Minor copy editing.

03-Gaussians.ipynb

@@ -30,6 +30,9 @@
        "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
        "@import url('http://fonts.googleapis.com/css?family=Fira_sans');\n",
        "\n",
+       ".CodeMirror pre {\n",
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+       "}\n",
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@@ -49,7 +52,7 @@
        "\t\n",
        "    div.input_area {\n",
        "        background: #F6F6F9;\n",
-       "        border: 1px solid #586e75;\n",
+       "        border: 1px solid #586e75;      \n",
        "    }\n",
        "\n",
        "    .text_cell_render h1 {\n",
@@ -108,6 +111,7 @@
        "    h5 {\n",
        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
        "    }\n",
+       "\n",
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        "        font-weight: 200;\n",
        "        font-style: normal;\n",
@@ -142,7 +146,8 @@
        "}\n",
        "\n",
        "    code{\n",
-       "      font-size: 70%;\n",
+       "        font-size: 6pt;\n",
+       "\n",
        "    }\n",
        "    .rendered_html code{\n",
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@@ -235,7 +240,8 @@
        "<script>\n",
        "    MathJax.Hub.Config({\n",
        "                        TeX: {\n",
-       "                           extensions: [\"AMSmath.js\", \"autobold.js\"]\n",
+       "                           extensions: [\"AMSmath.js\"],\n",
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@@ -243,7 +249,7 @@
        "                },\n",
        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
        "                \"HTML-CSS\": {\n",
-       "                    scale:100,\n",
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@@ -294,15 +300,19 @@
     "### Random Variables\n",
     "\n",
     "\n",
-    "If we roll a die we can get a value between 1 and 6. Each possible value has a probability of occuring attached to it: 1/6 for a fair die. This combination of values and associated probabilities is called a *random variable*, and the range of values is called the *sample space* These names are based on the idea that we will be randomly sampling from a population. If we rolled a fair die many times we'd expect the value 4 to occur 1/6 of the time. 'Random' does not mean the process is random - rolling a die is entirely deterministic. However, prior to the roll we cannot predict the outcome except in a probablistic manner.\n",
+    "Each time you roll a die the *outcome* will be between 1 and 6. If we rolled a fair die a million times we'd expect to get 1 1/6 of the time. Thus we say the *probability*, or *odds* of the outcome 1 is 1/6. Likewise, if I asked you the chance of 1 being the result of the next roll you'd reply 1/6.  \n",
     "\n",
-    "Another example of a random variable is the heights of students in a university. Here the sample space is a range of values in the real numbers between two limits defined by biology. This is random in the sense that we can randomly select students from random classes; the height of a student is determined by genetics, nutrition, age, and other factors.\n",
+    "This combination of values and associated probabilities is called a *random variable*. *Random* does not mean the process is nondeterministic, only that we lack information. The result of a die toss is deterministic, but we lack enough information to compute the result. We don't know what will happen, except probabilistically.\n",
     "\n",
-    "Random variables such as coin tosses and die rolls are *discrete random variables*. By this we mean their sample space is represented by either a finite number of values or a countably infinite number of values (such as the natural numbers). Heights of humans are called *continuous random variables* since they can take on any real value between two limits.\n",
+    "While we are defining things, the range of values is called the *sample space*. For a die the sample space is {1, 2, 3, 4, 5, 6}. For a coin the sample space is {H, T}. *Space* is a mathematical term which means a set with structure. The sample space for the die is a subset of the natural numbers in the range of 1 to 6.\n",
     "\n",
-    "Capital letters are typically used for random variables, usually from the latter half of the alphabet. So, we might say that $X$ is the random variable representing the die toss, or $Y$ are the heights of the students in the freshmen poetry class. \n",
+    "Another example of a random variable is the heights of students in a university. Here the sample space is a range of values in the real numbers between two limits defined by biology.\n",
     "\n",
-    "Do not confuse the *measurement* of the random variable with the actual value. If we can only measure the height of a person to 0.1 meters we would only record values from 0.1, 0.2, 0.3...2.7, yielding 27 discrete choices. Nonetheless a person's height can vary between any arbitrary real value between those ranges, and so height is a continuous random variable. "
+    "Random variables such as coin tosses and die rolls are *discrete random variables*. This means their sample space is represented by either a finite number of values or a countably infinite number of values such as the natural numbers. Heights of humans are called *continuous random variables* since they can take on any real value between two limits.\n",
+    "\n",
+    "Do not confuse the *measurement* of the random variable with the actual value. If we can only measure the height of a person to 0.1 meters we would only record values from 0.1, 0.2, 0.3...2.7, yielding 27 discrete choices. Nonetheless a person's height can vary between any arbitrary real value between those ranges, and so height is a continuous random variable. \n",
+    "\n",
+    "In statistics capital letters are used for random variables, usually from the latter half of the alphabet. So, we might say that $X$ is the random variable representing the die toss, or $Y$ are the heights of the students in the freshmen poetry class. In later chapters we will follow the convention of using  lower case for vectors, and upper case for matrices. Unfortunately these conventions clash, and you will have to determine which an author is using from context. "
    ]
   },
   {
@@ -628,9 +638,9 @@
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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvUAAAC1CAYAAADfhQDIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x71f4668>"
+       "<matplotlib.figure.Figure at 0x72c8940>"
       ]
      },
      "metadata": {},
@@ -664,9 +674,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvQAAADxCAYAAACkjiOMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvcAAADxCAYAAABPuZiPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x802a0b8>"
+       "<matplotlib.figure.Figure at 0x82f8668>"
       ]
      },
      "metadata": {},
@@ -676,8 +686,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "mean = 1.818\n",
-      "std  = 0.131\n"
+      "mean = 1.809\n",
+      "std  = 0.137\n"
      ]
     }
    ],
@@ -790,9 +800,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAACxCAYAAAALSUEOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\npysLuOkAAAAASUVORK5CYII=\n",
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtgAAACxCAYAAAD+t8q+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8005ac8>"
+       "<matplotlib.figure.Figure at 0x7bd5c50>"
       ]
      },
      "metadata": {},
@@ -884,9 +894,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7d24a20>"
+       "<matplotlib.figure.Figure at 0x8953160>"
       ]
      },
      "metadata": {},
@@ -922,9 +932,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x88d3978>"
+       "<matplotlib.figure.Figure at 0x89df780>"
       ]
      },
      "metadata": {},
@@ -961,9 +971,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x88d3f28>"
+       "<matplotlib.figure.Figure at 0x89dfe80>"
       ]
      },
      "metadata": {},
@@ -1044,9 +1054,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x88d8860>"
+       "<matplotlib.figure.Figure at 0x89e2c88>"
       ]
      },
      "metadata": {},
@@ -1170,9 +1180,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9a98da0>"
+       "<matplotlib.figure.Figure at 0x8a305c0>"
       ]
      },
      "metadata": {},
@@ -1225,9 +1235,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9b73630>"
+       "<matplotlib.figure.Figure at 0x9ca7470>"
       ]
      },
      "metadata": {},
@@ -1263,9 +1273,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9ad9780>"
+       "<matplotlib.figure.Figure at 0x8b02e10>"
       ]
      },
      "metadata": {},
@@ -1404,9 +1414,9 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[-2.166 -0.353  6.399  5.244  5.104  4.299 -0.337\n",
-      "  4.528  2.062 -1.354 -3.177  6.797  2.646  5.988\n",
-      "  1.212]\n"
+      "[ 0.409  2.668  6.657  2.062  4.686  4.65  -2.214\n",
+      " -2.35   6.065  1.219 -0.904  5.647  8.615 -4.476\n",
+      "  0.463]\n"
      ]
     }
    ],
@@ -1508,9 +1518,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x89fa588>"
+       "<matplotlib.figure.Figure at 0x8b4c358>"
       ]
      },
      "metadata": {},
@@ -1565,9 +1575,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x88fc080>"
+       "<matplotlib.figure.Figure at 0x9be8908>"
       ]
      },
      "metadata": {},
@@ -1618,9 +1628,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7d1aa20>"
+       "<matplotlib.figure.Figure at 0x9c5c668>"
       ]
      },
      "metadata": {},