Make small changes to Instructor NB1

Author: Hugo Bowne-Anderson

notebooks/01-Instructor-Probability_a_simulated_introduction.ipynb

@@ -9,7 +9,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -89,14 +89,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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yhrjPP//cWrFihWVZlnXo0CHr2Wef7b2vu7vbuu+++6yzZ89aXV1d1vz586329na3RnVM\nrD2fP3/euvfee63Ozk7Lsixr6dKl1u7du12Z0ymx9vuXLVu2WIWFhVZlZeVgjzcgYu05Go1aDz30\nkPXLL79YlmVZ9fX1VmtrqytzOinev/OsWbOsYDBodXV19f53bYKamhpr7ty51sKFC/9x+0D1a8if\nqce69EBra6syMjI0duxYJSUl6bbbbtP+/fvdGtUxsfaclJSkrVu3atSoUZKknp4eJScnuzKnU+Jd\nXuK7777TkSNHVFRU5MZ4AyLWnn/++WeNGzdOGzdu1GOPPaazZ88qMzPTrVEdE+/f+cYbb1QoFFJ3\nd7csy5LH43FjTMdlZGSourr6otsHql9DPuqXu/TAX/elpPz9a7Y+n08dHR2DPqPTYu05ISFB11xz\njSSptrZWnZ2dmjVrlitzOiXWfv/44w+98847Ki8vd2u8ARFrz8FgUIcOHdJjjz2mDz74QN988432\n7dvn1qiOibVnScrKytKCBQv0wAMPaM6cOUpNTXVjTMcVFBRc8jfrB6pfQz7qsS498P/vC4fD//gm\nDVfxLrcQjUa1du1aNTc3q7q6etif0cTa72effaZgMKjFixerpqZGu3bt0vbt290a1TGx9jxu3DhN\nmjRJU6ZM0YgRIzR79mwjLo4Xa8/Hjx/XF198oYaGBjU2NurMmTP69NNP3Rp1UAxUv4Z81GNdemDK\nlClqa2vT2bNn1d3drQMHDig7O9utUR0T73IL5eXl6urq0rp163pfhhnOYu338ccf1/bt21VbW6vF\nixdr7ty5mj9/vlujOibWnidOnKhwONz7g8QDBw4oKyvLlTmdFGvPKSkpGjlypJKTk5WYmKjx48fr\n3Llzbo06KAaqX0P+alv5+flqbm7WokWLei89sHPnTnV2dqqoqEilpaV6+umnZVmWFixYoOuuu87t\nkfst1p6nT5+ujz76SDk5OXriiSck/Td8+fn5Lk9tX7x/YxPF2/OqVau0bNkyWZal7OxszZkzx+2R\n+y3enouKiuT3+zVixAhlZGRo3rx5bo88IAa6X1wmAAAMMuRffgEA9B1RBwCDEHUAMAhRBwCDEHUA\nMAhRBwCDEHUAMMj/Aft2ydZaHWIRAAAAAElFTkSuQmCC\n",
+      "image/png": "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\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1133a8908>"
+       "<Figure size 432x288 with 1 Axes>"
       ]
      },
      "metadata": {},
@@ -118,24 +118,24 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'Number of clicks = 498'"
+       "'Number of clicks = 477'"
       ]
      },
-     "execution_count": 6,
+     "execution_count": 3,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "# Computed how many people click\n",
     "clicks = x <= 0.5\n",
-    "n_clicks = sum(pop)\n",
+    "n_clicks = sum(clicks)\n",
     "f\"Number of clicks = {n_clicks}\""
    ]
   },
@@ -148,16 +148,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'Proportion who clicked = 0.498'"
+       "'Proportion who clicked = 0.477'"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 4,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -207,15 +207,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Number of clicks = 688\n",
-      "Proportion who clicked = 0.688\n"
+      "Number of clicks = 676\n",
+      "Proportion who clicked = 0.676\n"
      ]
     }
    ],
@@ -367,7 +367,7 @@
     {
      "data": {
       "text/plain": [
-       "0.8508064516129032"
+       "0.8514056224899599"
       ]
      },
      "execution_count": 8,
@@ -404,7 +404,7 @@
     {
      "data": {
       "text/plain": [
-       "0.8519"
+       "0.852"
       ]
      },
      "execution_count": 9,
@@ -611,9 +611,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "**Note:** you may have noticed that the _binomial distribution_ can take on only  a finite number of values, whereas the _uniform distribution_ above can take on any number between $0$ and $1$. These are different enough cases to warrant special mention of this & two different names: the former is called a _probability mass function_ (PMF) and the latter a _probability distribution function_ (PDF). Time permitting, we may discuss some of the subtleties here. If not, all good texts will cover this. I like (Sivia & Skilling, 2006), among many others.\n",
-    "\n",
-    "**HBA: should this note ^ have come earlier?** "
+    "**Note:** you may have noticed that the _binomial distribution_ can take on only  a finite number of values, whereas the _uniform distribution_ above can take on any number between $0$ and $1$. These are different enough cases to warrant special mention of this & two different names: the former is called a _probability mass function_ (PMF) and the latter a _probability distribution function_ (PDF). Time permitting, we may discuss some of the subtleties here. If not, all good texts will cover this. I like (Sivia & Skilling, 2006), among many others.\n"
    ]
   },
   {
@@ -637,7 +635,9 @@
     "We have already encountered joint probabilities above, perhaps without knowing it: $P(A,B)$ is the probability two events $A$ and $B$ _both_ occurring.\n",
     "* For example, getting two heads in a row.\n",
     "\n",
-    "If $A$ and $B$ are independent, then $P(A,B)=P(A)P(B)$ but be warned: this is not always (or often) the case."
+    "If $A$ and $B$ are independent, then $P(A,B)=P(A)P(B)$ but be warned: this is not always (or often) the case.\n",
+    "\n",
+    "One way to think of this is considering \"AND\" as multiplication: the probability of A **and** B is the probability of A **multiplied** by the probability of B."
    ]
   },
   {
@@ -748,7 +748,7 @@
     {
      "data": {
       "text/plain": [
-       "0.7238716181061394"
+       "0.724891534007516"
       ]
      },
      "execution_count": 17,
@@ -778,7 +778,7 @@
     {
      "data": {
       "text/plain": [
-       "0.722899474"
+       "0.7238861042000001"
       ]
      },
      "execution_count": 18,
@@ -809,7 +809,7 @@
     {
      "data": {
       "text/plain": [
-       "0.72392"
+       "0.72493"
       ]
      },
      "execution_count": 19,
@@ -871,7 +871,7 @@
     {
      "data": {
       "text/plain": [
-       "0.8508064516129032"
+       "0.8514056224899599"
       ]
      },
      "execution_count": 20,
@@ -949,13 +949,6 @@
     "**Homework exercise for the avid learner:** verify the above relationship using simulation/resampling techniques in one of the cases above."
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "**TO-DO HBA: include Venn Diagram? Include mention earlier of probability AND being multiplication.**"
-   ]
-  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -1014,7 +1007,7 @@
     {
      "data": {
       "text/plain": [
-       "array([0.30026281])"
+       "array([0.32798931])"
       ]
      },
      "execution_count": 25,
@@ -1137,7 +1130,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.1"
+   "version": "3.6.6"
   }
  },
  "nbformat": 4,