2f-ddb31072916a').style.display = 'none'
+                document.getElementById('answer-f2d328b8-93a6-433f-8f56-385f971fd8b7').style.display = 'inline-block';
+                document.getElementById('button-f2d328b8-93a6-433f-8f56-385f971fd8b7').style.display = 'none'
             "
         >
             Show Answer
@@ -206,13 +206,13 @@ <h2>Problem #036</h2>
 <p>What is the largest value that <span class="math">\(f(\vec x)\)</span> can possibly have?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-15a8182d-47ea-4af8-969a-f7432fd0acce" style="display: none">1/6</span>
-    <span id="button-15a8182d-47ea-4af8-969a-f7432fd0acce">
+    <span id="answer-0521f914-a82b-49f8-bfc0-41c35fa2db61" style="display: none">1/6</span>
+    <span id="button-0521f914-a82b-49f8-bfc0-41c35fa2db61">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-15a8182d-47ea-4af8-969a-f7432fd0acce').style.display = 'inline-block';
-                document.getElementById('button-15a8182d-47ea-4af8-969a-f7432fd0acce').style.display = 'none'
+                document.getElementById('answer-0521f914-a82b-49f8-bfc0-41c35fa2db61').style.display = 'inline-block';
+                document.getElementById('button-0521f914-a82b-49f8-bfc0-41c35fa2db61').style.display = 'none'
             "
         >
             Show Answer
@@ -262,13 +262,13 @@ <h2>Problem #049</h2>
 <p>The density estimate within a particular bin of the histogram is 0.1. How many data points from <span class="math">\(\mathcal D\)</span> fall within that histogram bin?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-7017b6d3-7cb4-41ac-9fd5-1b5bf74d62b9" style="display: none">80</span>
-    <span id="button-7017b6d3-7cb4-41ac-9fd5-1b5bf74d62b9">
+    <span id="answer-6e8c5871-91e1-48a7-bf14-839bac30e172" style="display: none">80</span>
+    <span id="button-6e8c5871-91e1-48a7-bf14-839bac30e172">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-7017b6d3-7cb4-41ac-9fd5-1b5bf74d62b9').style.display = 'inline-block';
-                document.getElementById('button-7017b6d3-7cb4-41ac-9fd5-1b5bf74d62b9').style.display = 'none'
+                document.getElementById('answer-6e8c5871-91e1-48a7-bf14-839bac30e172').style.display = 'inline-block';
+                document.getElementById('button-6e8c5871-91e1-48a7-bf14-839bac30e172').style.display = 'none'
             "
         >
             Show Answer
@@ -298,13 +298,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the estimate of the Class 0 density at <span class="math">\(x = 3.5\)</span>? That is, what is the estimate for <span class="math">\(p(3.5 \given Y = 0)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-486241b2-8e03-4738-ad88-cf65e3b7c113" style="display: none">0.1</span>
-    <span id="button-486241b2-8e03-4738-ad88-cf65e3b7c113">
+    <span id="answer-593cde20-a07d-41ab-8448-481db5e58b41" style="display: none">0.1</span>
+    <span id="button-593cde20-a07d-41ab-8448-481db5e58b41">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-486241b2-8e03-4738-ad88-cf65e3b7c113').style.display = 'inline-block';
-                document.getElementById('button-486241b2-8e03-4738-ad88-cf65e3b7c113').style.display = 'none'
+                document.getElementById('answer-593cde20-a07d-41ab-8448-481db5e58b41').style.display = 'inline-block';
+                document.getElementById('button-593cde20-a07d-41ab-8448-481db5e58b41').style.display = 'none'
             "
         >
             Show Answer
@@ -319,13 +319,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>Using the same histogram estimator, what is the estimate of <span class="math">\(\pr(Y = 1 \given x = 3.5)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-629481ea-624a-45a7-a161-a0bd630e969f" style="display: none">0.5</span>
-    <span id="button-629481ea-624a-45a7-a161-a0bd630e969f">
+    <span id="answer-3f80a306-71eb-48cb-958a-44d7d0bd9c71" style="display: none">0.5</span>
+    <span id="button-3f80a306-71eb-48cb-958a-44d7d0bd9c71">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-629481ea-624a-45a7-a161-a0bd630e969f').style.display = 'inline-block';
-                document.getElementById('button-629481ea-624a-45a7-a161-a0bd630e969f').style.display = 'none'
+                document.getElementById('answer-3f80a306-71eb-48cb-958a-44d7d0bd9c71').style.display = 'inline-block';
+                document.getElementById('button-3f80a306-71eb-48cb-958a-44d7d0bd9c71').style.display = 'none'
             "
         >
             Show Answer
@@ -389,13 +389,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the estimate of the Class 0 density at <span class="math">\(x = 0.6\)</span>? That is, what is the estimate <span class="math">\(\hat p(0.6 \given Y = 0)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-276dd4fc-98b4-4b5d-b155-bba2cb3ee095" style="display: none">5/3</span>
-    <span id="button-276dd4fc-98b4-4b5d-b155-bba2cb3ee095">
+    <span id="answer-f80ec8a8-3f1a-4473-b609-3563d4d270f4" style="display: none">5/3</span>
+    <span id="button-f80ec8a8-3f1a-4473-b609-3563d4d270f4">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-276dd4fc-98b4-4b5d-b155-bba2cb3ee095').style.display = 'inline-block';
-                document.getElementById('button-276dd4fc-98b4-4b5d-b155-bba2cb3ee095').style.display = 'none'
+                document.getElementById('answer-f80ec8a8-3f1a-4473-b609-3563d4d270f4').style.display = 'inline-block';
+                document.getElementById('button-f80ec8a8-3f1a-4473-b609-3563d4d270f4').style.display = 'none'
             "
         >
             Show Answer
@@ -410,13 +410,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>Using the same histogram estimator, what is the estimate <span class="math">\(\hat\pr(Y = 1 \given x = 0.35)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-28d3aad9-9f40-486c-afd8-28ee38ee9c70" style="display: none">3/5 = 0.6</span>
-    <span id="button-28d3aad9-9f40-486c-afd8-28ee38ee9c70">
+    <span id="answer-d47e3fa5-51d3-4033-9c7f-bf2830562027" style="display: none">3/5 = 0.6</span>
+    <span id="button-d47e3fa5-51d3-4033-9c7f-bf2830562027">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-28d3aad9-9f40-486c-afd8-28ee38ee9c70').style.display = 'inline-block';
-                document.getElementById('button-28d3aad9-9f40-486c-afd8-28ee38ee9c70').style.display = 'none'
+                document.getElementById('answer-d47e3fa5-51d3-4033-9c7f-bf2830562027').style.display = 'inline-block';
+                document.getElementById('button-d47e3fa5-51d3-4033-9c7f-bf2830562027').style.display = 'none'
             "
         >
             Show Answer
@@ -431,13 +431,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>What is the estimate of the marginal density of <span class="math">\(x\)</span> at <span class="math">\(x = 0.1\)</span>? That is, what is <span class="math">\(\hat p(0.1)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-bb2cc1f3-c298-4e66-bdc0-21476e0ae87f" style="display: none">7/(19*0.25) = 1.47</span>
-    <span id="button-bb2cc1f3-c298-4e66-bdc0-21476e0ae87f">
+    <span id="answer-26e27b13-9716-452f-81c8-01f41e2a0230" style="display: none">7/(19*0.25) = 1.47</span>
+    <span id="button-26e27b13-9716-452f-81c8-01f41e2a0230">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-bb2cc1f3-c298-4e66-bdc0-21476e0ae87f').style.display = 'inline-block';
-                document.getElementById('button-bb2cc1f3-c298-4e66-bdc0-21476e0ae87f').style.display = 'none'
+                document.getElementById('answer-26e27b13-9716-452f-81c8-01f41e2a0230').style.display = 'inline-block';
+                document.getElementById('button-26e27b13-9716-452f-81c8-01f41e2a0230').style.display = 'none'
             "
         >
             Show Answer
@@ -454,13 +454,13 @@ <h3 class="subproblem-id">Part 4)</h3>
             \]</div>
 <p>
 <span class="inline-response-box">
-    <span id="answer-691af1aa-4fb0-4047-8b38-f2aa560fdc95" style="display: none">1</span>
-    <span id="button-691af1aa-4fb0-4047-8b38-f2aa560fdc95">
+    <span id="answer-1287d1e8-3f86-47e2-9858-16f11927599c" style="display: none">1</span>
+    <span id="button-1287d1e8-3f86-47e2-9858-16f11927599c">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-691af1aa-4fb0-4047-8b38-f2aa560fdc95').style.display = 'inline-block';
-                document.getElementById('button-691af1aa-4fb0-4047-8b38-f2aa560fdc95').style.display = 'none'
+                document.getElementById('answer-1287d1e8-3f86-47e2-9858-16f11927599c').style.display = 'inline-block';
+                document.getElementById('button-1287d1e8-3f86-47e2-9858-16f11927599c').style.display = 'none'
             "
         >
             Show Answer
@@ -489,13 +489,13 @@ <h2>Problem #119</h2>
 <p>If these estimates are used in place of the true class-conditional densities in the Bayes classifier, what will be the training error of the classifier? That is, what percentage of the data above will be misclassified? You may leave your answer as a fraction or a decimal.</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-35d2a982-4a99-450a-a41b-64e70de3c0af" style="display: none">4/14 = .2857</span>
-    <span id="button-35d2a982-4a99-450a-a41b-64e70de3c0af">
+    <span id="answer-c43724ee-bd9d-46b7-8d71-ec1f9b821738" style="display: none">4/14 = .2857</span>
+    <span id="button-c43724ee-bd9d-46b7-8d71-ec1f9b821738">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-35d2a982-4a99-450a-a41b-64e70de3c0af').style.display = 'inline-block';
-                document.getElementById('button-35d2a982-4a99-450a-a41b-64e70de3c0af').style.display = 'none'
+                document.getElementById('answer-c43724ee-bd9d-46b7-8d71-ec1f9b821738').style.display = 'inline-block';
+                document.getElementById('button-c43724ee-bd9d-46b7-8d71-ec1f9b821738').style.display = 'none'
             "
         >
             Show Answer
diff --git a/practice/tags/kernel ridge regression.html b/practice/tags/kernel ridge regression.html
index 6a98997a..b75eb4bc 100644
--- a/practice/tags/kernel ridge regression.html	
+++ b/practice/tags/kernel ridge regression.html	
@@ -169,13 +169,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the (2,3) entry of the kernel matrix?</p>
 <p><span class="math">\(K_{23} = \)</span>
 <span class="inline-response-box">
-    <span id="answer-26db91ab-fa30-4d99-9fd2-e2684eb6cd1f" style="display: none">1</span>
-    <span id="button-26db91ab-fa30-4d99-9fd2-e2684eb6cd1f">
+    <span id="answer-e024042d-15cc-4a05-8470-75b7901b79da" style="display: none">1</span>
+    <span id="button-e024042d-15cc-4a05-8470-75b7901b79da">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-26db91ab-fa30-4d99-9fd2-e2684eb6cd1f').style.display = 'inline-block';
-                document.getElementById('button-26db91ab-fa30-4d99-9fd2-e2684eb6cd1f').style.display = 'none'
+                document.getElementById('answer-e024042d-15cc-4a05-8470-75b7901b79da').style.display = 'inline-block';
+                document.getElementById('button-e024042d-15cc-4a05-8470-75b7901b79da').style.display = 'none'
             "
         >
             Show Answer
@@ -190,13 +190,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>Let <span class="math">\(\vec x = (1, 1, 0)^T\)</span> be a new point. What is <span class="math">\(H(\vec x)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-2bd54b44-bc46-4b8d-806f-d45ffe0bfefe" style="display: none">14</span>
-    <span id="button-2bd54b44-bc46-4b8d-806f-d45ffe0bfefe">
+    <span id="answer-cc5b9979-8b07-4d2b-a6f4-e053e705ad50" style="display: none">14</span>
+    <span id="button-cc5b9979-8b07-4d2b-a6f4-e053e705ad50">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-2bd54b44-bc46-4b8d-806f-d45ffe0bfefe').style.display = 'inline-block';
-                document.getElementById('button-2bd54b44-bc46-4b8d-806f-d45ffe0bfefe').style.display = 'none'
+                document.getElementById('answer-cc5b9979-8b07-4d2b-a6f4-e053e705ad50').style.display = 'inline-block';
+                document.getElementById('button-cc5b9979-8b07-4d2b-a6f4-e053e705ad50').style.display = 'none'
             "
         >
             Show Answer
@@ -247,13 +247,13 @@ <h2>Problem #095</h2>
 <p>Consider a new point <span class="math">\(\vec x = (1, 1, 1)\)</span>. What is <span class="math">\(H(\vec x)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-8d465591-63d5-4f05-838f-137f0339ee8d" style="display: none">50</span>
-    <span id="button-8d465591-63d5-4f05-838f-137f0339ee8d">
+    <span id="answer-84fcf8c6-e029-453e-926d-7fdc1aae3f6d" style="display: none">50</span>
+    <span id="button-84fcf8c6-e029-453e-926d-7fdc1aae3f6d">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-8d465591-63d5-4f05-838f-137f0339ee8d').style.display = 'inline-block';
-                document.getElementById('button-8d465591-63d5-4f05-838f-137f0339ee8d').style.display = 'none'
+                document.getElementById('answer-84fcf8c6-e029-453e-926d-7fdc1aae3f6d').style.display = 'inline-block';
+                document.getElementById('button-84fcf8c6-e029-453e-926d-7fdc1aae3f6d').style.display = 'none'
             "
         >
             Show Answer
@@ -311,13 +311,13 @@ <h2>Problem #112</h2>
 <p>Consider a new point <span class="math">\(\vec x = (2, 0, 1)^T\)</span>. What is <span class="math">\(H(\vec x)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-9df05bc7-0a61-4f92-a6c2-fff51667b4cf" style="display: none">37</span>
-    <span id="button-9df05bc7-0a61-4f92-a6c2-fff51667b4cf">
+    <span id="answer-aaab1aef-43b7-43ee-8c46-c13fb5078916" style="display: none">37</span>
+    <span id="button-aaab1aef-43b7-43ee-8c46-c13fb5078916">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-9df05bc7-0a61-4f92-a6c2-fff51667b4cf').style.display = 'inline-block';
-                document.getElementById('button-9df05bc7-0a61-4f92-a6c2-fff51667b4cf').style.display = 'none'
+                document.getElementById('answer-aaab1aef-43b7-43ee-8c46-c13fb5078916').style.display = 'inline-block';
+                document.getElementById('button-aaab1aef-43b7-43ee-8c46-c13fb5078916').style.display = 'none'
             "
         >
             Show Answer
diff --git a/practice/tags/least squares.html b/practice/tags/least squares.html
index e633be90..ec20f33e 100644
--- a/practice/tags/least squares.html	
+++ b/practice/tags/least squares.html	
@@ -266,13 +266,13 @@ <h2>Problem #080</h2>
 <p>What is the mean squared error of a least squares classifier trained on this data set (without regularization)? Your answer should be a number.</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-a3e45d12-4a0c-4e99-82c9-63b770f5b4df" style="display: none">0</span>
-    <span id="button-a3e45d12-4a0c-4e99-82c9-63b770f5b4df">
+    <span id="answer-f5024c2a-822f-49bf-aaa1-b66a77b24c7d" style="display: none">0</span>
+    <span id="button-f5024c2a-822f-49bf-aaa1-b66a77b24c7d">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-a3e45d12-4a0c-4e99-82c9-63b770f5b4df').style.display = 'inline-block';
-                document.getElementById('button-a3e45d12-4a0c-4e99-82c9-63b770f5b4df').style.display = 'none'
+                document.getElementById('answer-f5024c2a-822f-49bf-aaa1-b66a77b24c7d').style.display = 'inline-block';
+                document.getElementById('button-f5024c2a-822f-49bf-aaa1-b66a77b24c7d').style.display = 'none'
             "
         >
             Show Answer
diff --git a/practice/tags/linear prediction functions.html b/practice/tags/linear prediction functions.html
index b5f2fcfa..21702cb1 100644
--- a/practice/tags/linear prediction functions.html	
+++ b/practice/tags/linear prediction functions.html	
@@ -287,13 +287,13 @@ <h2>Problem #061</h2>
 <p>Let <span class="math">\(\vec x = (1, 2)^T\)</span>. What is <span class="math">\(H(\vec x)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-0dac0d25-d648-4aea-a32d-7bc8a2668561" style="display: none">3</span>
-    <span id="button-0dac0d25-d648-4aea-a32d-7bc8a2668561">
+    <span id="answer-6acdc6b7-1e9b-4b20-967b-8beb7b7b2aac" style="display: none">3</span>
+    <span id="button-6acdc6b7-1e9b-4b20-967b-8beb7b7b2aac">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-0dac0d25-d648-4aea-a32d-7bc8a2668561').style.display = 'inline-block';
-                document.getElementById('button-0dac0d25-d648-4aea-a32d-7bc8a2668561').style.display = 'none'
+                document.getElementById('answer-6acdc6b7-1e9b-4b20-967b-8beb7b7b2aac').style.display = 'inline-block';
+                document.getElementById('button-6acdc6b7-1e9b-4b20-967b-8beb7b7b2aac').style.display = 'none'
             "
         >
             Show Answer
@@ -332,13 +332,13 @@ <h2>Problem #063</h2>
 <p>What is the value of <span class="math">\(H\)</span> at the point <span class="math">\(\nvec{x}{4} = (0, 1)^T\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-4aac720e-adfc-47a7-bdee-ab36c49978aa" style="display: none">0</span>
-    <span id="button-4aac720e-adfc-47a7-bdee-ab36c49978aa">
+    <span id="answer-ec71fa4c-6d39-495e-b59e-56bacd29dd09" style="display: none">0</span>
+    <span id="button-ec71fa4c-6d39-495e-b59e-56bacd29dd09">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-4aac720e-adfc-47a7-bdee-ab36c49978aa').style.display = 'inline-block';
-                document.getElementById('button-4aac720e-adfc-47a7-bdee-ab36c49978aa').style.display = 'none'
+                document.getElementById('answer-ec71fa4c-6d39-495e-b59e-56bacd29dd09').style.display = 'inline-block';
+                document.getElementById('button-ec71fa4c-6d39-495e-b59e-56bacd29dd09').style.display = 'none'
             "
         >
             Show Answer
@@ -400,13 +400,13 @@ <h2>Problem #079</h2>
 <p>Let <span class="math">\(\vec x = (1, 2, 1)^T\)</span>. What is <span class="math">\(H(\vec x)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-4ed65675-881c-40a9-98d3-230bc72be43a" style="display: none"><span class="math">\(-3\)</span></span>
-    <span id="button-4ed65675-881c-40a9-98d3-230bc72be43a">
+    <span id="answer-2b63fd8c-dcd0-47a8-8796-65b31fd4558f" style="display: none"><span class="math">\(-3\)</span></span>
+    <span id="button-2b63fd8c-dcd0-47a8-8796-65b31fd4558f">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-4ed65675-881c-40a9-98d3-230bc72be43a').style.display = 'inline-block';
-                document.getElementById('button-4ed65675-881c-40a9-98d3-230bc72be43a').style.display = 'none'
+                document.getElementById('answer-2b63fd8c-dcd0-47a8-8796-65b31fd4558f').style.display = 'inline-block';
+                document.getElementById('button-2b63fd8c-dcd0-47a8-8796-65b31fd4558f').style.display = 'none'
             "
         >
             Show Answer
@@ -432,13 +432,13 @@ <h2>Problem #080</h2>
 <p>What is the mean squared error of a least squares classifier trained on this data set (without regularization)? Your answer should be a number.</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-d0b50fa6-c410-449b-880e-90981c00e505" style="display: none">0</span>
-    <span id="button-d0b50fa6-c410-449b-880e-90981c00e505">
+    <span id="answer-d7065e15-f48a-4dc6-92d7-e1419ddab872" style="display: none">0</span>
+    <span id="button-d7065e15-f48a-4dc6-92d7-e1419ddab872">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-d0b50fa6-c410-449b-880e-90981c00e505').style.display = 'inline-block';
-                document.getElementById('button-d0b50fa6-c410-449b-880e-90981c00e505').style.display = 'none'
+                document.getElementById('answer-d7065e15-f48a-4dc6-92d7-e1419ddab872').style.display = 'inline-block';
+                document.getElementById('button-d7065e15-f48a-4dc6-92d7-e1419ddab872').style.display = 'none'
             "
         >
             Show Answer
diff --git a/practice/tags/maximum likelihood.html b/practice/tags/maximum likelihood.html
index 485d887c..82f96ea6 100644
--- a/practice/tags/maximum likelihood.html	
+++ b/practice/tags/maximum likelihood.html	
@@ -166,13 +166,13 @@ <h2>Problem #040</h2>
 <p>Suppose a Gaussian with a diagonal covariance matrix is fit to 200 points in <span class="math">\(\mathbb R^4\)</span> using the maximum likelihood estimators. How many parameters are estimated? Count each entry of <span class="math">\(\mu\)</span> and the covariance matrix that must be estimated as its own parameter.</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-31c828d4-52ac-494d-840d-f473781f34ce" style="display: none">8</span>
-    <span id="button-31c828d4-52ac-494d-840d-f473781f34ce">
+    <span id="answer-1667b033-3749-4e7d-8c14-50f1a6b5fd88" style="display: none">8</span>
+    <span id="button-1667b033-3749-4e7d-8c14-50f1a6b5fd88">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-31c828d4-52ac-494d-840d-f473781f34ce').style.display = 'inline-block';
-                document.getElementById('button-31c828d4-52ac-494d-840d-f473781f34ce').style.display = 'none'
+                document.getElementById('answer-1667b033-3749-4e7d-8c14-50f1a6b5fd88').style.display = 'inline-block';
+                document.getElementById('button-1667b033-3749-4e7d-8c14-50f1a6b5fd88').style.display = 'none'
             "
         >
             Show Answer
@@ -214,13 +214,13 @@ <h2>Problem #053</h2>
 <p>Suppose a Gaussian with a diagonal covariance matrix is fit to 200 points in <span class="math">\(\mathbb R^4\)</span> using the maximum likelihood estimators. How many parameters are estimated? Count each entry of <span class="math">\(\vec\mu\)</span> and the covariance matrix that must be estimated as its own parameter (the off-diagonal elements of the covariance are zero, and shouldn't be included in your count).</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-9d8db5ee-9600-414c-9a2f-4bfeedd09e2d" style="display: none">8</span>
-    <span id="button-9d8db5ee-9600-414c-9a2f-4bfeedd09e2d">
+    <span id="answer-c9f0be63-f5dd-4d8f-8ba9-9b9f4febcc59" style="display: none">8</span>
+    <span id="button-c9f0be63-f5dd-4d8f-8ba9-9b9f4febcc59">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-9d8db5ee-9600-414c-9a2f-4bfeedd09e2d').style.display = 'inline-block';
-                document.getElementById('button-9d8db5ee-9600-414c-9a2f-4bfeedd09e2d').style.display = 'none'
+                document.getElementById('answer-c9f0be63-f5dd-4d8f-8ba9-9b9f4febcc59').style.display = 'inline-block';
+                document.getElementById('button-c9f0be63-f5dd-4d8f-8ba9-9b9f4febcc59').style.display = 'none'
             "
         >
             Show Answer
@@ -287,13 +287,13 @@ <h3 class="subproblem-id">Part 1)</h3>
             L(6, 5)\)</span>? Note that <span class="math">\(\mathcal L\)</span> is the likelihood, <i>not</i> the <i>log</i>-likelihood.</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-9642e426-ca17-4ef6-af8d-386d7db2e1bd" style="display: none"><span class="math">\(10^{-5}\)</span></span>
-    <span id="button-9642e426-ca17-4ef6-af8d-386d7db2e1bd">
+    <span id="answer-a7a955de-e1d7-4893-8baf-2bbfecee3298" style="display: none"><span class="math">\(10^{-5}\)</span></span>
+    <span id="button-a7a955de-e1d7-4893-8baf-2bbfecee3298">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-9642e426-ca17-4ef6-af8d-386d7db2e1bd').style.display = 'inline-block';
-                document.getElementById('button-9642e426-ca17-4ef6-af8d-386d7db2e1bd').style.display = 'none'
+                document.getElementById('answer-a7a955de-e1d7-4893-8baf-2bbfecee3298').style.display = 'inline-block';
+                document.getElementById('button-a7a955de-e1d7-4893-8baf-2bbfecee3298').style.display = 'none'
             "
         >
             Show Answer
@@ -308,13 +308,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is <span class="math">\(\mathcal L(3, 2)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-4f25119c-3751-4e1c-8844-bb87c05864ca" style="display: none">0</span>
-    <span id="button-4f25119c-3751-4e1c-8844-bb87c05864ca">
+    <span id="answer-3ce80c4e-defe-46cb-ad31-3a7a83c345c1" style="display: none">0</span>
+    <span id="button-3ce80c4e-defe-46cb-ad31-3a7a83c345c1">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-4f25119c-3751-4e1c-8844-bb87c05864ca').style.display = 'inline-block';
-                document.getElementById('button-4f25119c-3751-4e1c-8844-bb87c05864ca').style.display = 'none'
+                document.getElementById('answer-3ce80c4e-defe-46cb-ad31-3a7a83c345c1').style.display = 'inline-block';
+                document.getElementById('button-3ce80c4e-defe-46cb-ad31-3a7a83c345c1').style.display = 'none'
             "
         >
             Show Answer
@@ -329,13 +329,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>What are the maximum likelihood estimates of <span class="math">\(\alpha\)</span> and <span class="math">\(\beta\)</span>?</p>
 <p><span class="math">\(\alpha\)</span>: 
 <span class="inline-response-box">
-    <span id="answer-0e28a115-694a-4361-a0cd-4f5826e7d727" style="display: none">5</span>
-    <span id="button-0e28a115-694a-4361-a0cd-4f5826e7d727">
+    <span id="answer-0447965d-3fb8-4409-a007-ac68c6ed3b55" style="display: none">5</span>
+    <span id="button-0447965d-3fb8-4409-a007-ac68c6ed3b55">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-0e28a115-694a-4361-a0cd-4f5826e7d727').style.display = 'inline-block';
-                document.getElementById('button-0e28a115-694a-4361-a0cd-4f5826e7d727').style.display = 'none'
+                document.getElementById('answer-0447965d-3fb8-4409-a007-ac68c6ed3b55').style.display = 'inline-block';
+                document.getElementById('button-0447965d-3fb8-4409-a007-ac68c6ed3b55').style.display = 'none'
             "
         >
             Show Answer
@@ -344,13 +344,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 </span>
 <span class="math">\(\beta\)</span>: 
 <span class="inline-response-box">
-    <span id="answer-e256657f-97b5-4bf1-9425-8f60bf41e49c" style="display: none">4</span>
-    <span id="button-e256657f-97b5-4bf1-9425-8f60bf41e49c">
+    <span id="answer-6c2629d9-196f-4891-9772-caadd2035747" style="display: none">4</span>
+    <span id="button-6c2629d9-196f-4891-9772-caadd2035747">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-e256657f-97b5-4bf1-9425-8f60bf41e49c').style.display = 'inline-block';
-                document.getElementById('button-e256657f-97b5-4bf1-9425-8f60bf41e49c').style.display = 'none'
+                document.getElementById('answer-6c2629d9-196f-4891-9772-caadd2035747').style.display = 'inline-block';
+                document.getElementById('button-6c2629d9-196f-4891-9772-caadd2035747').style.display = 'none'
             "
         >
             Show Answer
@@ -393,13 +393,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the (1,2) entry of the sample covariance matrix?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-34e1616f-0755-4e36-a335-655a4130e429" style="display: none">1</span>
-    <span id="button-34e1616f-0755-4e36-a335-655a4130e429">
+    <span id="answer-d172b68e-4810-421a-bfd8-1992dad89b4d" style="display: none">1</span>
+    <span id="button-d172b68e-4810-421a-bfd8-1992dad89b4d">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-34e1616f-0755-4e36-a335-655a4130e429').style.display = 'inline-block';
-                document.getElementById('button-34e1616f-0755-4e36-a335-655a4130e429').style.display = 'none'
+                document.getElementById('answer-d172b68e-4810-421a-bfd8-1992dad89b4d').style.display = 'inline-block';
+                document.getElementById('button-d172b68e-4810-421a-bfd8-1992dad89b4d').style.display = 'none'
             "
         >
             Show Answer
@@ -414,13 +414,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is the (2,2) entry of the sample covariance matrix?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-dae0a093-5208-404f-98bb-ed5dece4340a" style="display: none">8/6</span>
-    <span id="button-dae0a093-5208-404f-98bb-ed5dece4340a">
+    <span id="answer-948e72b7-0e24-4be5-9a07-3b94cf5a1b0e" style="display: none">8/6</span>
+    <span id="button-948e72b7-0e24-4be5-9a07-3b94cf5a1b0e">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-dae0a093-5208-404f-98bb-ed5dece4340a').style.display = 'inline-block';
-                document.getElementById('button-dae0a093-5208-404f-98bb-ed5dece4340a').style.display = 'none'
+                document.getElementById('answer-948e72b7-0e24-4be5-9a07-3b94cf5a1b0e').style.display = 'inline-block';
+                document.getElementById('button-948e72b7-0e24-4be5-9a07-3b94cf5a1b0e').style.display = 'none'
             "
         >
             Show Answer
@@ -461,13 +461,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the (1,3) entry of the sample covariance matrix?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-3e65d1d4-4938-4652-a70d-d814e0d0db33" style="display: none">9/4</span>
-    <span id="button-3e65d1d4-4938-4652-a70d-d814e0d0db33">
+    <span id="answer-1087260d-a6de-4cc6-82d9-8071590e7534" style="display: none">9/4</span>
+    <span id="button-1087260d-a6de-4cc6-82d9-8071590e7534">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-3e65d1d4-4938-4652-a70d-d814e0d0db33').style.display = 'inline-block';
-                document.getElementById('button-3e65d1d4-4938-4652-a70d-d814e0d0db33').style.display = 'none'
+                document.getElementById('answer-1087260d-a6de-4cc6-82d9-8071590e7534').style.display = 'inline-block';
+                document.getElementById('button-1087260d-a6de-4cc6-82d9-8071590e7534').style.display = 'none'
             "
         >
             Show Answer
@@ -482,13 +482,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is the (1,2) entry of the sample covariance matrix?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-15dd24d9-d49f-41c5-a22b-d51dd2b8c77c" style="display: none">-3/4</span>
-    <span id="button-15dd24d9-d49f-41c5-a22b-d51dd2b8c77c">
+    <span id="answer-e022b4f6-5e91-4971-bec7-b40cf85b82f8" style="display: none">-3/4</span>
+    <span id="button-e022b4f6-5e91-4971-bec7-b40cf85b82f8">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-15dd24d9-d49f-41c5-a22b-d51dd2b8c77c').style.display = 'inline-block';
-                document.getElementById('button-15dd24d9-d49f-41c5-a22b-d51dd2b8c77c').style.display = 'none'
+                document.getElementById('answer-e022b4f6-5e91-4971-bec7-b40cf85b82f8').style.display = 'inline-block';
+                document.getElementById('button-e022b4f6-5e91-4971-bec7-b40cf85b82f8').style.display = 'none'
             "
         >
             Show Answer
diff --git a/practice/tags/maxium likelihood.html b/practice/tags/maxium likelihood.html
index c8862a45..f336d080 100644
--- a/practice/tags/maxium likelihood.html	
+++ b/practice/tags/maxium likelihood.html	
@@ -140,13 +140,13 @@ <h3 class="subproblem-id">Part 1)</h3>
             L(0, 2)\)</span>? Note that <span class="math">\(\mathcal L\)</span> is the likelihood, <i>not</i> the <i>log</i>-likelihood.</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-7d9935d9-0c5b-40a4-9bc0-9e2b66e1dd6e" style="display: none">0</span>
-    <span id="button-7d9935d9-0c5b-40a4-9bc0-9e2b66e1dd6e">
+    <span id="answer-f764c8a9-49d5-4c26-a90a-a332ccdc7f08" style="display: none">0</span>
+    <span id="button-f764c8a9-49d5-4c26-a90a-a332ccdc7f08">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-7d9935d9-0c5b-40a4-9bc0-9e2b66e1dd6e').style.display = 'inline-block';
-                document.getElementById('button-7d9935d9-0c5b-40a4-9bc0-9e2b66e1dd6e').style.display = 'none'
+                document.getElementById('answer-f764c8a9-49d5-4c26-a90a-a332ccdc7f08').style.display = 'inline-block';
+                document.getElementById('button-f764c8a9-49d5-4c26-a90a-a332ccdc7f08').style.display = 'none'
             "
         >
             Show Answer
@@ -161,13 +161,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>Let <span class="math">\(\mathcal X = \{0, 1, 2\}\)</span> be the same data set as in the previous part. What is <span class="math">\(\mathcal L(0, 4)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-166388f9-bc31-45a8-886c-64a425318631" style="display: none">3/64 = 0.0468</span>
-    <span id="button-166388f9-bc31-45a8-886c-64a425318631">
+    <span id="answer-caa6bd83-c17a-47bd-837f-880fe8b65a66" style="display: none">3/64 = 0.0468</span>
+    <span id="button-caa6bd83-c17a-47bd-837f-880fe8b65a66">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-166388f9-bc31-45a8-886c-64a425318631').style.display = 'inline-block';
-                document.getElementById('button-166388f9-bc31-45a8-886c-64a425318631').style.display = 'none'
+                document.getElementById('answer-caa6bd83-c17a-47bd-837f-880fe8b65a66').style.display = 'inline-block';
+                document.getElementById('button-caa6bd83-c17a-47bd-837f-880fe8b65a66').style.display = 'none'
             "
         >
             Show Answer
@@ -182,13 +182,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 <p>Now let <span class="math">\(\mathcal X = \{6, 7\}\)</span> be a new data set of just two points. What are the maximum likelihood estimates of <span class="math">\(\alpha\)</span> and <span class="math">\(\beta\)</span> with respect to this data? Remember, <span class="math">\(\beta > 0\)</span>.</p>
 <p><span class="math">\(\alpha\)</span>: 
 <span class="inline-response-box">
-    <span id="answer-59628e46-db5c-4c2c-b180-02e1cdaf7004" style="display: none">6</span>
-    <span id="button-59628e46-db5c-4c2c-b180-02e1cdaf7004">
+    <span id="answer-babb59e7-6783-4824-bede-5acb63038dcd" style="display: none">6</span>
+    <span id="button-babb59e7-6783-4824-bede-5acb63038dcd">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-59628e46-db5c-4c2c-b180-02e1cdaf7004').style.display = 'inline-block';
-                document.getElementById('button-59628e46-db5c-4c2c-b180-02e1cdaf7004').style.display = 'none'
+                document.getElementById('answer-babb59e7-6783-4824-bede-5acb63038dcd').style.display = 'inline-block';
+                document.getElementById('button-babb59e7-6783-4824-bede-5acb63038dcd').style.display = 'none'
             "
         >
             Show Answer
@@ -197,13 +197,13 @@ <h3 class="subproblem-id">Part 3)</h3>
 </span>
 <span class="math">\(\beta\)</span>: 
 <span class="inline-response-box">
-    <span id="answer-8544afe6-c8be-45ab-a28e-32ffff55440d" style="display: none">3</span>
-    <span id="button-8544afe6-c8be-45ab-a28e-32ffff55440d">
+    <span id="answer-9aa6efd9-77ad-4b01-8f36-e9f94cbd0991" style="display: none">3</span>
+    <span id="button-9aa6efd9-77ad-4b01-8f36-e9f94cbd0991">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-8544afe6-c8be-45ab-a28e-32ffff55440d').style.display = 'inline-block';
-                document.getElementById('button-8544afe6-c8be-45ab-a28e-32ffff55440d').style.display = 'none'
+                document.getElementById('answer-9aa6efd9-77ad-4b01-8f36-e9f94cbd0991').style.display = 'inline-block';
+                document.getElementById('button-9aa6efd9-77ad-4b01-8f36-e9f94cbd0991').style.display = 'none'
             "
         >
             Show Answer
diff --git a/practice/tags/naive bayes.html b/practice/tags/naive bayes.html
index f4856dbd..0af5c2af 100644
--- a/practice/tags/naive bayes.html	
+++ b/practice/tags/naive bayes.html	
@@ -147,13 +147,13 @@ <h2>Problem #045</h2>
 <p>If Gaussian Naive Bayes is trained on this data, how many univariate Gaussians will be fit?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-b92cdd07-736b-49bd-b7ac-4c387f9a9415" style="display: none">20</span>
-    <span id="button-b92cdd07-736b-49bd-b7ac-4c387f9a9415">
+    <span id="answer-39101f4d-d9fb-4e23-9d3e-3b3bbc3b4d64" style="display: none">20</span>
+    <span id="button-39101f4d-d9fb-4e23-9d3e-3b3bbc3b4d64">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-b92cdd07-736b-49bd-b7ac-4c387f9a9415').style.display = 'inline-block';
-                document.getElementById('button-b92cdd07-736b-49bd-b7ac-4c387f9a9415').style.display = 'none'
+                document.getElementById('answer-39101f4d-d9fb-4e23-9d3e-3b3bbc3b4d64').style.display = 'inline-block';
+                document.getElementById('button-39101f4d-d9fb-4e23-9d3e-3b3bbc3b4d64').style.display = 'none'
             "
         >
             Show Answer
diff --git a/practice/tags/subgradients.html b/practice/tags/subgradients.html
index 403f352b..41192bce 100644
--- a/practice/tags/subgradients.html
+++ b/practice/tags/subgradients.html
@@ -184,13 +184,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the gradient of this function at the point <span class="math">\((0, 0)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-83a1ebba-a675-4e1d-bad1-43dd881fffc5" style="display: none"><span class="math">\((2, 1)^T\)</span></span>
-    <span id="button-83a1ebba-a675-4e1d-bad1-43dd881fffc5">
+    <span id="answer-9d0643a4-bd28-4819-9aa9-72d7deba32c0" style="display: none"><span class="math">\((2, 1)^T\)</span></span>
+    <span id="button-9d0643a4-bd28-4819-9aa9-72d7deba32c0">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-83a1ebba-a675-4e1d-bad1-43dd881fffc5').style.display = 'inline-block';
-                document.getElementById('button-83a1ebba-a675-4e1d-bad1-43dd881fffc5').style.display = 'none'
+                document.getElementById('answer-9d0643a4-bd28-4819-9aa9-72d7deba32c0').style.display = 'inline-block';
+                document.getElementById('button-9d0643a4-bd28-4819-9aa9-72d7deba32c0').style.display = 'none'
             "
         >
             Show Answer
@@ -244,13 +244,13 @@ <h3 class="subproblem-id">Part 1)</h3>
 <p>What is the gradient of this function at the point <span class="math">\((1, 1)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-b8e6701b-e62d-4a59-93f3-69178261651a" style="display: none"><span class="math">\((-1,3)^T\)</span></span>
-    <span id="button-b8e6701b-e62d-4a59-93f3-69178261651a">
+    <span id="answer-a29fce48-a99e-48e8-bc4e-b32757eca9dc" style="display: none"><span class="math">\((-1,3)^T\)</span></span>
+    <span id="button-a29fce48-a99e-48e8-bc4e-b32757eca9dc">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-b8e6701b-e62d-4a59-93f3-69178261651a').style.display = 'inline-block';
-                document.getElementById('button-b8e6701b-e62d-4a59-93f3-69178261651a').style.display = 'none'
+                document.getElementById('answer-a29fce48-a99e-48e8-bc4e-b32757eca9dc').style.display = 'inline-block';
+                document.getElementById('button-a29fce48-a99e-48e8-bc4e-b32757eca9dc').style.display = 'none'
             "
         >
             Show Answer
@@ -265,13 +265,13 @@ <h3 class="subproblem-id">Part 2)</h3>
 <p>What is the gradient of this function at the point <span class="math">\((-1, -1)\)</span>?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-1a12365d-dca1-4c49-a236-f6299c7fb7d7" style="display: none"><span class="math">\((-2,0)^T\)</span></span>
-    <span id="button-1a12365d-dca1-4c49-a236-f6299c7fb7d7">
+    <span id="answer-8f427bdc-39be-4662-8287-ec5279577a2c" style="display: none"><span class="math">\((-2,0)^T\)</span></span>
+    <span id="button-8f427bdc-39be-4662-8287-ec5279577a2c">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-1a12365d-dca1-4c49-a236-f6299c7fb7d7').style.display = 'inline-block';
-                document.getElementById('button-1a12365d-dca1-4c49-a236-f6299c7fb7d7').style.display = 'none'
+                document.getElementById('answer-8f427bdc-39be-4662-8287-ec5279577a2c').style.display = 'inline-block';
+                document.getElementById('button-8f427bdc-39be-4662-8287-ec5279577a2c').style.display = 'none'
             "
         >
             Show Answer
@@ -336,13 +336,13 @@ <h2>Problem #085</h2>
 <p>Suppose that the initial weight vector is <span class="math">\(\vec w = (0, 0)^T\)</span> and that the learning rate is <span class="math">\(\eta = 1\)</span>. What will be the weight vector after one iteration of subgradient descent?</p>
 <p>
 <span class="inline-response-box">
-    <span id="answer-dda016dc-0e9b-4972-af87-394192cc123d" style="display: none"><span class="math">\((1, 3)^T\)</span></span>
-    <span id="button-dda016dc-0e9b-4972-af87-394192cc123d">
+    <span id="answer-1fc6956e-2b9a-49eb-8f44-301f1824f3a9" style="display: none"><span class="math">\((1, 3)^T\)</span></span>
+    <span id="button-1fc6956e-2b9a-49eb-8f44-301f1824f3a9">
         <button
             type="button"
             onclick="
-                document.getElementById('answer-dda016dc-0e9b-4972-af87-394192cc123d').style.display = 'inline-block';
-                document.getElementById('button-dda016dc-0e9b-4972-af87-394192cc123d').style.display = 'none'
+                document.getElementById('answer-1fc6956e-2b9a-49eb-8f44-301f1824f3a9').style.display = 'inline-block';
+                document.getElementById('button-1fc6956e-2b9a-49eb-8f44-301f1824f3a9').style.display = 'none'
             "
         >
             Show Answer