Nick Wilson 02-16-14 Segment 13 Problem 1.ipynb

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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "import numpy as np\n",
      "import scipy.stats"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def get_distributions(n, p):\n",
      "    \"\"\"Get a binomial distribution and its approximating normal distribution.\"\"\"\n",
      "    binom = scipy.stats.binom(n, p)\n",
      "    mu = n * p\n",
      "    sigma = np.sqrt(n * p * (1.0 - p))\n",
      "    normal = scipy.stats.norm(loc=mu, scale=sigma)\n",
      "    return binom, normal\n",
      "\n",
      "def binom_approx_pdf(n, normal_dist):\n",
      "    \"\"\"Approximate binomial PDF based on the given normal distribution.\"\"\"\n",
      "    cdf = normal_dist.cdf\n",
      "    return cdf(n + 0.5) - cdf(n - 0.5)\n",
      "\n",
      "vectorized_binom_approx_pdf = np.vectorize(binom_approx_pdf)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Visualize the difference between the binomial and its normal approximation for single values of n and p."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = 20\n",
      "p = 0.3\n",
      "\n",
      "x_int = np.array(range(0, n + 1))\n",
      "\n",
      "binom, normal = get_distributions(n, p)\n",
      "y_binom = binom.pmf(x_int)\n",
      "y_approx = vectorized_binom_approx_pdf(x_int, normal)\n",
      "\n",
      "# Plot the normal PDF.\n",
      "x = np.linspace(-1, n + 1, num=1000)\n",
      "y_norm = normal.pdf(x)\n",
      "plt.plot(x, y_norm, label='Normal')\n",
      "\n",
      "# Plot the binomial PDF.\n",
      "plot_x = np.array([-1] + list(x_int) + [n + 1]) + 0.5\n",
      "plot_y_binom = np.array([0] + list(y_binom) + [0])\n",
      "plt.step(plot_x, plot_y_binom, label='Binomial(n=20, p=0.3)', hold=True)\n",
      "\n",
      "# Plot the approximate binomial PDF based on the normal distribution.\n",
      "plot_y_approx = np.array([0] + list(y_approx) + [0])\n",
      "plt.step(plot_x, plot_y_approx, label='Binomial Approximation', hold=True)\n",
      "\n",
      "plt.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "<matplotlib.legend.Legend at 0xb61a1ac>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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PL9RfBLZu3aqbbrpJDz30kEJDQ7Vv3z698847Wrlypfbs2aOIiAj7viNHjlS/fv106NAh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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb57b8cc>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "From the same data as plotted above, show the absolute differences between the binomial and its normal approximation at each value."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "abs_diffs = abs(y_binom - y_approx)\n",
      "plt.step(plot_x, [0] + list(abs_diffs) + [0], label='Absolute diff. between exact and approx')\n",
      "plt.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "<matplotlib.legend.Legend at 0xb70efac>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Xmg4dOpjAwECfX3KKM2/ePNOqVSsTGBhomjVrZp599tliz0VMTEyxwTspKcln\nC8k9e/aYPn36mJo1a5rQ0FBz//33m40bN5YpeBtjzMSJE80VV1xhAgMDTZs2bcyCBQuK/Vkp62tM\nUfDOzs42Q4YMMWFhYaZWrVrmjjvuMHv37vWqLfq5KM6RI0fM8OHDTcOGDU1AQIBp3LixGTlypBvc\nv/nmG3PZZZeZG2+80efYBx54wFSvXt2sX7++xLlXZPB2/n8HVdrF8N8LA7Y5TsV9KLAi+7aF1wUA\nqHgej0fJycmaNm1aiXVz5szRfffdp48//ljXXnutpdGdn9LePy7k/YU13gAAAIAFBG8AAADAAoI3\nAAAAKlxlbtt5sWCNN1BFsca7ZLwuAADOB2u8AQAAgCqO4A0AAABYQPAGAAAALCB4AwAAABYQvAEA\nAAALCN4AAACABf6VPQAAqAghISHsGQsAOGchISEV1jf7eANVFPt4AwBgH/t4AwAAABc5gjcAAABg\nAcEbAAAAsIDgDQAAAFhA8AYAAAAsIHgDAAAAFhC8AQAAAAsI3gAAAIAFBG8AAADAAoI3AAAAYAHB\nGwAAALCA4A0AAABYQPAGAAAALCB4AwAAABYQvAEAAAALCN4AAACABQRvAAAAwAKCNwAAAGABwRsA\nAACwgOANAAAAWEDwBgAAACwgeAMAAAAWELwBAAAACwjeAAAAgAUEbwAAAMACgjcAAABgAcEbAAAA\nsIDgDQAAAFhA8AYAAAAsIHgDAAAAFhC8AQAAAAsI3gAAAIAFBG8AAADAAoI3AAAAYAHBGwAAALCA\n4A0AAABYQPAGAAAALCB4AwAAABYQvAEAAAALCN4AAACABQRvAAAAwAKCNwAAAGABwRsAAACwgOAN\nAAAAWFCm4D1t2jQ1btxYQUFBiouL0+rVq0us37Rpk7p27arg4GDVr19fY8aM8alZsWKFYmNjFRQU\npCZNmmj69Ok+NX/5y1/UokULBQcHq0GDBnr44Yd16NChMk4NAAAAuHiUGrwXLVqkoUOHasSIEVq/\nfr06deqknj176ptvvim2/uDBg+rRo4eioqKUk5OjyZMna+LEiZo0aZJbs3PnTvXq1UudO3fW+vXr\nlZ6erkceeUSLFy92a+bNm6c///nPGjVqlLZu3ap58+Zp2bJlSklJKYdpAwAAAHY5xhhTUkGHDh3U\nvn17ryvSzZs3V58+fTR+/Hif+szMTKWnpys/P1/Vq1eXJI0bN06ZmZnavXu3JGn48OFasmSJtm3b\n5h73wAPJlv7bAAAgAElEQVQPaPPmzVqzZo0k6eGHH9bnn3+u7Oxst+bxxx/X4sWLtWnTJu9JOI5K\nmQZwyXEcqaKe9hXZNwAAVdmF5M4Sr3gfP35c69atU2Jiold7YmKiG5DPtHbtWsXHx7uhu6j+22+/\n1a5du9ya4vrMyclRYWGhJKlnz57asGGDPvnkE0nS119/rb/97W+6+eabz3GKAAAAQOUrMXgXFBSo\nsLBQERERXu316tVTXl5escfk5eX51BfdLjomPz+/2JoTJ06ooKBAknTzzTdr3Lhxio+PV0BAgGJi\nYtSuXTs99dRT5zA9AAAA4OJQ7ruaOI5TLv28/fbb+tOf/qQXX3xR//rXv7R48WJ9+OGHevzxx8ul\nfwAAAMAm/5K+GRYWJj8/P+Xn53u15+fnKyoqqthjIiMjfa6GFx0fGRlZYo2/v7/CwsIkSU899ZR+\n//vf67777pMkXXnllTp06JDuv/9+Pf744/J4vH9nyMjIcP+dkJCghISEkqYGAAAAlCo7O9vrM4cX\nosTgHRAQoNjYWC1fvlx33HGH256VlaW+ffsWe0zHjh01fPhwHTt2zF3nnZWVpejoaDVq1Mitefvt\nt72Oy8rK0jXXXCM/Pz9JkjHGJ1x7PJ6zLmY/PXgDAAAA5eHMC7qjR48+775KXWqSlpamOXPmaNas\nWcrNzVVKSory8vKUnJwsSUpPT1f37t3d+v79+ys4OFhJSUnavHmzFi9erAkTJigtLc2tSU5O1p49\ne5Samqrc3FzNnDlTc+fO1bBhw9ya2267TS+99JIWLVqknTt3KisrSyNHjtQtt9ziE8gBAACAi12J\nV7wlqV+/ftq3b5/Gjh2rvXv3qk2bNlq2bJkaNGgg6dQHJnfs2OHW165dW1lZWRoyZIji4uIUGhqq\nYcOGKTU11a2JiYnRsmXLlJqaqszMTEVHR2vKlCnq3bu3WzN8+HAZYzRy5Ejt3r1b4eHhuuWWWzRu\n3LjynD8AAABgRan7eFcF7OONXyL28QYAwL4K28cbAAAAQPkgeAMAAAAWELwBAAAACwjeAAAAgAUE\nbwAAAMACgjcAAABgAcEbAAAAsIDgDQAAAFhA8AYAAAAsIHgDAAAAFhC8AQAAAAsI3gAAAIAFBG8A\nAADAAoI3AAAAYAHBGwAAALCA4A0AAABYQPAGAAAALCB4AwAAABYQvAEAAAALCN4AAACABQRvAAAA\nwAKCNwAAAGABwRsAAACwgOANAAAAWEDwBgAAACzwr+wBALj4hIRIjlMx/e7fX/79AgBQFTjGGFPZ\ng7hQjuPoEpgGcE4cR6pqT/uqOGYAAE53IbmTpSYAAACABQRvAAAAwAKCN4AqLzT01DKW8v4KDa3s\nmQEALiWs8QaqqKq4XrqixlzV+gUAVF2s8QYAAAAucgRvAAAAwAKCNwAAAGABwRsAAACwgOANAAAA\nWEDwBgAAACwgeAMAAAAWELwBAAAACwjeAAAAgAUEbwAAAMACgjcAAABgAcEbAAAAsIDgDQAAAFhA\n8AYAAAAsIHgDAAAAFhC8AQAAAAsI3gAAAIAFBG8AAADAAoI3AAAAYAHBGwAAALCA4A0AAABYQPAG\nAAAALCB4AwAAABYQvAEAAAALCN4AAACABQRvAAAAwAKCNwAAAGABwRsAAACwgOANAAAAWEDwBgAA\nACwgeAMAAAAWELwBAAAACwjeAAAAgAUEbwAAAMACgjcAAABggX9lDwAALlYhIZLjVFzf+/dXTN8A\ngIuTY4wxlT2IC+U4ji6BaQDnxHGkqva0r6gxcy4AALZcSO5kqQkAAABgAcEbAAAAsIDgDQAAAFhA\n8AYAAAAsIHgDAAAAFhC8AQAAAAsI3gAAAIAFBG8AAADAAoI3AAAAYAHBGwAAALCA4A0AAABYQPAG\nAAAALCB4AwAAABYQvAEAAAALyhS8p02bpsaNGysoKEhxcXFavXp1ifWbNm1S165dFRwcrPr162vM\nmDE+NStWrFBsbKyCgoLUpEkTTZ8+3afm4MGDevTRRxUdHa3AwEA1a9ZMb7zxRhmnBgAAAFw8/Esr\nWLRokYYOHarMzEx17txZU6dOVc+ePbVlyxY1aNDAp/7gwYPq0aOHEhISlJOTo9zcXA0cOFA1atRQ\nWlqaJGnnzp3q1auX7r//fi1cuFCrVq3S4MGDFR4erttvv12S9PPPP6tHjx4KCwvTG2+8ofr162v3\n7t0KCAgo51MAAAAAVDzHGGNKKujQoYPat2/vdUW6efPm6tOnj8aPH+9Tn5mZqfT0dOXn56t69eqS\npHHjxikzM1O7d++WJA0fPlxLlizRtm3b3OMeeOABbd68WWvWrJEkvfTSS3r66ae1detW+fuX/PuB\n4zgqZRrAJcdxpKr2tK+oMXMuAAC2XEjuLHGpyfHjx7Vu3TolJiZ6tScmJroB+Uxr165VfHy8G7qL\n6r/99lvt2rXLrSmuz5ycHBUWFkqSlixZok6dOmnIkCGKiorSlVdeqdGjR+vEiRPnPksAAACgkpUY\nvAsKClRYWKiIiAiv9nr16ikvL6/YY/Ly8nzqi24XHZOfn19szYkTJ1RQUCBJ2rFjh9544w0VFhZq\n2bJlGjNmjF588UWlp6efw/QAAACAi0Opa7zPleM45dLPyZMnFRERoRkzZshxHF111VXat2+fUlNT\nNXHiRJ/6jIwM998JCQlKSEgol3EAAADglys7O1vZ2dnl0leJwTssLEx+fn7Kz8/3as/Pz1dUVFSx\nx0RGRvpcDS86PjIyssQaf39/hYWFSZIuv/xyBQQEeAX5li1b6vDhw9q3b5/q1q3rdfzpwRsAAAAo\nD2de0B09evR591XiUpOAgADFxsZq+fLlXu1ZWVnq1KlTscd07NhRq1at0rFjx7zqo6Oj1ahRI7cm\nKyvLp89rrrlGfn5+kqTrr79eX3zxhdfi9e3bt6tGjRo+oRsAAAC42JW6j3daWprmzJmjWbNmKTc3\nVykpKcrLy1NycrIkKT09Xd27d3fr+/fvr+DgYCUlJWnz5s1avHixJkyY4G4lKEnJycnas2ePUlNT\nlZubq5kzZ2ru3LkaNmyYW/PQQw9p//79SklJ0bZt2/Tee+8pIyNDgwcPLs/5AwAAAFaUusa7X79+\n2rdvn8aOHau9e/eqTZs2WrZsmbuHd15ennbs2OHW165dW1lZWRoyZIji4uIUGhqqYcOGKTU11a2J\niYnRsmXLlJqaqszMTEVHR2vKlCnq3bu3W1O/fn0tX75caWlpuuqqqxQZGanf//73GjFiRHnOHwAA\nALCi1H28qwL28cYvUVXcB5p9vP+rKo4ZAFCB+3gDAAAAKB8EbwAAAMACgjcAAABgAcEbAAAAsIDg\nDQAAAFhA8AYAAAAsIHgDAAAAFhC8AQAAAAsI3gAAAIAFBG8AAADAAoI3AAAAYAHBGwAAALCA4A0A\nAABYQPAGAAAALCB4AwAAABYQvAEAAAALCN4AAACABQRvAAAAwAKCNwAAAGABwRsAAACwgOANAAAA\nWEDwBgAAACwgeAMAAAAWELwBAAAACwjeAAAAgAUEbwAAAMACgjcAAABgAcEbAAAAsIDgDQAAAFhA\n8AYAAAAsIHgDAAAAFhC8AQAAAAsI3gAAAIAFBG8AAADAAoI3AAAAYAHBGwAAALCA4A0AAABYQPAG\nAAAALCB4AwAAABYQvAEAAAALCN4AAACABQRvAAAAwAKCNwAAAGABwRsAAACwgOANAAAAWEDwBgAA\nACwgeAMAAAAWELwBAAAACwjeAAAAgAUEbwAAAMACgjcAAABgAcEbAAAAsIDgDQAAAFhA8AYAAAAs\nIHgDAAAAFhC8AQAAAAsI3gAAAIAFBG8AAADAAoI3AAAAYAHBGwAAALCA4A0AAABYQPAGAAAALCB4\nAwAAABYQvAEAAAALCN4AAACABQRvAAAAwAKCNwAAAGABwRsAAACwgOANAAAAWEDwBgAAACwgeAMA\nAAAWELwBAAAACwjeAAAAgAUEbwAAAMACgjcAAABgAcEbAAAAsIDgDQAAAFhA8AYAAAAs8K/sAQCX\nutBQ6cCB8u83JKT8+wQAABXHMcaYyh7EhXIcR5fANHCJchyJp+cpFXUuquI5ropjBgBcWO5kqQkA\nAABgQZmC97Rp09S4cWMFBQUpLi5Oq1evLrF+06ZN6tq1q4KDg1W/fn2NGTPGp2bFihWKjY1VUFCQ\nmjRpounTp5+1v1dffVUej0e33HJLWYYLAAAAXHRKDd6LFi3S0KFDNWLECK1fv16dOnVSz5499c03\n3xRbf/DgQfXo0UNRUVHKycnR5MmTNXHiRE2aNMmt2blzp3r16qXOnTtr/fr1Sk9P1yOPPKLFixf7\n9Ldjxw499thjio+Pl+M4FzBVAAAAoPKUusa7Q4cOat++vdcV6ebNm6tPnz4aP368T31mZqbS09OV\nn5+v6tWrS5LGjRunzMxM7d69W5I0fPhwLVmyRNu2bXOPe+CBB7R582atWbPGbfv555/VuXNnPfzw\nw/rggw9UUFCgpUuX+k6CNd64iLGW979Y4/1fVXHMAIAKXON9/PhxrVu3TomJiV7tiYmJXgH5dGvX\nrlV8fLwbuovqv/32W+3atcutKa7PnJwcFRYWum1//vOfdcUVV+iee+4hWAMAAKBKKzF4FxQUqLCw\nUBEREV7t9erVU15eXrHH5OXl+dQX3S46Jj8/v9iaEydOqKCgQJK0fPlyvfnmm+6VdsdxWGoCAACA\nKqvc9/Euj3D8n//8R0lJSXrttddUu3ZtSZIxpsSr3hkZGe6/ExISlJCQcMHjAAAAwC9bdna2srOz\ny6WvEoN3WFiY/Pz8lJ+f79Wen5+vqKioYo+JjIz0uRpedHxkZGSJNf7+/goLC9OqVauUl5enX//6\n1+73T548KUmqVq2atmzZombNmnkdf3rwBgAAAMrDmRd0R48efd59lbjUJCAgQLGxsVq+fLlXe1ZW\nljp16lTsMR07dtSqVat07Ngxr/ro6Gg1atTIrcnKyvLp85prrpGfn5+uvfZaff7559qwYYM2bNig\n9evX69Zbb1WXLl20YcMGxcTEnM9cAQAAgEpT6naCaWlpmjNnjmbNmqXc3FylpKQoLy9PycnJkqT0\n9HR1797dre/fv7+Cg4OVlJSkzZs3a/HixZowYYLS0tLcmuTkZO3Zs0epqanKzc3VzJkzNXfuXA0b\nNkySFBwcrNatW7tfV155perUqaOaNWuqdevWqlatWnmfBwAAAKBClbrGu1+/ftq3b5/Gjh2rvXv3\nqk2bNlq2bJkaNGgg6dQHJnfs2OHW165dW1lZWRoyZIji4uIUGhqqYcOGKTU11a2JiYnRsmXLlJqa\nqszMTEVHR2vKlCnq3bv3WcfBhysBAABQlZW6j3dVwD7euJixX/N/sY/3f1XFMQMAKnAfbwAAAADl\ng+ANAAAAWEDwBgAAACwgeAMAAAAWELwBAAAACwjeAAAAgAUEbwAAAMACgjcAAABgAcEbAAAAsIDg\nDQAAAFhA8AYAAAAsIHgDAAAAFhC8AQAAAAsI3gAAAIAFBG9UKaGhkuNUzFdoaGXPDgAAXMr8K3sA\nwLk4cEAypmL6dpyK6RcAAEDiijcAAABgBcEbAAAAsIDgDQAAAFhA8AYAAAAsIHgDAAAAFhC8AQAA\nAAsI3gAAAIAFBG8AAADAAoI3AAAAYAHBGwAAALCA4A0AAABYQPAGAAAALCB4AwAAABYQvAEAAAAL\nCN4AAACABQRvAAAAwAKCNwAAAGABwRsAAACwgOANAAAAWEDwBgAAACwgeAMAAAAWELwBAAAACwje\nAAAAgAUEbwAAAMACgjcAAABgAcEbAAAAsIDgDQAAAFhA8AYAAAAsIHgDAAAAFhC8AQAAAAsI3gAA\nAIAFBG8AAADAAoI3AAAAYAHBGwAAALCA4A0AAABYQPAGAAAALCB4AwAAABYQvAEAAAALCN4AAACA\nBQRvAAAAwAKCNwAAAGABwRsAAACwgOANAAAAWEDwBgAAACwgeAMAAAAWELwBAAAACwjeAAAAgAUE\nbwAAAMACgjcAAABgAcEbAAAAsIDgDQAAAFhA8AYAAAAsIHgDAAAAFhC8AQAAAAsI3gAAAIAFBG8A\nAADAAoI3AAAAYAHBGwAAALCA4A0AAABYQPAGAAAALCB4AwAAABYQvAEAAAALCN4AAACABQRvAAAA\nwAKCNwAAAGBBmYP3tGnT1LhxYwUFBSkuLk6rV68usX7Tpk3q2rWrgoODVb9+fY0ZM8anZsWKFYqN\njVVQUJCaNGmi6dOne31/xowZio+PV2hoqEJCQnTDDTfoo48+KuuQAQAAgItGmYL3okWLNHToUI0Y\nMULr169Xp06d1LNnT33zzTfF1h88eFA9evRQVFSUcnJyNHnyZE2cOFGTJk1ya3bu3KlevXqpc+fO\nWr9+vdLT0/XII49o8eLFbs2KFSt0991368MPP9Qnn3yiFi1a6MYbb9SXX355gdMGAAAA7HKMMaa0\nog4dOqh9+/ZeV6SbN2+uPn36aPz48T71mZmZSk9PV35+vqpXry5JGjdunDIzM7V7925J0vDhw7Vk\nyRJt27bNPe6BBx7Q5s2btWbNmrOOJSoqSiNGjNCQIUP+OwnHURmmAYtCQ6UDB8q/35AQaf/+8u9X\nkhxHqoinUUX1WxVxjv+rKo4ZAHBhubPUK97Hjx/XunXrlJiY6NWemJh41oC8du1axcfHu6G7qP7b\nb7/Vrl273Jri+szJyVFhYWGx/R47dkxHjx5VSEhIacNGJTtw4FSoKO+vigrdgG0hIafCd3l/hYZW\n9swAAGdTavAuKChQYWGhIiIivNrr1aunvLy8Yo/Jy8vzqS+6XXRMfn5+sTUnTpxQQUFBsf2OGDFC\ntWrV0q233lrasAHgorZ/f8X8cloRf2kCAJQP/4ro1HGccu9z8uTJeumll/T++++rZs2a5d4/AAAA\nUJFKDd5hYWHy8/NTfn6+V3t+fr6ioqKKPSYyMtLnanjR8ZGRkSXW+Pv7KywszKv9ueee06hRo/Tu\nu+8qLi6u2PvMyMhw/52QkKCEhITSpgYAAACUKDs7W9nZ2eXSV6nBOyAgQLGxsVq+fLnuuOMOtz0r\nK0t9+/Yt9piOHTtq+PDhOnbsmLvOOysrS9HR0WrUqJFb8/bbb3sdl5WVpWuuuUZ+fn5u26RJk5SR\nkaFly5apU6dOZx3n6cEbAAAAKA9nXtAdPXr0efdVpu0E09LSNGfOHM2aNUu5ublKSUlRXl6ekpOT\nJUnp6enq3r27W9+/f38FBwcrKSlJmzdv1uLFizVhwgSlpaW5NcnJydqzZ49SU1OVm5urmTNnau7c\nuRo2bJhbM3HiRKWnp2vWrFlq2rSp8vLylJeXp4MHD573hAEAAIDKUKbtBKVTWwQ+/fTT2rt3r9q0\naaNnn31WnTt3liQNHDhQK1as0I4dO9z6zz//XEOGDNGnn36q0NBQJScna+TIkV59rly5Uqmpqdq8\nebOio6M1fPhwDRo0yP1+48aN9fXXX/ts2ZKUlKTZs2f/dxJsJ3jRqYpbpVXFLRCrGrYTrHicCwCo\nWBeSO8scvC9mBO+LD2/+KA7Bu+JxLgCgYlXoPt4AAAAALhzBGwAAALCA4A0AAABYQPAGAAAALCB4\nAwAAABYQvAEAAAALCN4AAACABQRvAAAAwAKCNwAAAGABwRsAAACwgOANAAAAWEDwBgAAACwgeAMA\nAAAWELwBAKUKDZUcp2K+QkMre3YAYId/ZQ8AAHDxO3BAMqZi+naciukXAC42XPEGAAAALCB4AwAA\nABYQvAEAAAALCN4AAACABQRvAAAAwAKCNwAAAGABwRsAAACwgOANAAAAWEDwBgAAACwgeAMAAAAW\nELwBAAAACwjeAAAAgAUEbwAAAMACgjcAAABgAcEbAAAAsIDgDQAAAFhA8AYAAAAsIHgDAAAAFhC8\nAQAAAAsI3gAAAIAFBG8AAADAAv/KHgCAX46QEMlxKqZfAAAudo4xxlT2IC6U4zi6BKZxSXEciYcE\nsK+ifvYq8mea1wsAVcmF5E6WmgAAAAAWsNQEAC4hLOcBgIsXS01QIfjTMYCy4vUCQFXCUhMAAADg\nIsdSEwBAparI5TH795d/vwBwvlhqggrBn44BVDZehwBUBJaaAAAAABc5gjcAAABgAcEbAAAAsIDg\nDQAAAFhA8AYAAAAsIHgDAAAAFhC8AQAAAAsI3gAAAIAFBG8AAADAAoI3AAAAYAHBGwAAALCA4A0A\nAABYQPAGAAAALCB4AwAAABYQvAEAAAALCN4AAACABQRvAAAAwAKCNwAAAGABwRsAAACwgOANAAAA\nWEDwBgAAACwgeAMAAAAWELwBAAAACwjeAAAAgAUEbwAAAMAC/8oeAAAAFSEkRHKciul3//7y7xfA\npc8xxpjKHsSFchxHl8A0LimOI/GQALgU8foG/LJdSO5kqQkAAABgAcEbAAAAsIDgDQAAAFhA8AYA\nAAAsIHgDAAAAFhC8AQAAAAsI3gAAAIAFBG8AAADAAoI3AAAAYAHBGwAAALCgTMF72rRpaty4sYKC\nghQXF6fVq1eXWL9p0yZ17dpVwcHBql+/vsaMGeNTs2LFCsXGxiooKEhNmjTR9OnTfWreeusttW7d\nWoGBgbryyiu1ZMmSMk4LAAAAuLiUGrwXLVqkoUOHasSIEVq/fr06deqknj176ptvvim2/uDBg+rR\no4eioqKUk5OjyZMna+LEiZo0aZJbs3PnTvXq1UudO3fW+vXrlZ6erkceeUSLFy92a9auXau77rpL\n99xzjzZs2KDf/e536tu3rz799NNymDYAAOcnJERynIr5Cg2t7NkBqEiOMcaUVNChQwe1b9/e64p0\n8+bN1adPH40fP96nPjMzU+np6crPz1f16tUlSePGjVNmZqZ2794tSRo+fLiWLFmibdu2ucc98MAD\n2rx5s9asWSNJuvPOO/X999/rvffec2t69Oih8PBwLVy40HsSjqNSpgHLHEcq60OSnZ2thISECh0P\nKg6PX9XFY3fx4bXzl4HHrmq7kNxZ4hXv48ePa926dUpMTPRqT0xMdAPymdauXav4+Hg3dBfVf/vt\nt9q1a5dbU1yfOTk5KiwslCR9/PHH53S/qLqys7Mrewi4ADx+VRePXdXG41d18dj9cpUYvAsKClRY\nWKiIiAiv9nr16ikvL6/YY/Ly8nzqi24XHZOfn19szYkTJ1RQUFBiP2e7XwAAAOBi5l/eHTqOU95d\nAgDwi1C0frysRo8ue7/795/fmACUnxKDd1hYmPz8/JSfn+/Vnp+fr6ioqGKPiYyM9LkqXXR8ZGRk\niTX+/v4KCwsrsaaoj9M1adKEwH8ROrc3jzK+e+CixONXdfHYVXVle/wOHDi312RUPH72qq4mTZqc\n97ElBu+AgADFxsZq+fLluuOOO9z2rKws9e3bt9hjOnbsqOHDh+vYsWPuOu+srCxFR0erUaNGbs3b\nb7/tdVxWVpauueYa+fn5uTVZWVkaNmyYV83111/vc59ffvllWeYKAAAAVJpStxNMS0vTnDlzNGvW\nLOXm5iolJUV5eXlKTk6WJKWnp6t79+5uff/+/RUcHKykpCRt3rxZixcv1oQJE5SWlubWJCcna8+e\nPUpNTVVubq5mzpypuXPneoXslJQUffDBB5owYYK2bt2qJ598UtnZ2Ro6dGh5zh8AAACwotTtBKVT\nWwQ+/fTT2rt3r9q0aaNnn31WnTt3liQNHDhQK1as0I4dO9z6zz//XEOGDNGnn36q0NBQJScna+TI\nkV59rly5Uqmpqdq8ebOio6M1fPhwDRo0yKvmrbfe0ogRI7Rjxw41bdpU48aN02233VYe8waA/9fe\n/YU0vcZhAH9+TuYm5ihrbnMx1x8VtgLTJHdhK9IMQoiCyovKqN000EldGAMXidVNEIlgELGusm4r\nqED7M+wiKsmmEOEurHAYCLGhWNt7Ls5pnE2na6ez3xbPB34wX1/hgS8PvOrYS0RElFEpHbyJiIiI\niOi/SenK+Fxit9uRl5cX97S2tsodi5Lo7++H2WyGWq1GbW0tfD6f3JFoBR6PZ1HHDAaD3LEoiefP\nn6OlpQVGoxF5eXnwer2L9ng8HpSVlaGwsBC7du3C+Pi4DEkp0UqzO3HixKIu2mw2mdJSokuXLmH7\n9u3QaDTQarVoaWmB3+9ftI/9yz6pzC7d/v1xB29JknDy5ElMT0/Hnn/fuknZY3BwEB0dHXC73Rgd\nHYXNZsO+ffswNTUldzRaQVVVVVzHxsbG5I5ESYTDYWzduhXXrl2DWq1e9AlQV65cwdWrV9HX14dX\nr15Bq9WisbERoVBIpsT000qzkyQJjY2NcV18+PChTGkp0bNnz+B0OvHy5UsMDQ0hPz8fe/bswezs\nbGwP+5edUpld2v0Tfxi73S6cTqfcMSgFdXV1wuFwxK1t3rxZdHV1yZSIUtHd3S2sVqvcMSgNRUVF\nwuv1xr6ORqNCp9OJ3t7e2Nrc3JxYtWqVGBgYkCMiJZE4OyGEOH78uNi/f79MiehXhUIhoVAoxP37\n94UQ7F8uSZydEOn374/7izcA3LlzB+vWrYPVasW5c+f4m2MWWlhYwJs3b9DU1BS33tTUhJGREZlS\nUaomJydRVlaGDRs24OjRowgEAnJHojQEAgEEg8G4HqpUKjQ0NLCHOUCSJPh8PpSWlqKyshIOhwMz\nMzNyx6Ikvn37hmg0itWrVwNg/3JJ4uyA9Pv322+ulFtrayvKy8thMBjw/v17dHV14d27d3j06JHc\n0ehfvn79ikgkgtLS0rh1rVa76OIkyi47duyA1+tFVVUVgsEgenp6YLPZ4Pf7sWbNGrnj0S/42bWl\nevjlyxc5ItEvaG5uxsGDB2E2mxEIBOB2u7F79268fv0aSqVS7niUoL29HdXV1aivrwfA/uWSxNkB\n6fcvJw7ebrcbvb29y+55+vQpGhoacPr06diaxWLBxo0bUVdXh7dv36K6uvr/jkr0x2tubo69tlqt\nqEhYnfwAAAMNSURBVK+vh9lshtfrhcvlkjEZ/U68DTj7HT58OPbaYrGgpqYGJpMJDx48wIEDB2RM\nRok6OzsxMjICn8+XUrfYv+yRbHbp9i8nDt4ulwvHjh1bds/69euXXN+2bRsUCgU+fvzIg3cWWbt2\nLRQKBYLBYNx6MBiEXq+XKRWlo7CwEBaLhTfI5iCdTgfg794ZjcbYejAYjH2Pcoder4fRaGQXs4zL\n5cLdu3cxPDyM8vLy2Dr7l/2SzW4pqfYvJ97jXVJSgoqKimUftVq95M+OjY0hEonwMJdllEolampq\n8Pjx47j1J0+e8OOwcsz8/DwmJibYsRxkNpuh0+niejg/Pw+fz8ce5qCZmRl8/vyZXcwi7e3tGBwc\nxNDQECoqKuK+x/5lt+Vmt5RU+6fweDye35RRdpOTk7h+/TqKioqwsLCAkZEROBwOmEwmXLx4kf+6\nyTLFxcXo7u6GwWCAWq1GT08PfD4fbt26BY1GI3c8SuLs2bNQqVSIRqP48OEDnE4nJicnMTAwwLll\noXA4jPHxcUxPT+PmzZvYsmULNBoNvn//Do1Gg0gkgsuXL6OyshKRSASdnZ0IBoO4ceMG3ycss+Vm\nl5+fj/Pnz6O4uBg/fvzA6OgoTp06hWg0ir6+Ps4uC5w5cwa3b9/GvXv3YDQaEQqFEAqFIEkSlEol\nJEli/7LUSrMLh8Pp9+93ftyK3KampsTOnTtFSUmJKCgoEJs2bRIdHR1idnZW7miURH9/vygvLxcF\nBQWitrZWvHjxQu5ItIIjR44Ig8EglEqlKCsrE4cOHRITExNyx6IkhoeHhSRJQpIkkZeXF3vd1tYW\n2+PxeIRerxcqlUrY7Xbh9/tlTEw/LTe7ubk5sXfvXqHVaoVSqRQmk0m0tbWJT58+yR2b/pE4t5/P\nhQsX4vaxf9lnpdn9l/7xyngiIiIiogzIifd4ExERERHlOh68iYiIiIgygAdvIiIiIqIM4MGbiIiI\niCgDePAmIiIiIsoAHryJiIiIiDKAB28iIiIiogzgwZuIiIiIKAN48CYiIiIiyoC/ALYsd+yoJUm8\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb59b42c>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Print the index and the value of where the difference between the exact and approximate PDF differs the most"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "max_idx = np.argmax(abs_diffs)\n",
      "max_diff = abs_diffs[max_idx]\n",
      "print 'Max diff {0} at {1}'.format(max_diff, max_idx)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Max diff 0.00956993285131 at 4\n"
       ]
      }
     ],
     "prompt_number": 5
    }
   ],
   "metadata": {}
  }
 ]
}