updates to lab 7 and HW 7

modules/lab7/lab7-1.ipynb

@@ -155,6 +155,8 @@
     "\n",
     "Take one step through the Markov chain. What fraction of people live in the city after one step?\n",
     "\n",
+    "This can be defined as the fraction of people who live in the city and stay in the city + the fraction of people who lived in the suburbs but move into the city.\n",
+    "\n",
     "$p_{city,1}$ = 0.95 * 0.6 + 0.03 * 0.4"
    ]
   },
@@ -182,6 +184,8 @@
    "source": [
     "What fraction of people live in the suburbs?\n",
     "\n",
+    "Similar to above, this is the fraction of people who lived in the city and moved to the suburbs plus the fraction of people who live in the suburbs and stay in the suburbs.\n",
+    "\n",
     "$p_{suburb,1}$ = 0.05 * 0.6 + 0.97 * 0.4"
    ]
   },
@@ -313,7 +317,7 @@
     }
    ],
    "source": [
-    "# three steps all at once by taking our Pmarkov matrix to the 3rd power, then multipying by our original populaiton percentage vector\n",
+    "# three steps all at once by taking our Pmarkov matrix to the 3rd power, then multipying by our original population percentage vector\n",
     "percent3 = np.dot(percent0, np.linalg.matrix_power(Pmarkov,3))\n",
     "print(percent3)\n",
     "\n",
@@ -543,7 +547,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 22,
    "metadata": {},
    "outputs": [
     {
@@ -560,7 +564,7 @@
    ],
    "source": [
     "# This counts the transitions from each state to the next and marks that count\n",
-    "S = sparse.csr_matrix((np.ones_like(data[:-1]), (data[:-1], data[1:])), dtype=np.float)\n",
+    "S = sparse.csr_matrix((np.ones_like(data[:-1]), (data[:-1], data[1:])), dtype=float)\n",
     "\n",
     "# This converts those counts to matrix form\n",
     "tm = S.todense()\n",
@@ -704,7 +708,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.4"
+   "version": "3.8.12"
   }
  },
  "nbformat": 4,