Galton board fix typo

Pico/Galton/.ipynb_checkpoints/Galton_Stats-checkpoint.ipynb

@@ -47379,7 +47379,7 @@
     "\n",
     "For a Gaussian, 68% of data (in our case, dropped balls) fall within one standard deviation of the mean. 95% fall within two standard deviations. And 99.7% fall within three standard deviations. The standard deviation of a 1600-row Galton Board is $\\sqrt{\\frac{1600}{4}} = 20$. So, 68% of balls will land in bins that are within 20 position from which the ball is dropped ($\\frac{2000}{2}=1000$).\n",
     "\n",
-    "So, the range of bins that will catch 68% of balls (slightly more), is 980-1020. We figured that out really fast! The central limit theorem allows for these sorts of shortcuts *if the conditions under which it is true are satisfied!* That is, all our random variables are independent, identically distributed, and have finite variance/expected value."
+    "The range of bins that will catch 68% of balls, is 980-1020. We figured that out really fast! The central limit theorem allows for these sorts of shortcuts *if the conditions under which it is true are satisfied!* That is, if all our random variables are independent, identically distributed, and have finite variance/expected value."
    ]
   },
   {

Pico/Galton/Galton_Stats.html

@@ -60476,7 +60476,7 @@ <h2 id="Convergence-to-Gaussian-by-Central-Limit-Theorem">Convergence to Gaussia
 <div class="text_cell_render border-box-sizing rendered_html">
 <h2 id="A-quick-example">A quick example<a class="anchor-link" href="#A-quick-example">&#182;</a></h2><p>Let's suppose that we have a 1600-row Galton Board. Which range of bins will catch 68% of the balls?</p>
 <p>For a Gaussian, 68% of data (in our case, dropped balls) fall within one standard deviation of the mean. 95% fall within two standard deviations. And 99.7% fall within three standard deviations. The standard deviation of a 1600-row Galton Board is $\sqrt{\frac{1600}{4}} = 20$. So, 68% of balls will land in bins that are within 20 position from which the ball is dropped ($\frac{2000}{2}=1000$).</p>
-<p>So, the range of bins that will catch 68% of balls (slightly more), is 980-1020. We figured that out really fast! The central limit theorem allows for these sorts of shortcuts <em>if the conditions under which it is true are satisfied!</em> That is, all our random variables are independent, identically distributed, and have finite variance/expected value.</p>
+<p>The range of bins that will catch 68% of balls, is 980-1020. We figured that out really fast! The central limit theorem allows for these sorts of shortcuts <em>if the conditions under which it is true are satisfied!</em> That is, if all our random variables are independent, identically distributed, and have finite variance/expected value.</p>
 
 </div>
 </div>

Pico/Galton/Galton_Stats.ipynb

@@ -47379,7 +47379,7 @@
     "\n",
     "For a Gaussian, 68% of data (in our case, dropped balls) fall within one standard deviation of the mean. 95% fall within two standard deviations. And 99.7% fall within three standard deviations. The standard deviation of a 1600-row Galton Board is $\\sqrt{\\frac{1600}{4}} = 20$. So, 68% of balls will land in bins that are within 20 position from which the ball is dropped ($\\frac{2000}{2}=1000$).\n",
     "\n",
-    "So, the range of bins that will catch 68% of balls (slightly more), is 980-1020. We figured that out really fast! The central limit theorem allows for these sorts of shortcuts *if the conditions under which it is true are satisfied!* That is, all our random variables are independent, identically distributed, and have finite variance/expected value."
+    "The range of bins that will catch 68% of balls, is 980-1020. We figured that out really fast! The central limit theorem allows for these sorts of shortcuts *if the conditions under which it is true are satisfied!* That is, if all our random variables are independent, identically distributed, and have finite variance/expected value."
    ]
   },
   {