{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is a Python implementation of MATLAB demo code provided by the course *Monte Carlo Methods in Finance* provided by iversity.org\n",
      "\n",
      "https://iversity.org/my/courses/monte-carlo-methods-in-finance/\n",
      "\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Week 2"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      " demo_randm - Lecture 2.2"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Random numbers can be generated using either the <code>random</code> module or the <code>numpy.random</code> submodule. Here we use the latter."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import numpy as np\n",
      "from numpy import random\n",
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The function <code>numpy.random.rand</code> generates random numbers on the interval [0,1) with uniform probability (note that the interval is half-open)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print random.rand()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.0926675357494\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "An array of random numbers is generated by passing the shape of the array as an argument"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print random.rand(5,4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0.16573073  0.30142696  0.9401207   0.31052939]\n",
        " [ 0.95662973  0.1095877   0.00377109  0.04902205]\n",
        " [ 0.82546732  0.11588215  0.82999227  0.6284355 ]\n",
        " [ 0.68406566  0.14488838  0.53180516  0.97465852]\n",
        " [ 0.38534993  0.24335456  0.61923684  0.04330545]]\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In NumPy (psuedo-)random numbers are generated using a deterministic algorithm. The numbers are therefore not truly random. By fixing the seed we can reproduce the same sequence.\n",
      "\n",
      "( Note that numpy.random.seed is not thread safe, but it's sufficient for our purposes )"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "random.seed(seed=123)\n",
      "print random.rand(2,3)\n",
      "random.seed(seed=123)\n",
      "print random.rand(2,3) # give the same output"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0.69646919  0.28613933  0.22685145]\n",
        " [ 0.55131477  0.71946897  0.42310646]]\n",
        "[[ 0.69646919  0.28613933  0.22685145]\n",
        " [ 0.55131477  0.71946897  0.42310646]]\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally, we plot the PDF and CDF of the uniform distribution."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nPlots = 1000\n",
      "xPlot = np.linspace(-0.5, 1.5, nPlots)\n",
      "\n",
      "uniformPDF = np.where((xPlot >= 0) & (xPlot <= 1), 1, 0) \n",
      "# This is one of many ways in which you can define a piecewise function.\n",
      "# np.where(A, b, c) takes a boolean array A (or converts A to a boolean array) and checks the thruth-value of each element A[i,j]\n",
      "# The output is an array B of the same shape as A.\n",
      "# when A[i,j] = True, then B[i,j] = b, and when A[i,j] = False then B[i,j] = c\n",
      "# Note that here b and c are scalars, but they can be arrays as well\n",
      "\n",
      "uniformCDF = uniformPDF * xPlot + np.where(xPlot >= 1, 1, 0)\n",
      "\n",
      "plt.figure()\n",
      "ax = plt.subplot(211)\n",
      "plt.plot(xPlot, uniformPDF);\n",
      "ax.set_title('Uniform PDF')\n",
      "ax.set_xlabel('x')\n",
      "ax.set_ylabel('UniformPDF(x)')\n",
      "ax.set_ybound(-.25,1.25)\n",
      "\n",
      "ax = plt.subplot(212)\n",
      "ax.set_title('Uniform CDF')\n",
      "ax.set_xlabel('x')\n",
      "ax.set_ylabel('UniformCDF(x)')\n",
      "plt.plot(xPlot, uniformCDF);\n",
      "ax.set_ybound(-.25,1.25)\n",
      "\n",
      "plt.tight_layout()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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v3r24fv26WiDOzc1FVVUVzp49i8mTJ2PmzJl4//33Vc9LJBJ8+eWXqKqqUt1C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\nRCRaDFJERCRa/x9k0y46LIevIAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5b22530>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Alternatively, we can also define <code>uniformPDF</code> using slicing."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "uniformPDF = np.zeros_like(xPlot)\n",
      "uniformPDF[(xPlot >= 0) & (xPlot <= 1)] = 1\n",
      "\n",
      "\n",
      "fig = plt.figure()\n",
      "ax2 = plt.plot(xPlot, uniformPDF)\n",
      "ax = fig.get_axes()[0]\n",
      "ax.set_title('Uniform PDF')\n",
      "ax.set_xlabel('x')\n",
      "ax.set_ylabel('UniformPDF(x)')\n",
      "ax.set_ybound(-.1, 1.1)\n",
      "plt.tight_layout()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Xmprq+c9//hPO0qJGS0uL56KLLvLs2bPHc+zYMU9WVpZn27ZtPmNWrVrlyc3N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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5b1cfd0>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      " demo_randn - Lecture 2.3"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we look at <code>numpy.random.randn</code> which generates random numbers from a Gaussian distribution. This functions draws random samples from the normal distribution with mean zero and standard deviation 1. We write this as $S\\sim N(0,1)$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "random.seed(50)\n",
      "print random.randn()\n",
      "S = random.randn(3,4)\n",
      "print S"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "-1.56035210868\n",
        "[[-0.0309776  -0.62092842 -1.46458049  1.41194612]\n",
        " [-0.47673214 -0.78046921  1.07026774 -1.2822926 ]\n",
        " [-1.3274789   0.12633764  0.86219372  0.69673696]]\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The PDF and CDF of the normal and other distributions are stored in the <code>scipy.stats</code> module. Another excellent statistics module is <code>statsmodels</code>, but we will stick to <code>scipy.stats</code>.\n",
      "\n",
      "The class <code>scipy.stats.norm</code> (which we import below) holds different functions associated with the normal distribution, such as the PDF and the CDF.\n",
      "\n",
      "See http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html for more info."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nPlots = 1000\n",
      "alpha = 3\n",
      "xPlot = np.linspace(-alpha, alpha, nPlots)\n",
      "\n",
      "from scipy.stats import norm \n",
      "\n",
      "normPDF = norm.pdf(xPlot)\n",
      "normCDF = norm.cdf(xPlot)\n",
      "\n",
      "\n",
      "plt.figure()\n",
      "ax = plt.subplot(211)\n",
      "plt.plot(xPlot, normPDF);\n",
      "ax.set_title('Normal PDF')\n",
      "ax.set_xlabel('x')\n",
      "ax.set_ylabel('NormalPDF(x)')\n",
      "ax.set_ybound(-.1,.5)\n",
      "\n",
      "ax = plt.subplot(212)\n",
      "ax.set_title('Normal CDF')\n",
      "ax.set_xlabel('x')\n",
      "ax.set_ylabel('NormalCDF(x)')\n",
      "plt.plot(xPlot, normCDF);\n",
      "ax.set_ybound(-.2,1.2)\n",
      "\n",
      "plt.tight_layout()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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IyEBNTQ3+9a9/KXzg+lXQnZ2d8d5770mqoNdVQv/ll1/g6uoKd3d3LFmyBD/99JPCxyVt\nU0EBG07u5cWGkN+7B0ydysr+EP506cLKKyUns9+RoyMbrFJdzXdkpLWQ2d3n4uKC+Pj4BiPsADbK\nzsvLC7dv31ZJgPKg7j7NVV0N/Oc/wOefs6Un1q0DzMz4jorIkpzMumGzslg37NixfEdE+KRQd1+7\ndu0aJSgA0NfXhxZ9PSU84zjgxAk2ofTkSbaw33ffUYJSd337AqdPs9F/dWWn1Oj7LlFDTdY9ys/P\nb/QYx3Fyj8wjpCXcvMm+jYtErPLBmDF8R0ReRd1IwLffZoMrRo5k1xFDQ4Fu3fiOjqgbmd191tbW\nTSajx48ft1hQr4q6+zRDdjZbIiMyEggJAebNozWP2oJnz1iCCgsDPv0UWLiQDbwgbV+LLXqobihJ\ntW3Pn7OJuNu2scS0ciW7IE/alnv32OCXe/dYFYsJE6jaelun0DUpkUiEJUuWwM/PDytXrkRxcbHS\nAySkKbW1bJFBBwfg7l3g+nU2OZQSVNvk6MiuL+7cySpXjBoFJCbyHRXhm8wkNXPmTOjr62PRokUo\nKSnB4sWLVRkX0XAxMYCnJxsMceQI6wpqCyvhkub5+LDk9N57bPRfYCAbDUg0k8wklZubiy+++AJj\nxozBjh07kJSUpPSDN7dUx6FDhyAUCtG3b18MGTJE4XqBRP2lpLBunsBAtq7TpUvAwIF8R0VUTVsb\n+PBD4P59oHt3Nipw7Vq2MCXRLDKTFMdxyM/PR35+Pp49ewaxWCz5Wdqov1clFouxcOFCREdH486d\nOwgLC2tUL7B37944f/48kpOTsXr1asyfP1/h4xL19PQpsGgRMGQIMHgw697729/omoSm69KFlVZK\nSABSU1nX7549gFjMd2REVeQe3ffy0HNFR/dduXIFoaGhktp9GzZsAAB8+umnUvcvKCiAq6srMjMz\nGz1HAydar4oKNiDi66+B999n1yJoRRYiy9WrwCefsBbVpk3Am2/yHRFRhDyf3TIH8KalpSk7ngbk\nXaqjzu7du+Hr69uiMRHVqa1l1bL/+U/A3Z1169nb8x0VUXdeXsCFC2zdqg8+AJyc2BccJye+IyMt\nRWaSqivoKku/fv0UOvCrTAg+d+4c9uzZg0uXLsnch5bqaD3On2dDjTkOOHAAGD6c74hIayIQAJMn\nA+PGAd9+y/5+3n2XzZ0zNeU7OtIUpS7V4e3t3WQiOXfu3Csd6GXyLtWRnJyMSZMmITo6Gra2tlLf\ni7r7Woe7d1nLKSGBXWcICKACsERxz56xmo2HDrFKJEuWAFIquhE1pNaTeWtqauDg4ICzZ8/C3Nwc\nAwYMQFhYGJzqtdvT09MxatQoHDx4EAObGOJFSUq9PXnCKgqcPMlaUIsXAx078h0VaWtSU4HVq4HY\nWOCzz4CgIKpcoe6UlqRu3bqFu3fvoqKiQvLYzJkzFQ4wKioKS5cuhVgsxty5c7Fy5UrJMh0ffPAB\n5s2bh2PHjsHKygoAoKOjg/j4+MYnQUlKLYlEwJdfAgcPAh99xC54GxryHRVp6xITWZK6e5d1AU6f\nDrRrx3dURBqlJKmQkBDExsbi9u3b8PPzQ1RUFIYOHYojR44oNVhFUJJSL4WFbOTVzp3AjBmsjBFV\nJyeqduEC+9srKHixlAtNaVAvCpVFqnPkyBGcOXMGPXr0wN69e5GUlITCwkKlBUnajuJidq3J3h7I\nyWHXnv7v/yhBEX4MG8YS1ddfs+7mgQOBqCg2YIe0Hs0mKV1dXbRr1w7a2tooKiqCqakpMjIyVBEb\naSUKCtiHgI0NWxvo/Hlg926gVy++IyOaTiAAfH3ZF6ZPPmFL2A8YAEREULJqLZpNUp6enigoKEBQ\nUBA8PDzg7u6OwYMHqyI2ouaePWNLZ9jZAWlpwOXL7PqToyPfkRHSkJYWq2CSlMS6AENC2Py8I0fY\nnD2ivl5pdN/jx49RUlKCvn37tmRMr4yuSalWTg6wZQtrLU2ezNYA6t2b76gIkR/HAb/9xoauP3/O\npkb87W+Ajg7fkWkWpY3uS0pKQlpaGsRisaQ80qRJk5QWqKIoSanGn3+ydZ0iIoBp04B//AP438BL\nQloljgNOnWKjUB8/Zkvaz5sHdO7Md2SaQSkDJwIDAzF37lwcPXoUv/76K06ePIlff/1VKQE2VwX9\n3r17GDRoEDp27IjNmzcr5Zjk1XAccOYMW6LdxwewtWXzUbZvpwRFWj+BgC1jHxvLSi1duwa88Qb7\nAkaX3tVDsy0pZ2dn3L59+5XKGMlDLBbDwcEBZ86cgYWFBTw9PRtN5n369CmePHmC48ePw8jICJ98\n8on0k6CWlNKVlQHh4cDWrUB1NbvoPG0aTY4kbd+TJ+zvft8+tp7VwoVsZCANX1c+pbSkPD09cefO\nHaUFVSc+Ph62trawtraGjo4OAgICEBER0WCfbt26wcPDAzrUUawy9+8Dy5axVtIvv7Ah5X/+CcyZ\nQwmKaIZevYBvvgEePQL69QNmzmSDLL7/ntaz4oNc3X2DBg2Cvb09XF1d4erqqpSBE9KqoGfR8pu8\nqK5mCenNN1mxzo4dWbfHyZPsmyR9gySayNCQ9SDcvw989RWbY2VlxVpWf/7Jd3SaQ2YV9Dpz587F\nwYMH0adPH2gpsRqosrsPqQr6q7t5k3VphIWxCbgLFrDRetRiIuQFLS3grbfYlpEB/PADu29hAcye\nzQold+3Kd5Stw+tUQW82SZmamsLf3/91Y5LJwsKiwaTgjIwMWFpavvb71U9SRDaRiFWL3r+flS+a\nORO4eJHNdSKENK1nTzZsfc0aNqBo/35WJ3D0aGDWLNbzQFcnZHu5AREaGtrsa5pNUm5ubpg6dSrG\njx+P9u3bA4BShqB7eHggNTUVaWlpMDc3R3h4OMLCwqTuS4MiFPP0KXDsGJu4eO0a8M47rFzRiBG0\nVAYhr0Nbm414HTMGKCoCDh9mXYLz5rEage++C3h7U8JShmZH9wUGBkp9fO/evQofvLkq6Lm5ufD0\n9ERxcTG0tLRgYGCAO3fuQF9fv+FJ0Oi+Rv76iw2pPXIEuH6d/WeaMoV906O1dghpGWlp7P/czz+z\ngRfvvMMS1qhRlLCkUXgyr1gsxooVK9R+jhIlKTaf6eZNNos+MpLV0PP1Zf9BxowB9PT4jpAQzfLk\nCRuQ9PPPwL17bJ6hnx/7okgrCDNKqTgxcOBAXLlyRekDHZRJU5NUfj4QE8OSUmQkayH5+bHkNGIE\nDYAgRF3k5LDRgZGR7FqWvT37v/r224CHB+s+1ERKSVIffvghsrOz8e6770Lvf1/HqSwSPwoL2dID\n586x7eFDYPBg1lLy86PBD4S0BlVVwKVLrNfj9GnWRTh0KDByJNvc3DRnkUalJKnZs2dL3qw+ZVyT\nUpa2mKQ4jvVpX73KtkuX2HyNgQPZBdmRIwFPT+rnJqS1e/qUlWWq+/KZk8O+fA4cCHh5saVF2uqK\n1korMKvuWnuS4jggKwtITmaDHK5eBeLj2aRaLy+2DRrEkhJ14RHStuXmAleuAHFxbEtIYEPf6xKW\nUAi4ugIGBnxHqjilJKmMjAwsXrwYFy9eBAAMHz4cW7duVWhOk7K1piRVVMRaRLdusbVtkpPZ1r49\n0LcvK79Sl5gsLPiOlhDCt5oaVuHi6lU2hSQ5mQ2M6t6dfWYIhWxzdmbFcf83U6hVUEqSevPNNzFt\n2jRMnz4dAHDo0CEcOnQIp0+fVl6kClK3JFVSwvqZU1PZlpLCttRUVvvLzo79cdXfaIl1Qoi8xGL2\neZKczL7sJiWxEYSZmazVZW/fcOvdm33pVbcEppQkJRQKkZSU1OxjryM6OloyT2revHkIDg5utM/i\nxYsRFRUFPT097Nu3D+7u7o32UVWS4jg2eEEkYltmJpCezkqlpKe/uF9VxWp82dm9+COpu29uTrXw\nCCEto6qKXcuu+2KcksJ6btLS2LUuU1P22WRlxQrpWlkBlpasVWZmxjZdXdXFK89nd7MDH7t27Yof\nf/wRU6dOBcdx+Omnn2BiYqJwcGKxGAsXLmywVIe/v3+DpToiIyPx4MEDpKam4urVq1iwYAHi4uIU\nPjYAVFayhCNre/aMTYgViRre6umxX7SZGfvl9uzJmtljxrD7VlaAsTElIkKI6rVvDzg6su1lNTVA\ndjb7Mv3kCbv98082NL7ui7dIxK57109apqaAkVHTm4FBy33mNZuk9uzZg0WLFuHjjz8GAAwePFgp\nI/vqL9UBQLJUR/0kdeLECcyaNQsA4OXlhcLCQohEIphJ6Rv717/YMtBlZU3flpay60JiMfvHNTSU\nvhkbA05OLxKSqSnbOnZU+NQJIUTltLVftKKGDpW+D8exz0eRiA3gEInY6MOCAtYSu32b3X95q6hg\n8zTrNn192bd6eqy1Jm+LrdkkZW1trbSVeOuTtlTH1atXm90nMzNTapKqqgK6dGHdaXp67B9ET6/h\n/bp/QEND9g9ErR1CCHlBIHjxRd3BQf7XVVezRkBdQ+Dl+/Vvy8pYT1V5uXzvLTNJyapOWzdfas2a\nNfKfQRPv05yX+ytlva5duxBUVrJuvL59aakOQghRFR2dF8mtKXVLddQ1IOQhM0l16tSpUUJ4/vw5\ndu/ejby8PIWTlDxLdby8T2ZmJixkjMumpToIIUS9KXWpjuXLl0vuFxcXY9u2bdi7dy8CAgLwySef\nKBYp5Fuqw9/fHzt27EBAQADi4uJgaGgotauPEEJI29TkNalnz55hy5YtOHToEGbOnImEhAQYGRkp\n58Da2tixYwfefvttyVIdTk5ODZbq8PX1RWRkJGxtbdGpUye1KsVECCGk5cmcJ7V8+XIcO3YM8+fP\nx0cffQQDNa7BoW6TeQkhhDRPocm8WlpaaN++PXSkVDAVCAQoLi5WTpRKQEmKEEJaH4Um89bW1io9\nIEIIIeRVaPEdACGEECILJSlCCCFqi5IUIYQQtcVLksrPz4ePjw/s7e3x1ltvobCwUOp+c+bMgZmZ\nGVxdXVUcofqLiYnhOwSVo3PWHJp43pp4zvLgJUlt2LABPj4+SElJwejRo7Fhwwap+wUGBiI6OlrF\n0bUOmvgHTeesOTTxvDXxnOXBS5KqX9181qxZOH78uNT9hg0bprTJw4QQQlofXpJU/eU2zMzMIBKJ\n+AiDEEKImmt2Zd7X5ePjg9zc3EaPf/HFF5g1axYKCgokjxkbGyM/P1/q+6SlpWH8+PG4deuWzGPZ\n2tri4cOHigdNCCFEZWxsbPDgwYMm92l2PanXdfr0aZnPmZmZITc3F927d0dOTg5MTU0VOlZzJ0kI\nIaR14qW7z9/fH/v37wcA7N+/HxMmTOAjDEIIIWqOlyT16aef4vTp07C3t8cff/yBTz/9FACQnZ0N\nPz8/yX7vv/8+Bg8ejJSUFPTs2ZOqoBNCiIZpsWtShBBCiKLaRMWJ1atXQygUws3NDaNHj26wmm9b\n9Y9//ANOTk4QCoWYNGkSioqK+A5JJX7++We4uLigXbt2SEhI4DucFhUdHQ1HR0fY2dlh48aNfIfT\n4jR18n5GRgZGjhwJFxcX9OnTB9u2beM7pBZXUVEBLy8vuLm5wdnZGStXrpS9M9cGFBcXS+5v27aN\nmzt3Lo/RqMapU6c4sVjMcRzHBQcHc8HBwTxHpBp3797l7t+/z3l7e3M3btzgO5wWU1NTw9nY2HCP\nHz/mqqqqOKFQyN25c4fvsFrU+fPnuYSEBK5Pnz58h6JSOTk5XGJiIsdxHFdSUsLZ29u3+d81x3Hc\n8+fPOY7juOrqas7Ly4u7cOGC1P3aREuq/oKMpaWlMDEx4TEa1fDx8YGWFvv1eXl5ITMzk+eIVMPR\n0RH29vZ8h9Hi4uPjYWtrC2tra+jo6CAgIAARERF8h9WiNHXyfvfu3eHm5gYA0NfXh5OTE7Kzs3mO\nquXp6ekBAKqqqiAWi2FsbCx1vzaRpADgs88+g5WVFfbv3y8ZiKEp9uzZA19fX77DIEqUlZWFnj17\nSn62tLREVlYWjxERVUhLS0NiYiK8vLz4DqXF1dbWws3NDWZmZhg5ciScnZ2l7tdqkpSPjw9cXV0b\nbb/++isANkk4PT0ds2fPxrJly3iOVjmaO2eAnXf79u0xdepUHiNVLnnOu60TCAR8h0BUrLS0FFOm\nTMHWrVv9aBA+AAAgAElEQVShr6/PdzgtTktLCzdv3kRmZibOnz8vs3Zhi03mVbamJgfXN3Xq1DbT\nqmjunPft24fIyEicPXtWRRGphry/67bMwsKiwQCgjIwMWFpa8hgRaUnV1dWYPHkypk+frnHzRrt0\n6QI/Pz9cv34d3t7ejZ5vNS2ppqSmpkruR0REwN3dncdoVCM6Ohpff/01IiIi0LFjR77D4QXXhmdP\neHh4IDU1FWlpaaiqqkJ4eDj8/f35Dou0AI7jMHfuXDg7O2Pp0qV8h6MSeXl5kiWaysvLcfr0admf\n26oby9FyJk+ezPXp04cTCoXcpEmTOJFIxHdILc7W1pazsrLi3NzcODc3N27BggV8h6QSR48e5Swt\nLbmOHTtyZmZm3JgxY/gOqcVERkZy9vb2nI2NDffll1/yHU6LCwgI4Hr06MG1b9+es7S05Pbs2cN3\nSCpx4cIFTiAQcEKhUPL/OSoqiu+wWlRycjLn7u7OCYVCztXVlfvqq69k7kuTeQkhhKitNtHdRwgh\npG2iJEUIIURtUZIihBCitihJEUIIUVuUpAghhKgtSlKEEELUFiUpQgghaouSFCGEELVFSYoQNXTt\n2jUIhUJUVlbi+fPn6NOnD+7cucN3WISoHFWcIERNrV69GhUVFSgvL0fPnj0RHBzMd0iEqBwlKULU\nVHV1NTw8PKCrq4srV67Q8h1EI1F3HyFqKi8vD8+fP0dpaSnKy8v5DocQXlBLihA15e/vj6lTp+LR\no0fIycnB9u3b+Q6JEJVrNYseEqJJDhw4gA4dOiAgIAC1tbUYPHgwYmJipC4KR0hbRi0pQgghaouu\nSRFCCFFblKQIIYSoLUpShBBC1BYlKUIIIWqLkhQhhBC1RUmKEEKI2qIkRQghRG1RkiKEEKK2KEkR\nQghRW5SkCGmFvL29sXv3br7DIKTFUZIiRApra2uYmZmhrKxM8tiuXbswcuRIHqN6QSAQNLl0R0pK\nCt59911069YNhoaGEAqF2LJlC2pra5GWlgYtLS0YGBjAwMAA3bt3x/jx43HmzJkG72FtbQ09PT3J\nfp07d0Zubm5LnxohDVCSIkSG2tpabN26VeH34TgOqiyR+fDhQ3h5eaFXr174888/UVhYiJ9//hk3\nbtxAaWmpZL+ioiKUlJQgOTkZPj4+mDhxIvbv3y95XiAQ4OTJkygpKUFJSQmKi4vRvXt3lZ0HIQAl\nKUKkEggEWL58OTZt2oSioiKp+1y+fBmenp4wNDTEgAEDcOXKFclz3t7eWLVqFYYMGQJ9fX08evQI\nWlpa2LlzJ+zs7NC5c2esWbMGDx8+xKBBg2BoaIiAgABUV1cDAAoLCzFu3DiYmprC2NgY48ePR1ZW\nllyxr127FkOHDsWmTZtgZmYGALC3t8fBgwfRuXPnRvubmppi8eLFCAkJodV/idqhJEWIDB4eHvD2\n9samTZsaPZefnw8/Pz8sXboU+fn5+Pjjj+Hn54eCggLJPgcPHsSuXbtQUlICKysrAMCpU6eQmJiI\nuLg4bNy4EUFBQQgLC0N6ejpu3bqFsLAwAKwVN3fuXKSnpyM9PR26urpYuHChXHGfPXsWU6ZMeeXz\nnThxIv766y/cv39f8hgtkkD4RkmKEBkEAgHWrVuH7du3Iy8vr8Fzv/32GxwcHDBt2jRoaWkhICAA\njo6OOHHihOS1s2fPhpOTE7S0tKCjowMAWLFiBfT19eHs7AxXV1eMHTsW1tbW6Ny5M8aOHYvExEQA\ngLGxMSZOnIiOHTtCX18f//znPxEbGytX3M+ePUOPHj1e+XzNzc0BsAQMsAQ1YcIEGBkZwcjICJMm\nTXrl9yREUbToISFNcHFxwbhx47BhwwY4OTlJHs/Ozpa0jur06tUL2dnZkp979uzZ6P3qut8AQFdX\nt9HPdQMTysrKsGzZMvz++++S1llpaSk4jmtywAQAdO3atUEc8qrrTjQ2NgbAEm1ERARGjRr1yu9F\niLJQS4qQZoSGhuKHH35ocE3IwsICT548abDfkydPYGFhIfm5uWTSlM2bNyMlJQXx8fEoKipCbGys\n3AMw3nzzTfzyyy+vfMxjx47BzMwMDg4OrxMyIS2CkhQhzbCxscF7773XYKTf2LFjkZKSgrCwMNTU\n1CA8PBz37t3DuHHjJPvIk1Dq71P/fmlpKXR1ddGlSxfk5+cjNDS0ydfWFxoaisuXL2PFihUQiUQA\ngAcPHmDGjBkoLi5u9HqRSIQdO3Zg3bp1WL9+fbMxE6JKlKQIkcOaNWtQVlYmaR117doVJ0+exObN\nm2FiYoJNmzbh5MmTkq4yoHFLSlrLqv5j9ec+LV26FOXl5TAxMcHgwYMxduxYud4PAHr37o0rV64g\nLS0NLi4uMDQ0xJQpU+Dp6Ql9fX3JfoaGhtDX10ffvn0RHR2NI0eOYPbs2a/2D0NICxNwPA7fmTNn\nDn777TeYmpri1q1bjZ4/dOgQvvrqK3AcBwMDA+zcuRN9+/blIVJCCCF84LUlFRgYiOjoaJnP9+7d\nG+fPn0dycjJWr16N+fPnqzA6QgghfOM1SQ0bNgxGRkYynx80aBC6dOkCAPDy8kJmZqaqQiOEEKIG\nWs01qd27d8PX15fvMAghhKhQq5gnde7cOezZsweXLl2S+rybmxuSkpJUHBUhhBBFCIVC3Lx5s8l9\n1L4llZycjKCgIJw4cUJm12BSUpJkDommbGvXruU9BjpnOmc6bzpnRTZ5GhdqnaTS09MxadIkHDx4\nELa2tnyHQwghRMV47e57//33ERsbi7y8PPTs2ROhoaGSKtAffPAB1q1bh4KCAixYsAAAoKOjg/j4\neD5DJoQQokK8Jqm6is+y7Nq1C7t27VJRNK2Lt7c33yGoHJ2z5tDE89bEc5YHr5N5lUUgEKANnAYh\nhGgUeT671fqaFCGEEM1GSYoQQoja4i1JzZkzB2ZmZnB1dZW5z+LFi2FnZwehUChZDI4QQojm4C1J\nNVe3LzIyEg8ePEBqaiq+//57yQg/QgghmkOu0X13795FWloatLS00KtXLzg6Oip84GHDhiEtLU3m\n8ydOnMCsWbMAsLp9hYWFEIlEDVYyJYQQ0rbJTFKPHz/Gli1bEBkZCQsLC5ibm4PjOOTk5CAzMxPj\nxo3DsmXLYG1t3SKBZWVlNVh+29LSEpmZmZSkCCGkFeM4ttXWyre/zCQVHByMoKAgbN68GTo6Og2e\nq66uxrlz57BixQocPnxYoYCb8vLQxKaW4w4JCZHc9/b2pjkHhJA2geOAsjKgtJRtZWVARcWLrbKy\n4c+ynquuBmpq2Fb/fnM/178vFrPkUn+rSzjybGJxDICYVzp/XudJpaWlYfz48VIXPPzwww/h7e2N\ngIAAAICjoyNiY2OltqRonhQhRB3V1AAFBQ23/PzGj5WWAiUlLxJR/a2sDOjYEdDXZ1unTkCHDuyx\nuu3ln19+rEMHQEeHbdraL7b6Pzf3XLt27L6W1otNIGj4szybQMA2QL7P7mavSa1atQohISHQ1ma7\nFhUVYcmSJdi3b5/Cv8Cm+Pv7Y8eOHQgICEBcXBwMDQ2pq48Qwrvnz4GsLOCvvwCRSPb29ClLMF26\nAEZGgLExu62/9egBODkBnTu/SEL6+oCBwYv7enosQWiqZpOUWCzGgAEDsHfvXohEIixatAgLFy5U\n+MDN1e3z9fVFZGQkbG1t0alTJ+zdu1fhYxJCSFNqaoCMDODJE3YrbSsvB8zNATOzhlvfvg1/7taN\nJR8tmo2qELm6+86cOYPx48fDyMgIsbGxsLOzU0VscqPuPkKIvKqqgMePgQcPgIcP2W3dlp4OmJoC\nvXoBPXs23Kys2G3Xri+6q4hi5PnsbjZJxcbGYsGCBZg+fTpu3bqFwsJC7Nq1CxYWFkoNVhGUpAgh\nL6usBO7fB27fBu7cYbe3b7NWkqUlYGvbeLO2ZtdwiGooJUkNGDAA+/btg7OzMwDg6NGjWLlyJe7f\nv6+8SBVESYoQzfbXX0BCwovtzz9ZMnrjDcDZGXBxebHZ2QHt2/MdMQGUlKRqamokgybq5OXlwcTE\nRPEIlYSSFCGaQyQCrl0Dbtx4kZRKSoB+/V5sffsC9vaUjNSdQklq3759mD59eqMEVaeqqgqHDh1C\nYGCg4pEqiJIUIW2TWMxaRZcvv9jy8wFPT6B/f5aQ+vdnLSa6TtT6KDQEvbS0FJ6ennB0dISnpye6\nd+8OjuOQm5uL69ev4969ewgKClIowOjoaCxduhRisRjz5s1DcHBwg+fz8vIwffp05ObmoqamBsuX\nL8fs2bMVOiYhRH1VVABXrgCxsSwhXb3KhmkPHgyMGAGsXAk4OtKIOU3SZHcfx3G4dOkSLl68iPT0\ndABAr169MHToUAwePLjJChDNEYvFcHBwwJkzZ2BhYQFPT0+EhYXByclJsk9ISAgqKyuxfv165OXl\nwcHBASKRqFHrjlpShLRO1dWs6+6PP4Bz54D4eHbdyNsbGDoUGDgQUKMrC0TJFJ7MKxAIMHToUAwd\nOlSpgQFAfHw8bG1tJbX/AgICEBER0SBJ9ejRA8nJyQCA4uJidO3aVWb3IyFE/XEcG2kXHQ2cPQtc\nvAjY2ACjRgEffwwMG8bmFhFSR2aj+a233pLcX79+vdIPLK2AbFZWVoN9goKCcPv2bZibm0MoFGLr\n1q1Kj4MQ0rJKS4ETJ4APP2RDvP382JykefPYfKXERGDzZvY4JSjyMpnNkqdPn0ruHz58GCtXrlTq\ngeXpKvzyyy/h5uaGmJgYPHz4ED4+PkhKSoKBgUGjfanALCHqIzUVOHkSiIpi15gGDAB8fYElS9g1\nJRrkoJliYmIQExPzSq/hre/MwsICGRkZkp8zMjJgaWnZYJ/Lly/js88+AwDY2NjgjTfewP379+Hh\n4dHo/eonKUKIanEcaxEdOwYcPcqKpo4bB3z0EfDLL6wWHSEvNyBCQ0ObfY3MJPXo0SP4+/uD4zg8\nfvwY48ePlzwnEAhw4sQJhYL18PBAamoq0tLSYG5ujvDwcISFhTXYx9HREWfOnMGQIUMgEolw//59\n9O7dW6HjEkKUQywGLl1iSen4cVYpe+JEYNcuwMuLRuAR5ZA5uq+pJplAIMCIESMUPnhUVJRkCPrc\nuXOxcuVKfPfddwBYkdm8vDwEBgYiPT0dtbW1WLlyJaZOnSo1HhrdR0jLE4vZ8PCffmKJycKCJaaJ\nE4E+fagbj7wapVScAF5cn+rWrZtyIlMySlKEtByOA+LiWGI6fJhVAA8IAKZMYZNoCXldCg1B5zgO\noaGh2LFjB8RiMQCgXbt2WLRoEdauXavcSAkhaoXjgORklph++okVXX3/fSAmBnBw4Ds6oklk9hpv\n2bIFly5dwrVr11BQUICCggLEx8fj0qVL+Oabb1QZIyFERZ48AT7/nE2ofecdlqyOH2dzm9asoQRF\nVE9md5+bmxtOnz7dqIvv6dOn8PHxwc2bN1USoDyou4+Q11daygY/7NvHWk9/+xswYwar9kDXmEhL\nkuezW2ZLqqamRuo1qG7duqGmpkbx6MBq9zk6OsLOzg4bN26Uuk9MTAzc3d3Rp08fmvtEiJLU1rKu\nu9mz2UJ+hw+z4eJZWcC//w0MGkQJiqgHmdekdHR0ZL6oqefkJRaLsXDhwga1+/z9/RuURSosLMTf\n//53/P7777C0tEReXp7CxyVEkz18COzfD/z4I5u7NHs2sGED0L0735ERIp3MJJWcnCy1sgMAlJeX\nK3xgeWr3/fe//8XkyZMlk3zVaQ0rQlqL8nLg55/Z/KV794CpU1n3npsbtZaI+pOZpOpG9LUUabX7\nrl692mCf1NRUVFdXY+TIkSgpKcGSJUswY8aMFo2LkLYiORn44Qfgv/9lk2uXLWP18WghQNKayExS\n8fHxyMvLg6+vb4PHIyMjYWZmhv79+yt0YHlq91VXVyMhIQFnz55FWVkZBg0ahIEDB8LOzq7RvlS7\njxA2CCI8HPj+eyA7G5gzh61c26sX35ERouTafcHBwdi7d2+jx52dnREYGIhz5869coD1yVO7r2fP\nnjAxMYGuri50dXUxfPhwJCUlNZukCNE0N26wxHT4MDB8OBsuPmYM0K4d35ER8sLr1O6TObqvpKRE\ncr2oPmtra6UMYKhfu6+qqgrh4eHw9/dvsM8777yDixcvQiwWo6ysDFevXoWzs7PCxyakLSgqAnbu\nZEuoT57MRun9+ScQEcG69ShBkbZAZkuqsLBQ5ouUMXBCW1sbO3bswNtvvy2p3efk5NSgdp+joyPG\njBmDvn37QktLC0FBQZSkiEarK1H0ww+s4vjo0Wx03ptvUkFX0jbJnMz7wQcfwMTEBJ9//rnk+lFt\nbS3Wrl0LkUiE77//XqWBNoUm85K2rqCADRv/4QegogIICgJmzQLMzPiOjJDXp1CB2dLSUsybNw/x\n8fFwc3MDACQlJcHDwwO7du2SOTydD5SkSFvEcWzBwO++Y114Y8cC8+cDI0ZQq4m0DUqpgv7w4UPc\nvn0bAoEALi4uarmeEyUp0pYUFrJW0/ffA5WVLDHNmgWo6SIEhLw2hZLUjRs3JN18dbvUHzber18/\nZcWpMEpSpLWru9b03XesoOuYMcAHHwDe3jThlrRdCiUpb2/vJucyKToEHWC1++oWPZw3bx6Cg4Ol\n7nft2jUMGjQIhw8fxqRJkxo9T0mKtFaFhcDBg6zVVF7OWk2zZ1OriWgGpS162BLEYjEcHBwa1O4L\nCwtrUBapbj8fHx/o6ekhMDAQkydPbvRelKRIa8JxwNWrrNV07Bjw9tsvWk10rYloEoUWPazv1q1b\nuHv3LioqKiSPzZw5U6Hg5KndBwDbt2/HlClTcO3aNYWORwjfiopetJqeP2etpo0bAVNTviMjRH01\nm6RCQkIQGxuL27dvw8/PD1FRURg6dKjCSUqe2n1ZWVmIiIjAH3/8gWvXrslVSokQdVI3Qm/3blbU\n1ccH2LwZGDWKWk2EyKPZJHXkyBEkJSWhX79+2Lt3L0QiEaZNm6bwgeVJOEuXLsWGDRskTULq0iOt\nRW4uG6G3Zw9bu2nOHFaBnOY1EfJqmk1Surq6aNeuHbS1tVFUVARTU9MGNfdelzy1+27cuIGAgAAA\nQF5eHqKioqCjo9OofBJABWYJ/6qrgagolphiY4GJE9nyGIMH0wg9QoDXKzDb7MCJjz76CF988QXC\nw8OxefNmdOrUCe7u7lKLz76KmpoaODg44OzZszA3N8eAAQOkDpyoExgYiPHjx9PoPqJ27t1jienH\nH4HevYG5c4F332WLChJCZFPKwIl///vfAIAPP/wQb7/9NkpKStC3b1+Fg5Ondh8h6qqwEDhyBNi7\nF3j0CJg5Ezh3DnB05DsyQtoWuYagJyUlIS0tDWKxGBzHQSAQSG3R8IVaUkQVqqpYd97Bg8CpU6yo\n68yZgK8voKPDd3SEtD5KaUkFBgbi1q1bcHFxgVa94UjqlKQIaSl1o/MOHmRLsDs5AdOnszlOxsZ8\nR0dI29dskrp69aqkdh8hmiIlBTh0iCUnHR1gxgwgPh544w2+IyNEszSbpDw9PXHnzh24uLioIh5C\neJOaylpLP/8M5OQAAQFsKfb+/Wl0HiF8afaaVExMDPz9/dG9e3d06NCBvUggQHJyskoClAddkyKv\n68EDlpQOH2aJafJkNjJv2DBa2ZaQlqaU2n02NjbYsmUL+vTp0+CalLSl5V9VcwVmDx06hK+++goc\nx8HAwAA7d+6UOrKQkhSRF8exIePHj7PklJ1NiYkQviglSQ0aNAhXrlxRamCAfAVmr1y5AmdnZ3Tp\n0gXR0dEICQlBXFxc45OgJEWaUFMDXLoEnDjBtspKYPx4YMoUYPhwSkyE8EUpo/vc3NwwdepUjB8/\nHu3bt5e8saKj++QpMDto0CDJfS8vL2RmZip0TKI5SkqA339nSSkyErCyAt55h3XrubnRNSZCWotm\nk1RFRQU6dOiAU6dONXhc0SQlT4HZ+nbv3g1fX1+FjknartpaIDGRJaZTp4AbN1g5onfeAb74Aqj3\np0YIaUWaTFJisRjGxsbYvHmz0g/8KkPaz507hz179uDSpUsy96HafZonJ4clpN9/B06fBrp2ZWsz\nrVgBjBgBdOrEd4SEkPpep3Zfk0mqXbt2uHTpkqTKhDLJU2AWAJKTkxEUFITo6GgYGRnJfL/6SYq0\nTTk5rHDr+fPsNicHGD0aeOstYP16oFcvviMkhDTl5QZEaGhos69pduDEhx9+iOzsbLz77rvQ09Nj\nL1LCNSl5Csymp6dj1KhROHjwIAYOHCj7JGjgRJuUkcGSUd2Wl8dG4I0YwTahENCWa9lOQog6UsrA\niYqKChgbG+OPP/5o8LiiSUqeArPr1q1DQUEBFixYAADQ0dFBfHy8Qscl6un5c+D6dbaset1WWclG\n340YASxcCLi60kKBhGgauQrMqjtqSbUuFRXA7dvAzZus1FBcHJtU6+oKeHm92Hr3plF4hLRlSpkn\nlZGRgcWLF+PixYsAgOHDh2Pr1q1Srx/xhZKU+srNBZKS2HbzJrt99Aiws2PddQMGsIQkFAL/K2hC\nCNEQSklSb775JqZNm4bp06cDYFUgDh06hNOnTysvUgVRkuKXWAw8ecIqOdTf7t5lQ8OFQra5ubFb\nJydKSIQQJSUpoVCIpKSkZh/jEyWplldeDqSlAY8fN9xSU9lmasoW/Ht5696duuwIIdIpZeBE165d\n8eOPP2Lq1KngOA4//fQTTExMlBJgc7X7AGDx4sWIioqCnp4e9u3bB3d3d6Ucm7xQWclq2NXfsrLY\nVpeM8vNZ1YY33nixeXoC9vZsozlJhJCW0GxLKi0tDYsWLZLUzBs8eDC2b98OKysrhQ4sT+2+yMhI\n7NixA5GRkbh69SqWLFlCtfvkIBazpJKXJ3sTiV4kpOJioEcPwNy84WZh8SIhmZvTyDpCiHIppSVl\nbW2NX3/9VWlB1ZGndt+JEycwa9YsAKx2X2FhIUQiEczMzJQeD584ji1NXlbGutVevi0pYYmkqIjd\n1r//8mOFhezW0BAwMWm89ejBRtF168aSkLk5e5wSECFEHclMUrJmAtdVnlizZo1CB5andp+0fTIz\nM6UmqevX2UX62lrWkqi7L+3n19lHLGbVtKuqgOrqxrfSHpN2W17eMAHVbdragK4uoKfX8FZXF+jc\n+cXWpQu7tbBo/Fjnziw5GRlRZW9CSNsgM0l16tSpUSmk58+fY/fu3cjLy1M4SclbZunlpqCs1/n7\nh0AgYBfpu3TxhrGxN7S00GBr167pn5vbR0eHbe3bs9uOHQEDg4aPvXz78v2Xk1DdLSUVQkhbp9Ta\nfcuXL5fcLy4uxrZt27B3714EBATgk08+ee0g68hTu+/lfTIzM2FhYSH1/bKzQxSOiRBCSMt5ndp9\nTV6JePbsGVatWgWhUIjq6mokJCRg48aNMDU1VThYDw8PpKamIi0tDVVVVQgPD4e/v3+Dffz9/XHg\nwAEAQFxcHAwNDdvc9ShCCCGyNdmSOnbsGObPn4/k5GQYGBgo98By1O7z9fVFZGQkbG1t0alTJ+zd\nu1epMRBCCFFvMoega2lpoX379tDR0Wn8IoEAxcXFLR6cvGgIOiGEtD4KDUGvra1VekCEEELIq6DZ\nMYQQQtQWJSlCCCFqi5IUIYQQtcVLksrPz4ePjw/s7e3x1ltvobCwsNE+GRkZGDlyJFxcXNCnTx9s\n27aNh0jV16tOiGsL6Jw1hyaetyaeszx4SVIbNmyAj48PUlJSMHr0aGzYsKHRPjo6OtiyZQtu376N\nuLg4fPvtt7h79y4P0aonTfyDpnPWHJp43pp4zvLgJUnVLxw7a9YsHD9+vNE+3bt3h5ubGwBAX18f\nTk5OyM7OVmmchBBC+MVLkqpfydzMzAwikajJ/dPS0pCYmAgvLy9VhEcIIURNNLue1Ovy8fFBbm5u\no8e/+OILzJo1CwUFBZLHjI2NkZ+fL/V9SktL4e3tjVWrVmHChAlS97G1tcXDhw+VEzghhBCVsLGx\nwYMHD5rcp9n1pF7X6dOnZT5nZmaG3NxcdO/eHTk5OTJrAVZXV2Py5MmYPn26zAQFoNmTJIQQ0jrx\n0t3n7++P/fv3AwD2798vNQFxHIe5c+fC2dkZS5cuVXWIhBBC1ECLdfc1JT8/H3/729+Qnp4Oa2tr\nHD58GIaGhsjOzkZQUBB+++03XLx4EcOHD0ffvn0la0itX78eY8aMUXW4hBBCeMJLkiKEEELk0SYq\nTqxevRpCoRBubm4YPXp0g4US26p//OMfcHJyglAoxKRJk1BUVMR3SCrx888/w8XFBe3atUNCQgLf\n4bSo6OhoODo6ws7ODhs3buQ7nBY3Z84cmJmZwdXVle9QVEoTCxdUVFTAy8sLbm5ucHZ2xsqVK2Xv\nzLUBxcXFkvvbtm3j5s6dy2M0qnHq1ClOLBZzHMdxwcHBXHBwMM8Rqcbdu3e5+/fvc97e3tyNGzf4\nDqfF1NTUcDY2Ntzjx4+5qqoqTigUcnfu3OE7rBZ1/vx5LiEhgevTpw/foahUTk4Ol5iYyHEcx5WU\nlHD29vZt/nfNcRz3/PlzjuM4rrq6mvPy8uIuXLggdb820ZKqvyBjaWkpTExMeIxGNXx8fKClxX59\nXl5eyMzM5Dki1XB0dIS9vT3fYbS4+Ph42NrawtraGjo6OggICEBERATfYbWoYcOGwcjIiO8wVE5T\nCxfo6ekBAKqqqiAWi2FsbCx1vzaRpADgs88+g5WVFfbv349PP/2U73BUas+ePfD19eU7DKJEWVlZ\n6Nmzp+RnS0tLZGVl8RgRUQVNKlxQW1sLNzc3mJmZYeTIkXB2dpa6X6tJUj4+PnB1dW20/frrrwDY\nJOH09HTMnj0by5Yt4zla5WjunAF23u3bt8fUqVN5jFS55Dnvtq5uRCvRHKWlpZgyZQq2bt0KfX19\nvsNpcVpaWrh58yYyMzNx/vx5mbULW2wyr7I1NTm4vqlTp7aZVkVz57xv3z5ERkbi7NmzKopINeT9\nXYNrI5kAAAJESURBVLdlFhYWDQYAZWRkwNLSkseISEuSt3BBW9SlSxf4+fnh+vXr8Pb2bvR8q2lJ\nNSU1NVVyPyIiAu7u7jxGoxrR0dH4+uuvERERgY4dO/IdDi+4Njx7wsPDA6mpqUhLS0NVVRXCw8Ph\n7+/Pd1ikBXAaWLggLy9PskRTeXk5Tp8+LftzW3VjOVrO5MmTuT59+nBCoZCbNGkSJxKJ+A6pxdna\n2nJWVlacm5sb5+bmxi1YsIDvkFTi6NGjnKWlJdexY0fOzMyMGzNmDN8htZjIyEjO3t6es7Gx4b78\n8ku+w2lxAQEBXI8ePbj27dtzlpaW3J49e/gOSSUuXLjACQQCTigUSv4/R0VF8R1Wi0pOTubc3d05\noVDIubq6cl999ZXMfWkyLyGEELXVJrr7CCGEtE2UpAghhKgtSlKEEELUFiUpQgghaouSFCGEELVF\nSYoQQojaoiRFCCFEbVGSIoQQorYoSRGihq5duwahUIjKyko8f/4cffr0wZ07d/gOixCVo4oThKip\n1atXo6KiAuXl5ejZsyeCg4P5DokQlaMkRYiaqq6uhoeHB3R1dXHlyhVavoNoJOruI0RN5eXl4fnz\n5ygtLUV5eTnf4RDCC2pJEaKm/P39MXXqVDx69Ag5OTnYvn073yERonKtZtFDQjTJgQMH0KFDBwQE\nBKC2thaDBw9GTEyM1EXhCGnLqCVFCCFEbdE1KUIIIWqLkhQhhBC1RUmKEEKI2qIkRQghRG1RkiKE\nEKK2KEkRQghRW5SkCCGEqK3/B5sXRnCxOLIbAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x6187970>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "demo_normcdf and demo_normpdf - Lecture 2.4"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We consider a normal distrubtion with mean mu and standard deviation sigma."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mu = 4\n",
      "sigma = 2\n",
      "\n",
      "alpha = 4\n",
      "xMin = mu - alpha*sigma\n",
      "xMax = mu + alpha*sigma\n",
      "\n",
      "nPlot = 1000\n",
      "xPlot = linspace(xMin,xMax,nPlot)\n",
      "normPDF = norm.pdf(xPlot,mu,sigma) # the mean and standard deviation are passed as arguments to the pdf and cdf functions.\n",
      "normCDF = norm.cdf(xPlot,mu,sigma)\n",
      "def plotFigures(): # We use this figure again below\n",
      "    plt.figure()\n",
      "    ax = plt.subplot(211)\n",
      "    ax.set_title('Normal CDF')\n",
      "    ax.set_xlabel('x')\n",
      "    ax.set_ylabel('NormalCDF(x)')\n",
      "    plt.plot(xPlot, normCDF);\n",
      "    ax.set_ybound(0,1.02)\n",
      "    \n",
      "    ax = plt.subplot(212)\n",
      "    plt.plot(xPlot, normPDF)\n",
      "    ax.set_title('Normal PDF')\n",
      "    ax.set_xlabel('x')\n",
      "    ax.set_ylabel('NormalPDF(x)')\n",
      "    ax.set_ybound(0,1.1*norm.pdf(mu,mu,sigma))\n",
      "    \n",
      "    plt.tight_layout()\n",
      "plotFigures()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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nR2ilKi5uc9/7rD5JbdiwAVdXV7p166Z3KOW2atUqhg0bpncYxSpuUnVaWpqO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\nNE3VJHvpJTUScN48aN9e76hqt0pLUiV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       "text": [
        "<matplotlib.figure.Figure at 0x5bbbc10>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next we plot symmetric intervals around the mean for the PDF and CDF: $[\\mu - \\alpha \\sigma, \\mu + \\alpha \\sigma]$ with $\\alpha$ integer.\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mu = 4\n",
      "sigma = 2\n",
      "\n",
      "plotFigures()\n",
      "for alpha in range(0,4):\n",
      "    xLower = mu - alpha * sigma\n",
      "    xUpper = mu + alpha * sigma\n",
      "    \n",
      "    cdfLower = norm.cdf(xLower, mu, sigma)\n",
      "    cdfUpper = norm.cdf(xUpper, mu, sigma)\n",
      "    plt.subplot(211)\n",
      "    plt.plot([xLower, xLower], [0, cdfLower], 'k:')\n",
      "    plt.plot([xMin, xLower], [cdfLower, cdfLower], 'k:')\n",
      "    plt.plot([xUpper, xUpper], [0, cdfUpper], 'k:')\n",
      "    plt.plot([xMin, xUpper], [cdfUpper, cdfUpper], 'k:')\n",
      "    \n",
      "    plt.subplot(212)\n",
      "    plt.plot([xLower, xLower], [0, norm.pdf(xLower,mu,sigma)], 'k:')\n",
      "    plt.plot([xUpper, xUpper], [0, norm.pdf(xUpper,mu,sigma)], 'k:')\n",
      "\n",
      "plt.tight_layout()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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5opVk6tXTJldt2FBrE7p2K7rdsCE0awaurn/dXFygVq2/fm9GnE/OiDGD9i3Z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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5bbbc30>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "demo_normpdf"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This demo again plots symmetric intervals around the mean"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mu    = 4\n",
      "sigma = 2\n",
      "\n",
      "alpha = 4\n",
      "xMin = mu - alpha*sigma\n",
      "xMax = mu + alpha*sigma\n",
      "\n",
      "nPlot = 1000\n",
      "xPlot = linspace(xMin,xMax,nPlot)\n",
      "\n",
      "normalPdf = norm.pdf(xPlot,mu,sigma);\n",
      "\n",
      "fig = plt.figure()\n",
      "plt.plot(xPlot, normPDF)\n",
      "ax = fig.get_axes()[0]\n",
      "ax.set_title('Normal PDF')\n",
      "ax.set_xlabel('x')\n",
      "ax.set_ylabel('NormalPDF(x)')\n",
      "ax.set_ybound(0,1.1*norm.pdf(mu,mu,sigma))\n",
      "\n",
      "for alpha in [0,1,2,3]:\n",
      "   xLower = mu-alpha*sigma\n",
      "   xUpper = mu+alpha*sigma\n",
      "   plot([xLower, xLower],[0, norm.pdf(xLower,mu,sigma)],'k:');\n",
      "   plot([xUpper, xUpper],[0, norm.pdf(xUpper,mu,sigma)],'k:');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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OW86jyO3hh9UufmfPqm1fhbjzl+iYmJhinW+1pqfQ0FAOHTpEcnIy169fZ+nSpURGRuZ7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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb8a6290>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "demo_graphicalComparisonPdf -- Lecture 2.5"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If $Log[S]$ is normally distributed we write $\\log[S] \\sim N(\\mu, \\sigma)$. Then the distribution of $S$ is lognormal, denoted $S\\sim \\log N(\\mu, \\sigma)$.\n",
      "\n",
      "We generate lognormal data as"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random.seed(99)\n",
      "mu    = 1\n",
      "sigma = 0.5\n",
      "\n",
      "M = 1e3  # sample size\n",
      "S = np.exp(mu + sigma*random.randn(M))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Sample estimates of input parameters of the distribution are"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hat_mu    = np.mean(np.log(S))\n",
      "hat_sigma = np.std(np.log(S))\n",
      "print hat_mu, hat_sigma"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.02927514347 0.501400277218\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next we graphically compare the sample to the true distribution. For this we define a function graphicalComparisonPdf."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def graphicalComparisonPdf(X, modelPdf, scale = True, xMin = None, xMax = None):\n",
      "    _X = X[np.logical_not(np.isnan(X))]\n",
      "    if xMax is None:\n",
      "        xMax = np.max(_X) # default parameter of xMax\n",
      "    if xMin is None:\n",
      "        xMin = np.min(_X) # default parameter of xMin\n",
      "    nPlot = 1000\n",
      "    xPlot = np.linspace(xMin, xMax, nPlot)\n",
      "    yPlot = modelPdf(xPlot)\n",
      "    \n",
      "    nBins = np.min([np.sqrt(X.size), 40])  \n",
      "    widthHistogram          = np.max(_X)- np.min(_X)\n",
      "    averageHeightHistogram  = _X.size/nBins\n",
      "    areaHistogram           = widthHistogram*averageHeightHistogram\n",
      "    \n",
      "    pdfScaleFactor = areaHistogram if not scale else 1 \n",
      "    # if scale = False we rescale modelPDF(x) by the area of the histogram\n",
      "    # if scale = True the histogram is scaled, such that its area is 1 (as is the case for modelPDF(x))\n",
      "    \n",
      "    fig = plt.figure()\n",
      "    ax = fig.add_subplot(111)\n",
      "    _, _, p = plt.hist(_X, bins=nBins, normed = scale)\n",
      "    l, = plt.plot(xPlot, yPlot * pdfScaleFactor, 'r', linewidth=3)\n",
      "    \n",
      "    ax.set_xlabel('x')\n",
      "    ax.set_ylabel('pdf(x)')\n",
      "    if scale:\n",
      "        plt.legend([l, p[0]], ['pdf(x)', 'scaled histogram'])\n",
      "    else:\n",
      "        plt.legend([l, p[0]], ['scaled pdf(x)', 'histogram'])\n",
      "    plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We now want to compare our sample distribution to the exact lognormal distribution. scipy.stats again comes with a built-in lognormal distribution:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.stats import lognorm"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "However, this function is **not** the same as the matlab function lognpdf (or rather lognorm.pdf is not the same as matlab's lognpdf). In fact, the lognormal distribution of scipy.stats is a bit tricky, see here for more info:\n",
      "\n",
      "http://nbviewer.ipython.org/url/xweb.geos.ed.ac.uk/~jsteven5/blog/lognormal_distributions.ipynb\n",
      "\n",
      "The numpy version of Matlab's lognpdf can be defined in two ways: in terms of elementary functions, or by rescaling lognorm.pdf."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def lognpdf_1(x,mean,sig):\n",
      "    return np.where((x > 0) & np.isfinite(x) , np.exp(-(np.log(x)-mean)**2/(2.*sig**2)) /(x*sig*np.sqrt(2*np.pi)), 0 )\n",
      "\n",
      "def lognpdf_2(x,mean,sig):\n",
      "    return lognorm.pdf(x, scale = np.exp(mean), s = sig)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "These funtions create the same pdf."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def lognpdf_fixed_mu_sigma_1(x):\n",
      "    return lognpdf_1(x, hat_mu, hat_sigma)\n",
      "def lognpdf_fixed_mu_sigma_2(x):\n",
      "    return lognpdf_2(x, hat_mu, hat_sigma)\n",
      "\n",
      "graphicalComparisonPdf(S, lognpdf_fixed_mu_sigma_1)\n",
      "plt.show()\n",
      "graphicalComparisonPdf(S, lognpdf_fixed_mu_sigma_2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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4kteQRCGEqIq9351V3qMoTQCbN1e8QfrRRx9Z1Wl0yt+fcIa1squxiZHmstyn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\nkkQhhBCiWv8PIro4BgI2GqQAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x63ad850>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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4kteQRCGEqIq9351V3qMoTQCbN1e8QfrRRx9Z1Wl0yt+fcIa1squxiZHmstyn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\nkkQhhBCiWv8PIro4BgI2GqQAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5bb4770>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "demo_histogramNormpdf: Comparison of histogram and normpdf -- Lecture 2.5"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random.seed(55)\n",
      "#parameters\n",
      "mu = -4\n",
      "sigma = 2\n",
      "# sample size\n",
      "M = 1e4;\n",
      "\n",
      "# X ~ N(mu,sigma)\n",
      "X = mu + sigma*np.random.randn(M)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure()\n",
      "nBins = 40;    # number of bins for the histogram\n",
      "plt.hist(X,nBins); # generate histogram\n",
      "\n",
      "# base of histogram\n",
      "xMin = np.min(X);\n",
      "xMax = np.max(X);\n",
      "\n",
      "# area of histogram\n",
      "areaHistogram = (xMax-xMin)*M/nBins;"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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77beVKGlSTS6XS7hcrvjvVVVV4tChQ1mva9GiRfHXsVhMFBQUZL2GC91+++3C\n4/HEfy8qKhJffPGFYvW8//77orCwUBgMBmEwGIRGoxHXXnutCIfDitV0vhdeeEHccsst4tSpU4rV\n8M4774iqqqr477t37xZut1uxes6JRqPCbreL3/zmN0qXIoQQ4tFHHxWyLAuDwSB0Op245JJLxNat\nWxWtKRQKCYPBEP/94MGD4s4775x2fcVC/d13343/PjIyIlatWiX+9Kc/KVHOlDWdu1F6+vRp8emn\nn4rrr79exGKxrNdVXl4eD9ADBw6IioqKrNdwod/97nfil7/8pRBCiGPHjonly5crXNFEuXSj9LXX\nXhMWi0V8/vnnitZx5swZcf3114uBgQFx+vTpnLhRGovFxNatW8WOHTsUrWM6Ho9HfP/731e6DCGE\nELfeeqs4duyYEEKIXbt2ibq6umnXzWqo//GPfxSyLIuLL75YSJIkbr/9diGEEL/61a/EpZdeKsrK\nyuI/2foSTFeTEEI88cQToqioSNxwww3xHijZ1tvbKyorK0Vpaam4+eabxZEjRxSp43zRaFT86Ec/\nEitXrhSrV68Wb7zxhtIlTXDdddflTKgbjUZxzTXXxD/XP/nJTxSrZf/+/cJkMomioiKxe/duxeo4\n5+DBgyIvL0+UlpbG/31ee+01pcuK83g8OdP75b333hMVFRVi1apVYvPmzQl7v/DhIyIiFcmN27tE\nRJQWDHUiIhVhqBMRqQhDnYhIRRjqREQqwlAnIlIRhjoRkYow1ImIVOT/AcOpMmmHNq4qAAAAAElF\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5cfedb0>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# compute values of the pdf in [xMin,xMax]\n",
      "nPlot = 1000\n",
      "xPlot = np.linspace(xMin,xMax,nPlot)\n",
      "yPlot = norm.pdf(xPlot,mu,sigma)\n",
      "\n",
      "# plot scaled pdf\n",
      "fig = plt.figure()\n",
      "_, _, p = plt.hist(X,nBins)\n",
      "l, = plt.plot(xPlot,yPlot*areaHistogram,'r',linewidth=1.5)\n",
      "ax = fig.get_axes()[0]\n",
      "ax.set_xlabel('x')\n",
      "ax.set_ylabel('count')\n",
      "plt.legend([l, p[0]], ['scaled pdf(x)', 'histogram']);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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a9FQWTUqn03GcPqTTjWB237yU5tVT+dflSim4807o1Am+/LKGdYW4PdJTWVgc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\nAYCHIABQCQIAD0EAoBIEAB6CAEBVL4d1d1z9g3MQAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5cfe030>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Same figure but now with the histogram scaled\n",
      "\n",
      "# plot scaled histogram\n",
      "fig = plt.figure()\n",
      "_, _, p = plt.hist(X,nBins, normed = True)\n",
      "l, = plt.plot(xPlot,yPlot,'r',linewidth=1.5)\n",
      "ax = fig.get_axes()[0]\n",
      "ax.set_xlabel('x')\n",
      "ax.set_ylabel('count')\n",
      "plt.legend([l, p[0]], ['pdf(x)', 'scaled histogram']);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Ly4uJEyeWeNm8HNLHar90Oh3beJjapPMABwqbAznmULbpe+gMQBdi802Tz4Mo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\nByGEEAVIcRBCCFHA/wNbwioglNI9VwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x6187ad0>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "demo_graphicalComparisonCdf -- Lecture 2.6 --  Comparison of empirical cdf and normcdf"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We consider a sample of normally distributed random variables."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random.seed(501)\n",
      "mu = -4\n",
      "sigma = 2\n",
      "\n",
      "M = 1e2 # sample size\n",
      "X = mu + sigma*np.random.randn(M)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can define an emperical CDF from this sample using. It appears that <code>scipy.stats</code> does not come with a built-in emperical CDF function, so we import it from statsmodels instead.\n",
      "\n",
      "This ECDF automatically sorts the data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from statsmodels.distributions import ECDF as empericalCDF\n",
      "eCDF = empericalCDF(X)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "eCDF holds both the x and emperical CDF(x) values in eCDF.x and eCDF.y. To plot the CDF as a stair-like plot we use <code>plt.step</code>."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.step(eCDF.x, eCDF.y);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXIAAAEACAYAAACuzv3DAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAByORg4ADkcjBwCHo5EDgMPRyAHA4f4HGVxbu+wWsXAAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xbb502b0>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next we compare this graphically to the true CDF. For this we define ``graphicalComparisonCdf``"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def graphicalComparisonCdf(X, modelCdf, xMin = None, xMax  =None):\n",
      "    _X = X[np.logical_not(np.isnan(X))] # get rid of possible nan's.\n",
      "    if xMin is None:\n",
      "        xMin = np.min(_X)\n",
      "    if xMax is None:\n",
      "        xMax = np.max(_X)\n",
      "    \n",
      "    nPlots = 1000\n",
      "    fig = plt.figure()\n",
      "    ax = plt.subplot(111)\n",
      "    xPlot = np.linspace(xMin,xMax, nPlots)\n",
      "    yPlot = modelCdf(xPlot)\n",
      "    ecdf = empericalCDF(X)\n",
      "    plt.step(ecdf.x, ecdf.y, label = 'empfcdf(x)');\n",
      "    plt.plot(xPlot,yPlot,'r', label = 'normcdf(x)')\n",
      "    ax.set_xlabel('x')\n",
      "    ax.set_ylabel('probability')\n",
      "    plt.legend(loc='lower right')\n",
      "    plt.show();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And the plot."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def cdf(x):\n",
      "    return norm.cdf(x, mu, sigma)\n",
      "graphicalComparisonCdf(X, cdf, mu - 3 * sigma, mu + 3 * sigma)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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XKuXpqVR8fLGHyK/b8uRvTtOiRQu1evXqcn8uISFB6XQ6pdfrlVJKTZ06VYWH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\nEEJUY5IEhBCiGpMkIIQQ1dj/B2Bz+uJI5avJAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x62f3490>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "demo_graphicalComparisonCdf: Comparison of empirical and model cdf -- Lecture 2.6"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We now perform a similar analysis for the lognormal distribution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random.seed(999)\n",
      "mu = 1\n",
      "sigma = .5\n",
      "M = 1e2\n",
      "S = np.exp(mu + sigma * np.random.randn(M))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Sample estimates are"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hat_mu = np.mean(np.log(S))\n",
      "hat_sigma = np.std(np.log(S))\n",
      "print hat_mu, hat_sigma"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.09480438278 0.485396888756\n"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The emperical CDF is"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "eCDF_lognorm = empericalCDF(S)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next we define the exact CDF of the lognormal distribution. Again, the CDF provided by scipy.stats.lognorm needs to be used ''with care''."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.stats import lognorm\n",
      "def lognormCDF(x):\n",
      "    return lognorm.cdf(x, scale = np.exp(hat_mu), s = hat_sigma)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "... and compare this with the emperical CDF"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "graphicalComparisonCdf(S, lognormCDF) # note that graphicalComparisonCdf determines the ECDF itself"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9+/Yivy8hIQEPDw9ycnIAOHbsGO3bt6d69eo899xzAOzevZvbbrutSPvr3bu3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\nIyLiNE4bVC7qgNSVl1W73EB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       "text": [
        "<matplotlib.figure.Figure at 0x62fa170>"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "demo_cdfinvNewtonRaphson: Inverse cdf with Newton-Raphson method -- Lecture 2.7"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We again define the pdf and cdf of the normal distribution, with fixed parameters mu and sigma."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mu = 1\n",
      "sigma = 3\n",
      "\n",
      "def pdf(x):\n",
      "    return norm.pdf(x, mu, sigma)\n",
      "def cdf(x):\n",
      "    return norm.cdf(x, mu, sigma)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we define a function cdfinvNewtonRaphson, which computes the inverse of the CDF using the Newton-Raphson method."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def cdfinvNewtonRaphson(p, pdf, cdf, x0):\n",
      "    \"\"\"\n",
      "    Input:\n",
      "    p : probability 0 <= p <= 1\n",
      "    pdf : probability density function\n",
      "    cdf : cumulative density function\n",
      "    x0 : seed\n",
      "    \n",
      "    Output:\n",
      "    x : where x solves cdf(x) = p\n",
      "    \"\"\"\n",
      "    MAXITER = 100\n",
      "    TOLABS = 1e-6\n",
      "    \n",
      "    x = np.ones_like(p, dtype = np.float)\n",
      "    x.fill(x0) # initial seed\n",
      "    \n",
      "    dx = np.ones_like(p, dtype =np.float)\n",
      "    dx.fill(10 * TOLABS)\n",
      "    nIter = 0\n",
      "    while (nIter < MAXITER) and (np.any(np.abs(dx) > TOLABS)):\n",
      "        nIter += 1\n",
      "        dx = (cdf(x) - p) / pdf(x)\n",
      "        x = x - dx\n",
      "    if nIter == MAXITER:\n",
      "        print \"Maximum number of iterations in NR reached\"\n",
      "    return x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M = 10000\n",
      "p = np.arange(1, 2*M, 2, dtype = np.float) / (2*M)\n",
      "X = cdfinvNewtonRaphson(p, pdf, cdf, mu)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We compare this to the true pdf using the earlier defined graphicalComparisonPdf."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "graphicalComparisonPdf(X, pdf)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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tcUbXujW7CgqMax7t3h2dToebm9zUbu5qTRQHDhygR48ehISEcPfddzN16lS+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\nG5d/ww66aRiLaBhJFMI2fVD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XLl3Cu2yQQG9vby5duqRxRJZXn/edzSaK0aNH069fv5t+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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5bbb930>"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "demo_qqplot: quantile-quantile plot"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It's time to apply some of the techniques to real data. This data is loaded using pandas"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pandas as pd\n",
      "from pandas.io.data import DataReader\n",
      "from datetime import datetime\n",
      "import matplotlib.pyplot as plt\n",
      "S = DataReader([\"IBM\", \"GOOG\"],  \"yahoo\", datetime(2007,7,1), datetime(2013,6,30))['Adj Close']\n",
      "Stocks = S.join(np.log(S).diff(), rsuffix='_log_diff' )\n",
      "Stocks.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>GOOG</th>\n",
        "      <th>IBM</th>\n",
        "      <th>GOOG_log_diff</th>\n",
        "      <th>IBM_log_diff</th>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>Date</th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>2007-07-02</th>\n",
        "      <td> 530.38</td>\n",
        "      <td> 93.52</td>\n",
        "      <td>      NaN</td>\n",
        "      <td>      NaN</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2007-07-03</th>\n",
        "      <td> 534.34</td>\n",
        "      <td> 94.92</td>\n",
        "      <td> 0.007439</td>\n",
        "      <td> 0.014859</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2007-07-05</th>\n",
        "      <td> 541.63</td>\n",
        "      <td> 96.23</td>\n",
        "      <td> 0.013551</td>\n",
        "      <td> 0.013707</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2007-07-06</th>\n",
        "      <td> 539.40</td>\n",
        "      <td> 97.10</td>\n",
        "      <td>-0.004126</td>\n",
        "      <td> 0.009000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2007-07-09</th>\n",
        "      <td> 542.56</td>\n",
        "      <td> 97.05</td>\n",
        "      <td> 0.005841</td>\n",
        "      <td>-0.000515</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 36,
       "text": [
        "              GOOG    IBM  GOOG_log_diff  IBM_log_diff\n",
        "Date                                                  \n",
        "2007-07-02  530.38  93.52            NaN           NaN\n",
        "2007-07-03  534.34  94.92       0.007439      0.014859\n",
        "2007-07-05  541.63  96.23       0.013551      0.013707\n",
        "2007-07-06  539.40  97.10      -0.004126      0.009000\n",
        "2007-07-09  542.56  97.05       0.005841     -0.000515"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We create a list of all log returns for easy access."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "returns = [colnames for colnames in Stocks.columns if colnames.endswith('_diff') ]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mu = Stocks[returns].mean()\n",
      "sigma = Stocks[returns].std()\n",
      "print mu\n",
      "print \n",
      "print sigma"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "GOOG_log_diff    0.000336\n",
        "IBM_log_diff     0.000467\n",
        "dtype: float64\n",
        "\n",
        "GOOG_log_diff    0.020984\n",
        "IBM_log_diff     0.015495\n",
        "dtype: float64\n"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "``matplotlib`` does not have a built-in plot function for qqplots, so we import it from ``scipy.stats``."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.stats import probplot"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for s in returns:\n",
      "    print s\n",
      "    mu = Stocks[s].mean()\n",
      "    sigma = Stocks[s].std()\n",
      "    def pdf(x): return norm.pdf(x, mu, sigma)\n",
      "    def cdf(x): return norm.cdf(x, mu, sigma)\n",
      "    graphicalComparisonPdf(Stocks[s].values, pdf)\n",
      "    graphicalComparisonCdf(Stocks[s].values, cdf)\n",
      "    \n",
      "    _S = Stocks[s].values \n",
      "    _S = _S[np.logical_not(np.isnan(_S))] # probplot cannot handle nan values, so we first get rid of them\n",
      "    probplot(_S, dist = \"norm\", plot = pylab)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "GOOG_log_diff\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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iiIqKYtWqVb4I21LR+Eu7v7eU9vxFdTS04/svTafH//mf/+Gqq66i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\niIhYlBRERMTy/0ejB9iXUUO2AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xc1b0730>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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R75K9rfnC69e3OyQRl6qMz84S7yQefPBB9u7dy5AhQ1i4cCE+Pj4AxMbG0rVr1+Iv7OnJ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\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xba8b270>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "IBM_log_diff\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9nU2bNnH69GmSkpJ48MEHjVpsa5DwEEK9ZeuD0+fdvFlSAXgWw/keVYFxzavG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\nnQ6BMzlniE6KJiY5hsPnDzN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gwIFs3LhRP4YihBCi9XXq+3kIIYRoHV1mhfmaNWswMzMj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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5bbb330>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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qb/t2KCrSytdfb6vKMcrVVwzSiVKIcqq8Yvjqq68YMGAA4eHhmEwmjh49Spcu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\nDEsMa9asoWvXrnTu3Jn58+c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       "text": [
        "<matplotlib.figure.Figure at 0xc02fcb0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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wzU0ieXz7rdmulJMgAD78EDp2VIIQ52MYBsePH6dly5alPtexY8fy3PqflJRE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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb8a6d10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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713jN8sTExMZV1wwkPERbp9H0rfhJAdditTtKmwPO5XC2ixoYiT1AZ3Hbmbe3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\nPIQQQhhNwkMIIYTR/j+C0PtYUzJw/gAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xbaa8d70>"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The tails of the data is usually too fat for a normal distribution. Therefore we consider a t-distribution instead."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.stats import t as student_t"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 41
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The student-t distribution is defined in terms of three parameters: mean, standard deviation and the degrees of freedom nu. To infer these from the data requires some special techniques, and so we use the fit method instead."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "_S = Stocks[returns[0]].values \n",
      "_S = _S[np.logical_not(np.isnan(_S))] \n",
      "hat_nu, hat_mean, hat_sig = student_t.fit(_S)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for s in returns:\n",
      "    print s\n",
      "    _S = Stocks[returns[0]].values \n",
      "    _S = _S[np.logical_not(np.isnan(_S))] \n",
      "    hat_nu, hat_mean, hat_sig = student_t.fit(_S)\n",
      "    \n",
      "    def pdf(x): return student_t.pdf(x, hat_nu, hat_mean, hat_sig)\n",
      "    def cdf(x): return student_t.cdf(x, hat_nu, hat_mean, hat_sig)\n",
      "    graphicalComparisonPdf(Stocks[s].values, pdf)\n",
      "    graphicalComparisonCdf(Stocks[s].values, cdf)\n",
      "    \n",
      "    _S = Stocks[s].values \n",
      "    _S = _S[np.logical_not(np.isnan(_S))] # probplot cannot handle nan values, so we first get rid of them\n",
      "    probplot(_S, sparams=(hat_nu, hat_mean, hat_sig), dist = \"t\", plot = pylab)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "GOOG_log_diff\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9+/fHZDJx7NgxR9QpmhIdQuGS9czFiw7ZpxDOqMZQkNtlCoezHmR2UCgkWc+U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\nGV4AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xc1b3090>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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hJycHZWVlv38PMkydOhWhoaGwtrbG4sWL8fXXX7fYj5+Wlob8/Hy8++67sLKy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\nKhYJIiJqFYsEERG16v8AXJuNDLhNn5AAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xbab2dd0>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "IBM_log_diff\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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yMDPzypNYnHQ/NerCMwkwJBr2WMD39nCtFbrZX7fQTTO2AbIZNMiN7OytkliE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\nI/bQ3r69scMSQogyM8qYy4ULF7C1tQX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       "text": [
        "<matplotlib.figure.Figure at 0xba8eb30>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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DDy56ZSE8U62JYfr06Zw4cYI//elPPPHEE6SkpDBt2jRXxCaamtJSOHzYMuvK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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xc0d3c70>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Ab7zxBrm5uUyaNIkePXrQp08fc4YkLMGaNeDlBZ07oxTMmQPPPKN3UEKUtWzZ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\nEEJUSJKEEEKICv0/oRnSBDPWwpQAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5ecc710>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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p0CZet9HkKSvY4gC3TSk8BVkSizCsKltEef36dX777TdWrFhBSkoKL774YoVu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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xc1e9ff0>"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "expectedValue.m -- Lecture 2.9"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A function required for the last two demos of this week is the expected value of a function g(X) given a pdf f_X."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.integrate import quad\n",
      "def expectedValue(g, f_X, xLow, xUpp):\n",
      "    \"\"\"\n",
      "    Input:\n",
      "    g          : handle to the function g(X)\n",
      "    f_X        : X ~ f_X (the pdf of X)\n",
      "    xLow, xUPP : integration limits\n",
      "    \n",
      "    Output:\n",
      "    E[g(X) | xLow <= X <= xUPP]\n",
      "    \"\"\"\n",
      "    TOL = 1e-10\n",
      "    def integrand(x):\n",
      "        return f_X(x) * g(x)\n",
      "    return quad(integrand, xLow, xUpp,  epsabs=TOL, epsrel=TOL)[0] / quad(f_X, xLow, xUpp,  epsabs=TOL, epsrel=TOL)[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 44
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "demo_sampleAverage: Expected values vs. sample averages -- Lecture 2.10"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Parameters of the distribution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mu = 3.\n",
      "sigma = 2."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 45
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Emperical support"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "R = 10.\n",
      "xLow = mu - R * sigma\n",
      "xUpp = mu + R * sigma"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 46
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Generate B samples of size M"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "B = 10000\n",
      "M = 200\n",
      "X = mu + sigma * np.random.randn(M,B)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 47
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Sample mean"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sampleMean = np.mean(X, axis = 0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 48
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Expected value, variance and standard deviation.\n",
      "\n",
      "( The notation lambda x: g(x) is a short way of defining a function g. )"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def f_X(x):\n",
      "    return norm.pdf(x, mu, sigma)\n",
      "E_X = expectedValue(lambda x: x, f_X, xLow, xUpp)\n",
      "var_X = expectedValue(lambda x: (x-E_X)**2, f_X, xLow, xUpp)\n",
      "std_X = np.sqrt(var_X)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 49
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The central limit theorem predicts that *mean* of our $B$ samples of data (each sample of size $M$) follows the normal distribution with mean $\\mu$\n",
      "and standard deviation $\\sigma / \\sqrt{M}$. Here we compare this statement graphically"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def modelPdf(x): return norm.pdf(x, E_X, std_X/np.sqrt(M) )\n",
      "graphicalComparisonPdf(sampleMean, modelPdf, scale = True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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vly9f5uLFi3h7e1O5cs6dYvXr1y8w3ho1auDmlnM6q1KlCknZQ7OCqe3gjTfeIDAw0DTO\nRPY4EHm5dOmSxdClBoOBgIAAYmNjuXTpkmk87Gz33hlVs2ZNKlTIGeL19u3bjBs3jgYNGuDl5UWX\nLl24efOmRbuGr6+vabpSpUrUqlXLomx+TLZk07uS0tLSGDBgAMOHD8/zpG8+SHjPnj2ZMGEC8fHx\n+ORxG9+0adNM06GhoYSGhtoiZOGifLnMYH4wlT/hZR2jcQ7Dhg1j2LBhJCYmMm7cON566y2WLVtG\nQEAAUVFRBAUFWay/e/du3n//fXbs2EHz5s0Bbcxn8xNftnr16jFixAgWLVqUa9n58+e5ceMGt2/f\npkqVKqZ55cqVK/UxVatWjXnz5jFv3jyOHz/OY489Rrt27ejatWuuO5/q1q3L77//biorpYiOjjaN\neW3ePgDaMKeBgYGm8r37++CDDzh16hQHDx6kVq1aHD16lDZt2qCUyvOuq5LciWU0GjEajcXe7l42\nu2JQSjFmzBiCgoKYOHFinutcuXLF9KE5mNWZWF5JAbTEkP2SpCCKaxwLqaAN1sleOhBJG50jcmyn\nTp1ix44dpKSkULFiRSpVqmQ6MT/33HO8++67REVFoZTi2LFjxMfHk5SUhLu7O/fddx+pqanMmDGD\nW7du5bn/4cOHs2HDBrZu3UpGRgZ3797FaDQSGxtL/fr1adu2LVOnTiUtLY09e/awcePGEh+LeWLa\nuHGjKW5PT0/KlStnutLw9fW1GH968ODBbNq0iR07dpCWlsYHH3xApUqV6NChAw8//DDlypVjwYIF\npKens379eg4dOlRgHElJSVSuXBkvLy/i4+PzHBbVPNa8EmphQkNDLc6VJWWzxLB3716WL19OeHi4\n6XbULVu2sHDhQhYu1O4FWbVqFS1btiQkJISJEyeycuVKW4UjyrDypPICX5jKjny14OHhTU6X39Z/\nafsvXEpKCpMnT6ZmzZrUqVOHuLg4/vWvfwHwv//7vwwePJhu3brh5eXF2LFjuXv3Lt27d6dHjx40\nadKEBg0aULly5VxVMdm/gv39/Vm/fj2zZs2iVq1a1KtXjw8++MA09vN3333HgQMH8PHxYcaMGYwa\nNarAeAv6dW3+vlFRUTzxxBN4eHjQoUMHXnzxRbpkDd86efJkZs6cibe3Nx9++CFNmjRh+fLlvPzy\ny9SsWZNNmzaxYcMG3N3dqVChAmvWrOGrr77C29ubb7/9lj59+lhUHd0b08SJE7lz5w733XcfHTp0\noGfPnrnWKWiY1MKO05qkd1Xh0gwGA4P4nh8YAsBF6lCf86RTPnsNKFEPqiXrXTX3Mvlsu4r27dsz\nYcKEQpOYLUjvqkIU03P8xzS9iOfNkoIQJbdr1y4uX75Meno6S5cu5b///S89evTQOyyrkC4xhEur\nB/wP2wHIxMDXPKtvQMJl/PnnnwwePJjk5GQaNWrEqlWrLO4qcmZSlSRc2jSDgWlZ0z/TjR78fM8a\nUpUknJ9UJQlRVBkZPGNW/IoxuoUihDORxCBc1/btZD8WFUcN1vOkruEI4SwkMQjX9dVXpslvGKFD\nL6pCOCdpYxCuKS4O6taFNO2hthb8znFa5LGivm0M7u4+pKfr1xW2cA3e3t7Ex+ceZ6Ok5065K0m4\npu+/NyWFA7TLJynoLz09r0FzDKjly2H4cK3YpAn88QfY6eEmIaQqSbim5ctNk/Yfoc0KnnoKsvsS\nO3UKDhzQNx5RpkhiEK7nr78gIgKANOBHBukbT0lUqQKDzOJeulS/WESZI4lBuJ5vvzVNbgGuc59+\nsZSGedcKK1fC3bv6xSLKFEkMwrUoZZEYvi1gVYfXqRM0bKhNJyTApk36xiPKDEkMwrUcPqzVyQN4\neLBB32hKx80tpwEatKsGIexAEoNwLWaNzvztb9zRLxLrGDo0Z3rjRkhM1C8WUWZIYhCuIz3d8le1\n+a9tp+Ju6ovf0Lw5x7Jn373Lc7Vq6xmYKCMkMQjXsX07XL2qTdepA1276htPiaWjPQCnvVYwy7Sk\n/93begUlyhBJDMJ1mF8tDB0KVhgj2BF8nzXIEEB3gDyecBXCmiQxCNeQkgLr1uWUhw3TLxYrO8v9\nHKAdgDbE0OrVusYjXJ8kBuEatm+Hmze16QYNoG1bXcOxthWYJTq5O0nYmCQG4Rp++CFnetAgl+tX\n6EcGkUnWMYWHw6VL+gYkXJokBuH8UlJg/fqc8uDB+sViIxfxYxePagWl4Mcf9Q1IuDRJDML5bdtm\nWY304IO6hmMrUp0k7EUSg3B+5r+eBw92uWqkbKsZQHp2Yf9+iI3VMxzhwiQxCOd2bzXSICfsSbWI\nrnMfRvMZa9boFIlwdZIYhHMzr0Zq2NBlq5GyWdyoKretChuRxCCcm1k10pyzZzG4ueV0J+GCVUpr\nIaeqbPduuHJFz3CEi5LEIJzXPQ+1/cBhzLuSKHhMZud0BbTuuAEyMy0f6hPCSiQxCOe1bRvcugXA\nGRryK210Dsge3Hl1925TaesLL5iujjw9fXSMS7gSSQzCeZlVI2nDd7pe1VFu6azhgqn0GOXwIQ5Q\nJCbe0C8s4VJslhiio6Pp2rUrzZs3p0WLFnz88cd5rvfKK6/QuHFjgoODiYyMtFU4wtWkpcGGnGF4\nVjFQx2DsK4YAImgPgDsZ9CNM54iEq7FZYihfvjwfffQRx48fJyIigk8//ZSTJ09arLN582aioqI4\nffo0ixYtYvz48bYKR7ia3bvhhvYLORo4jGv1jVSY1QwwTQ9A7k4S1mWzxFC7dm1CQkIAqFatGs2a\nNePixYsW64SFhTEqa8Dz9u3bk5CQwBW5y0IUhVmjqzZVFqqRcpgnhifYhic3dYxGuBq7tDGcO3eO\nyMhI2rdvbzE/NjaWgIAAU9nf35+YmBh7hCScmVJ5JIay5Sz38yutAahIKn3YqHNEwpW42/oNkpKS\nGDhwIPPnz6datWq5litleUthfveeT5s2zTQdGhpKaGioNcMUzuTXXyE6Wpv29mbXjbLZ6LqaAbRB\na5cbwGq+0zkeoT+j0YjRaCz1fgzq3jOzFaWlpdGnTx969uzJxIkTcy1/4YUXCA0NZWjWgOdNmzZl\n586d+Pr6WgZpMORKIKIMe/ddmDlTmx4xAsM335D/MwuGApYVtryky+yzbRP+5E+aAnCHStzHXZLl\neyLMlPTcabOqJKUUY8aMISgoKM+kANCvXz+WLVsGQEREBNWrV8+VFITIZe3anOn+/fWLQ2eneIDj\nBAFQmbs8oXM8wnXYrCpp7969LF++nFatWtG6tVYXOmvWLC5c0O7BHjduHL169WLz5s0EBgZStWpV\nFi9ebKtwhKs4fRqOH9emK1WC7t31jUdn6+hPc04AUHZTpLA2m1YlWYtUJQmT99+HN9/Upvv1g/Xr\ns9qlyl5VEkBbDnEoazzo60CNtDRwt3nToXASDleVJIRNmPcNVIarkbId4UFi8AOgBsCePbrGI1yD\nJAbhPC5f1gaoAXBzg7599Y3HASjcWM+TOTOkUz1hBZIYhPMIC9OeYQDo3Bnuu0/feBzEOvPWhXXr\ncv6PhCghSQzCeUg1Up520oUEvLTC+fPw22/6BiScniQG4Rxu3YJffskpS2IwSaMCm+idM0Oqk0Qp\nSWIQzmHLFkhN1aZDQqBBA13DcTS5qpOEKAW5XVU4hVXlKzAwPQ2AfwLv5VqjbN6umq0aicThScXs\nGWfOaGNgizJNblcVrislhW5ZSQFgHb/hysN3lkQSHmw3n7F+vV6hCBcgiUE4vvBwPLMmz9CQ32mp\naziOyqICSaqTRClIYhCOz+wkt5anKGtjLxTVBoDs3ol374a4OD3DEU5MEoNwbJmZFtUi66RHoHxd\nAXjkEa2QmQkbZYwGUTKSGIRjO3BAe+IZuEpN9tFB54AcXH+5O0mUniQG4djMutgOox+ZlNMxGCdg\nnhi2boXbt/WLRTgtSQzCcSllkRikGqkIGjeGIG2MBu7c0ZKDEMUkiUE4rpMnISoKgCRgO/+jbzzO\nQqqTRClJYhCOy+xqYQuQQiX9YnEm5olhwwZIT9cvFuGUJDEIx2X2a1d+9xbDgw+CnzZGA/Hx2q2r\nQhSDJAbhmKKj4fBhbdrdnU36RuNc3NzgSbMxGuQpaFFMkhiEQ/D09MFgMJheL9WrZ1q2NT2dmzrG\n5pTMq5PWrpUxGkSxFDkx3L17l5SUFFvGIsqwxMQbmPd/1J/HTcvW8aleYTmv0FDwyhqj4cIFOHpU\n13CEc8k3MWRmZrJmzRoGDRqEn58fDRs2pH79+vj5+TFw4EDWrl0rPZ4Km6jODUIxmsoWQ1eKoilf\nHvr0ySmbNeQLUZh8E0NoaChHjhxh0qRJnDlzhkuXLnH58mXOnDnDpEmTOHToEF26dLFnrKKM6MNG\n3MkA4ADtuJg12L0oJrltVZRQvuMxpKSkULFixbwWFWsda5DxGFyfwZAzzsAqBjCANQBMZhazmYzj\njZvgWOMxZC+z+J4kJWnjYmdXAUdFQaNGBbyvcDVWH48h+4S/ffv2XMuWLl1qsY4Q1lKJO/TgJ1NZ\n601VFI27RQO+wcODDWbtgu80l+7KRdEU2vg8ffp0xo8fT3JyMpcvX6Zv376EhYXZIzZRBj3BNqqi\n9e/zBw/wJ011jsiZpGM5gJFiLV+ZlvZKuaNTXMLZFJoYdu7cyf33309wcDCdO3dm2LBhrF692h6x\niTKoP/eOvSBKYwN9ycj6mncAuHJF13iEcyg0Mdy4cYNDhw7RqFEjKlSowIULF6S+X9hEOdLpR87V\nqHSaV3px1GQPnYCsL7tc7YsiKDQxPPLII3Tv3p2ff/6ZQ4cOERsbS8eOHe0RmyhjOrKX+7gOwEXq\ncIiHdI7INVgkWLk7SRRBoYlh27ZtjBkzBoAqVarwySef8K9//atIO3/22Wfx9fWlZcu8G72MRiNe\nXl60bt2a1q1bM3PmzGKELlyNeTXSOvqj5MF8q7BIDNu3Q2KifsEIp5DvN++vv/4CoH79+rmWZT+/\nkL1Ofp555hl++umnAtfp0qULkZGRREZGMmXKlEIDFq7r3sQgrOMcDTlKsFZITYUtW/QNSDg89/wW\nvPPOOyQnJ9OvXz/atm1LnTp1UEpx6dIlDh8+TFhYGB4eHqxcuTLfnXfu3Jlz584VGIC0VwiAYKAh\n5wBIwAsjoXqG43LW8hQh/KYV1q2DwYP1DUg4tHwTw/fff09UVBQrV67kH//4B+fPnwe0K4hOnTrx\nySefcP/995fqzQ0GA/v27SM4OBg/Pz/mzZtHUPboU6JMMb8+2ERv0qigWyyuaB39mc40rbBpk3bl\nUEH+j0Xe8k0MP/74I4MGDeLpp5+2WRVPmzZtiI6OpkqVKmzZsoX+/ftz6tSpPNedNm2aaTo0NJTQ\n0FCbxCT0YZ4YpBrJ+o7RijPA/QC3bkF4OHTvrnNUwtqMRiNGo7HU+8m3S4zWrVsTGRlJmzZt+PXX\nX0v8BufOnaNv3778/vvvha7bsGFDjhw5go+Pj2WQ0iWGazt7FrKuPu9SkZpcIwmPe1ZytK4rHLNL\njIL2+wEG/je7MG4cfPFFATEIV1DSc2e+Vww1atTgiSee4MyZM/Tt2zfXm1nj6ecrV65Qq1YtDAYD\nBw8eRCmVKymIMsDsFsrt/E8eSUFYw1rISQzr18Nnn2mD+ghxj3wTw6ZNm4iMjGT48OFMmjTJIuto\nHZ4VbtiwYezcuZO4uDgCAgKYPn06aWlpAIwbN45Vq1bx+eef4+7uTpUqVQpsyBYubJ3cjWQP+0Dr\nVC8uDi5fhgMH4JFH9A5LOKB8q5KyXbt2jZo1a9ornjxJVZILu3YNateGzEwyMVCby1yjVh4rOlqV\nj/NVJUF5/kM6Y7JKc4C3s6Y9PLy5dSu+gG2FM7J6VZJ59dG9O7dWVZIQbNgAmZkA7KVjPklBWEc6\na9nAGLTv9lM05m3+BAwkJhatFkCUDfkmhtdffx2AtWvXcvnyZYYPH45SihUrVuDr62u3AIWLWyed\n5tmT1oZTlWok04TTNOMkJ5FbxIWlQquSHnzwQY4cOVLoPFuSqiQXlZgINWuaBpJpRBRnyG8gGUer\n8nHGqiRt+Q8MYhCrAPgHM5nFP8g1yI9wCVYfqCfb7du3Lbq+OHPmDLdv3y72Gwnh6eljMZDMEE9P\nU1L4DQp3e1XSAAAbHElEQVRICsKazBv4zbshESJbvlVJ2T766CO6du3K/fffj1KKc+fOsWjRInvE\nJlxMYuINzH/RDmQQZP1yXaVPSGWS9mS5O+VJ5yEO4080MXoHJRxKoVcMXbp04fnnn6d69eqUK1eO\ncePGmTrRE6KkqpBMLzabypIY7Ocm1Qmnq6n8FGt1jEY4okITw8iRIzl79iyvvvoqU6ZM4cyZM4wY\nMcIesQkX1oOfTEN4HieIP3SOp6xZw99M0wMlLYt7FNr4HBQUxIkTJwqdZ0vS+OwatAcjtb/jdwxj\nGNoDjdP5J9OYgXM1Ejtv4zNATa5yiTqUQ3t+xA/FJfmOuRybNT63adOG/fv3m8oRERE8+OCDxX4j\nIbJV5C592Ggqr2aAjtGUTdeoxU60KmE3lPwFhIVCG58PHz5Mx44dCQgIwGAwcOHCBR544AFatmyJ\nwWDg2LFj9ohTuJBubMWDJABO0ZjfyXuEP2FbqxjIY4QDMFDnWIRjKTQxFDYCmxDFZV6nvYqBaFUc\nwt7W8DcW8BJuKB4Frf+k2rX1Dks4gELbGByBtDG4BoPBQAXucgVfqnMTgDYcIZI2OEK9u2Ps174x\nhRNKKDu1wqefwoQJBWwvnI3N2hiEsKbH+cWUFM7SgEha6xxR2fYjg3IKq+TuJKGRxCDsagCrTdNS\njaS/NfyNzOy/wc6dcPWqvgEJhyCJQdiNO5ZdMKySJk/dXaYOe+ikFTIzYc0afQMSDkESg7CbUKAG\nWp//FwjgIO10jUdoLKqTfvxRv0CEw5DEIOxmiNm09uStVCM5AovnSIxGbfAkUaZJYhD2kZJi8RDV\nSobqFoqwdIm67MkuZGbCWuk7qayTxCDsY+tWvLMmz9KAA7TXNRxhyaIC6Ycf9ApDOAhJDMI+Vqww\nTWpXC1KN5EhWARiy/ibh4drDbqLMksQgbC85GdavNxWlGsnxXAR49FGtkJkpVw1lnCQGYXsbN0LW\nqH8naMYxWukckMjNnXE7d5pKEa++ahppz9PTR8e4hB4kMQjbW7kyZ1KqkRxUOquIIy2r+7SHgYb8\nBaiskfdEWSKJQdhWQgJszhmpbQXDdAxGFCSeGvxED1N5GCsKWFu4MkkMwrbWrYPUVAAOA1E01jce\nUaDveNo0/Xe+peBO+YSrksQgbMvibiTh6MLoRzJVAAjiJK2Q8VbKIkkMwnauXoVffjEVv9cxFFE0\nt6nKep40laU6qWySxCBs5/vvISNDm+7UiRh9oxFFZF6dNIwVcqtAGWTTxPDss8/i6+tLy5b5D934\nyiuv0LhxY4KDg4mMjLRlOMLeli7NmR4xQr84RLFspRvX0W5Rrc8FOugcj7A/myaGZ555psChQTdv\n3kxUVBSnT59m0aJFjB8/3pbhCHs6fhyOHNGmK1aEQYMKXl84jDQqWHSJ/ncdYxH6sGli6Ny5M97e\n3vkuDwsLY9SoUQC0b9+ehIQErly5YsuQhL18803OdL9+UMDnQDieb83SwVCAu3d1i0XYn65tDLGx\nsQQEBJjK/v7+xMRITbTTy8iA5ctzyiNH6heLKJE9dOIMDQG0zg/DwnSNR9iXu94B3DtQtcGQd1PX\ntGnTTNOhoaGEhobaMCpRKuHhEBurTdesCd276xuPKDaFG0sZxXSmaTOWLIHBg/UMSRSB0WjEaDSW\nej+6JgY/Pz+io6NN5ZiYGPz8/PJc1zwxCAe3bFnO9NNPQ/ny+sUiSmwZI3MSw88/w8WLULeurjGJ\ngt37o3n69Okl2o+uVUn9+vVjWdZJJCIigurVq+Pr66tnSKK0kpJg9eqcclYbknA+52hIOKFaITPT\nsnpQuDSbXjEMGzaMnTt3EhcXR0BAANOnTyctLQ2AcePG0atXLzZv3kxgYCBVq1Zl8eLFtgxH2MOa\nNaaeVGnRAkJC9I1HlMoSRtMVY1ZhCbzxRs64DcJlGdS9lfwOyGAw5GqLEI5pp3t5umSkA/AGMC/X\nGvn9HQ0FLCtseUmXOeJ+HSumqiRxGQ+qZc84cADatSvgPYQjKem5U558FtYTFWVKChm48S2xaCeb\n7JdwNslUsxz2c8kSnSIR9iSJQVjPf/5jmtxEby4hDZWuYIl5YcUKeaahDJDEIKwjLc3i1+SXjNUv\nFmFVuwEaas80kJCgtSMJlyaJQVjHhg2Q9dR6LHXZQk+dAxLWogDGjMmZ8cUXeoUi7EQSg7COL780\nTS7mGTL0f3ZSWNOzz4J71t909244cULfeIRNSWIQpXf+vPYAVJavGFPAysIp1amj9XmVbdEi/WIR\nNieJQZTe119D1i1xW9EejBKuxB2DwUA3s7aFG/PnU9lgwGAw4Onpo2NswhYkMYjSSU/XEkOWLwtY\nVTirdECxnQz+4n5A61hvEEsBRWLiDT2DEzYgiUGUzoYNkN0jbs2arNc3GmFDCjeLu83GsVDHaIQt\nSWIQpfPJJznTY8eSpl8kwg4W8wxpWTcWdGQfLfhd54iELUhiEMXi6emDIatuubnBoHWxjVbZEDBr\nlr7BCZu7ii9recpUfpFPdYxG2IokBlEsWn2y1sXFS7xgmr+OAcRItxdlwqe8aJoeyTJkbD7XI4lB\nlIgXCYwkZ9yFBbykYzTCnnbxKJFoveZW4Y484+6CJDGIEhnNEqqida/9Oy3YSRedIxL2Y2A+r5pK\nL4HWJYpwGZIYRLG5kWFRt6xdLUgf/WXJSoZyhVoABACsXatrPMK6JDGIYutHGI2JAiABL5YzXOeI\nhL2lUInPGZ8z49//1i8YYXWSGESxvcH7punPGc9tquoYjdDLF7xAKlnjee/fDwcP6huQsBpJDKJY\nOgAd2A9AChX4mFf0DUjo5gq1WcGwnBkffqhfMMKqJDGIYnnDbHo5w7lMHd1iEfr7NxNzCj/+CFFR\n+gUjrEYSgyi6P/6gv1lxHpN0C0U4hqO0xtSvbmYmzJ2rZzjCSiQxiKL74APT5Ab68AfNdAxGOIp/\nmReWLoWLF/UKRViJJAZRNNHRsCzngba5vKljMMKR7AR45BGtkJoqbQ0uQBKDKJrZs7UvPbCXDuyh\nk84BCYcyeXLO9BdfwPXr+sUiSk0SgyhcTAz85z+m4nSmIg+0CQu9e0OLFtp0cjJ8/LG+8YhSkcQg\nCmd2tbAP2MYT+sYjHI+bm+VVw0cfyVWDE5PEIAoWEwNf5ozLNh2QqwWRpyFDoGlTbToxEd5/v+D1\nhcOSxCAKZna1wMMPs1XfaIRD0saENri7M+iPP0xzb8+ZQ2C16jrGJUpKEoPI35kzsGhRTnnqVP1i\nEQ5MGxMaFKvJ4CjBAFQBXk6+qWdgooRsmhh++uknmjZtSuPGjZkzZ06u5UajES8vL1q3bk3r1q2Z\nOXOmLcMRRZQ9StuKRo1M3SnvBQw9e+obmHB4CjemkPM9fgG0W52Fc1E2kp6erho1aqTOnj2rUlNT\nVXBwsDpx4oTFOuHh4apv376F7suGYYo8AOpBDikFptcj7M2axHx2Hq+Clpd0WVnaryPGVNz9Zqr9\ntM+ZMXq03h/pMquk506bXTEcPHiQwMBAGjRoQPny5Rk6dCjr16/PKzHZKgRRCnN4yzS9lv7sp4OO\n0QjnYuAdzMb/XroUjhzRLxxRbDZLDLGxsQQEBJjK/v7+xMbGWqxjMBjYt28fwcHB9OrVixMnTtgq\nHFEMPYDH2QFAOuWYbNnpgRCFCucxwuirFZSC117LurgQzsBmicFgKPyWxjZt2hAdHc1vv/3Gyy+/\nTP/+/QvdRthYairmQ678h+f4k6a6hSOc1yTmYRrwc/duWL1az3BEMbjbasd+fn5EmzU6RUdH4+/v\nb7GOh4eHabpnz55MmDCB+Ph4fHx8cu1v2rRppunQ0FBCQ0OtHrMA/v1vHsiavIkn05imZzTCiZ2m\nCQuA17JnvPkm9OkDlSrpGJVrMxqNGI3G0u/Iuk0dOdLS0tT999+vzp49q1JSUvJsfL58+bLKzMxU\nSil14MABVb9+/Tz3ZcMwhbmYGKWqVjU1Gr7KRw7cwOmq+3XEmEq+3+qglI9Pzoz33tP7U16mlPTc\nabOqJHd3dxYsWED37t0JCgpiyJAhNGvWjIULF7Jw4UIAVq1aRcuWLQkJCWHixImsXLnSVuGIonjj\nDa2fG+B3WrCAl3QOSDi7BIAZM3JmzJwpg/k4AUNWVnFoBoMBJwjTuW3dCt27m4qhhLOT0DxWNAAF\n/S0KWl7SZWVpv44YU2n2Wx430jkAtM2asw3oljXt4eHNrVvxBexblEZJz53y5LOApCR4/nlTcQXk\nkxSEKK50MlE8zxEysk43TwB/5xtAkZh4Q9foRN4kMQitV8zz57XpGjXMR/EVwioiacN8XjWVP+I1\n7uOajhGJgkhiKOt274YFC3LK8+dzVb9ohAv7JzO4gPZsU03iWMTzhWwh9CJtDGWQp6cPiYk3qAZE\nAoFZ8zdC9iNJOFc9tivt1xFjst5+u/EzP9PDVB4NLJHvts1IG4MoMq1eV/EpI0xJ4SaevEA0BZ8A\nhCidrXTnUyaYyh8DnDunVzgiH5IYyqin+ZaRfGMqv8AXxOJfwBZCWMebzOUUjQHwBBg+3NSLr3AM\nkhjKoPuBzxlvKi9lJCsZpl9Aoky5TVVG8A3plNNm7N0L77yjb1DCgiSGsiY5mbWAJ4kAnCaQl1hQ\n8DZCWNlB2luM28C8ebB2rX4BCQvS+FyWKAVDh8IPPwCQQgU6sYfDPHTPis7dwOnc+3XEmGyzXwOZ\nrKdczg0Pnp5w6BA0aVLAe4nikMZnUbi5c01JAWA8n+eRFISwD4UbIwEaNNBm3LoFvXvD9es6RiVA\nEkPZ8eOP2oNsWT5lAot5VseAhMjqS2n1aqhcWZsRFQVPPQUpKXqGVeZJVVJZYDRq/SClpgKwC/gf\nUkijQj4buE51hfPt1xFjsu2xKqW05DBwYM7sv/8dli0DN/ntWhpSlSTyduwY9O9vSgo88ABPQQFJ\nQQgdDBgAc+bklL/9Fl55JatXb2FvcsXgojw9faiXeIMdQK2seReBDoDWK5L82nXM/TpiTHa4YgAt\nCbzwAixalLP4zTdh9mwowoiQIreSnjttNoKb0Ff9xBvs4D5qEgdoTzb3ZBfnCUb7sgrhCNwthgF2\nA74FhmbPmDsX3N21cRwkOdiNVCW5osOH2QEWSaE7P3OMYH3jEiKXdLQrCu2ViWIEqazjyZxVZs2C\nl16CzEydYix7pCrJ1WzcCEOGwO3bgJYUurGVg7Q3W0mqQRx3v44Yk/2PtQIprKEyvc2WrUDrdC8V\nGeCnqKTxuaxTCj7/HJ580pQUruPDE2y7JykI4fhSqchTKL4z66plGLCDDtTisgzwY2OSGFzB7dvw\n7LMwYYLpcvsM0IF9HKKdvrEJUUJpwHCWW/TG2pF9HKYtD+oXVpkgicHZnToFHTrAkiU589q25RHg\nFA/oFZUQVqFw4yUW8DrzTEODBhDDXoAPP5R2BxuRNgZnlZnJW1WqMTXlDlXMZi8FxgN3AEeqM5b9\nOnNMjnGs3fiZlQzFW3teGoCfgWfRbsU2J20QGmljKEtOnIDHHmOOWVJIoQLPs5DRZHJHBtsRLmgr\n3XmIQxyirWled+AkHrzMfNzM7nCSNojSkSsGZ5KQANOmaWM0Z2SYZv9GK0axlN8IMVvZ8X8Byn6d\nJSbHOtbypDKDiryJATez5Udow0T+zR46Y/HgXBkmVwyuLDFRe/ozMBDmzzclhXRgJv/gIQ7dkxSE\ncF1pVGAyEIqRkzQ1zX+QX9nNo2yilzyxU0pyxeDIrl7Vugf46COIv6e+tGtXWoaH818X+AUo+3X0\nmBz3WCuQwiTmMYWZVOau5Sq9e8Prr0NoaJl9arqk505JDI5GKdi/Hz77jJRvv6XiPYvPAm8Aq3M2\nyGdHzvlFl/06YkyOf6z1Ocd0pjKCbyyqlwBo3RrGjtUGqfL2LiAW1yOJwZkpBb//DitXaq+zZ3Ot\ncoaGzGQK3zCCdMpnzXXdL3rZ3a8jxuQ8x9qc/zKDf9KftbnryStU0B4AHTQIevQAD48C4nINkhic\nzc2bsGMH/PST9rpwIc/V9vMwnzGBlQw1SwjZXP+LXvb264gxOd+xNsad18hgNFA5rxUqVICuXbXq\npi5doEULlxz7wSETw08//cTEiRPJyMjgueee46233sq1ziuvvMKWLVuoUqUKS5YsoXXr1rmDdPbE\ncPcu/PmnNp5tRIT2OnGC/PqaTwB+BD4HIuWLXsb264gxOe+xehPPMFYwmiU8xOH8V/f2hs6d4eGH\nISREe9Wu7fRtEw6XGDIyMnjggQfYvn07fn5+PPTQQ6xYsYJmzZqZ1tm8eTMLFixg8+bNHDhwgFdf\nfZWIiIjcQTpDYkhO1n71Z7/OnoWTJ+H4cTJOn6ZcAZsagTZ4sJlerGAYP9GDVCqi95fKOtsagVAd\nY7L1fo3kHJ+jxGTN/RqBrjbYb2m3Lf5+m/NfBvEj/ZhB9s9PI3n/9QCoWROaN9fuBmzUKOdff3+o\nUcMprjAcbjyGgwcPEhgYSIMGDQAYOnQo69evt0gMYWFhjBo1CoD27duTkJDAlStX8PX1tVVYeVNK\n+1WfnAxJSdq/eb3i47WByuPiLP+9fDn3XUNm8koK6ZTjKCH8zBEWMppLLMqjqsgVGCngq+cCjLj+\n8bmG47TgOC2YxizqkU4f4CrQDMjzjHPtmjYsrtGYe5m7O/j6alcVdepArVpQvTp4eeX8m/3y8IBK\nlbRxrStVypmuWBHKFfSTUT82SwyxsbEEBASYyv7+/hw4cKDQdWJiYuybGJKSwNMz32oda8gEztCI\n32nJfh4hgoc5woPcpiraL5v64JJJQQhHlM4FFJ8BMI1VTKUJp+jMbkIYSwgdCeY3PEgqYBfpEBur\nvUohFbgLpGPAp1ZNKF9eSzr3vh55ROs92U5slhgMRaybu/cyp6jbWU3lylZJCilANHDB7PUncDzr\n37tElfo9hBC2YOAUD2R1OjkW2IOBTO7nDI05TSBRNOIvAonifjZRh+oW/TWVRoWsFyjtuaX81KqV\n/zIbsFli8PPzIzo62lSOjo7G39+/wHViYmLw8/PLta9GjRrZP2FYXUHxT896FXe7wpaXdJm1t51e\nwLLS7Ncay6yx35L87Zz1WB1pW2vt996/nwEF/JX1ys06SaFYtm0rUUN4o0aNSvR2NksMbdu25fTp\n05w7d466devy/fffs2LFCot1+vXrx4IFCxg6dCgRERFUr149z2qkqCj5tS2EEPZis8Tg7u7OggUL\n6N69OxkZGYwZM4ZmzZqxcOFCAMaNG0evXr3YvHkzgYGBVK1alcWLF9sqHCGEEEXkFA+4CSGEsB+H\nuRE3Ojqarl270rx5c1q0aMHHH3+c77qHDh3C3d2dNWvW2DHCkivqsRmNRlq3bk2LFi0IDQ21b5Cl\nUJTji4uLo0ePHoSEhNCiRQuWmI845+Du3r1L+/btCQkJISgoiMmTJ+e53iuvvELjxo0JDg4mMjLS\nzlGWXFGO79tvvyU4OJhWrVrRsWNHjh07pkOkJVPUvx8437mlqMdW7HOLchCXLl1SkZGRSimlEhMT\nVZMmTdSJEydyrZeenq66du2qevfurVatWmXvMEukKMd248YNFRQUpKKjo5VSSl27ds3ucZZUUY5v\n6tSp6u2331ZKacfm4+Oj0tLS7B5rSSUnJyullEpLS1Pt27dXu3fvtli+adMm1bNnT6WUUhEREap9\n+/Z2j7E0Cju+ffv2qYSEBKWUUlu2bHG541PKOc8tShV+bCU5tzjMFUPt2rUJCdHGFKhWrRrNmjXj\n4sV7B+yDTz75hIEDB1KzZk17h1hiRTm27777jgEDBpju3LrvvvvsHmdJFeX46tSpw61btwC4desW\nNWrUwN3dZk1cVlelijZWXmpqKhkZGfj4+Fgsz+9hTWdR2PE98sgjeHl5AdrxxcTE2D3G0ijs+MA5\nzy1Q+LGV5NziMInB3Llz54iMjKR9+/YW82NjY1m/fj3jx48HdHjmwQryO7bTp08THx9P165dadu2\nLd98841OEZZOfsc3duxYjh8/Tt26dQkODmb+/Pk6RVgymZmZhISE4OvrS9euXQkKCrJYnt/Dms6i\nsOMz99VXX9GrVy87Rld6Rfn7Oeu5pbBjK8m5xeESQ1JSEgMHDmT+/PlUq1bNYtnEiROZPXu2qf8P\n5WTt5gUdW1paGr/++iubN2/m559/5r333uP06dM6RVoyBR3frFmzCAkJ4eLFixw9epQXX3yRxMRE\nnSItPjc3N44ePUpMTAy7du3CmEc3Cfd+Hp3p5FKU4wMIDw/n66+/Zs6cOfYNsJQKOz5nPrcUdmwl\nObc4VGJIS0tjwIABDB8+nP79++dafuTIEYYOHUrDhg1ZvXo1EyZMICwsTIdIi6+wYwsICKBbt25U\nrlyZGjVq8Oijj/Lbb7/pEGnJFHZ8+/btY9CgQYD20E3Dhg35888/7R1mqXl5edG7d28OH7bsqbOo\nD2s6uvyOD+DYsWOMHTuWsLAwvJ10wJv8js+Zzy3Z8ju2Ep1brNoKUgqZmZlqxIgRauLEiUVaf/To\n0Wr16tU2jso6inJsJ0+eVI8//rhKT09XycnJqkWLFur48eN2jLLkinJ8r732mpo2bZpSSqnLly8r\nPz8/df36dXuFWCrXrl1TN27cUEopdfv2bdW5c2e1fft2i3XMG5/379/vVI2zRTm+8+fPq0aNGqn9\n+/frEWKpFOX4zDnTuaUox1aSc4vDtP7t3buX5cuX06pVK9OYDLNmzeJC1gA248aN0zO8UinKsTVt\n2pQePXrQqlUr3NzcGDt2bIH1vI6kKMf3zjvv8MwzzxAcHExmZiZz587NswHQEV26dIlRo0aRmZlJ\nZmYmI0aM4PHHH3eZhzWLcnwzZszgxo0bpjr48uXLc/DgQT3DLrKiHJ+zKsqxleTcIg+4CSGEsOBQ\nbQxCCCH0J4lBCCGEBUkMQgghLEhiEEIIYUESgxBCCAuSGIQQQliQxCCEEMKCJAYhhBAWJDEIUQKH\nDh0iODiYlJQUkpOTadGiBSdOnNA7LCGsQp58FqKE3n33Xe7evcudO3cICAjgrbfe0jskIaxCEoMQ\nJZSWlkbbtm2pXLky+/fvd6putoUoiFQlCVFCcXFxJCcnk5SUxJ07d/QORwirkSsGIUqoX79+PP30\n05w5c4ZLly7xySef6B2SEFbhMN1uC+FMli1bRsWKFRk6dCiZmZl06NABo9FIaGio3qEJUWpyxSCE\nEMKCtDEIIYSwIIlBCCGEBUkMQgghLEhiEEIIYUESgxBCCAuSGIQQQliQxCCEEMKCJAYhhBAW/h9/\nABIQ5uNVIwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xc02f6d0>"
       ]
      }
     ],
     "prompt_number": 50
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "demo_MC_BlackScholes: MC calculation of E[ST] -- Lecture 2.12"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we look at the Black-Scholes model"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "S0    = 100  # initial asset price\n",
      "mu    = 0.1  # drift\n",
      "sigma = 0.4  # volatility\n",
      "T     = 2.0  # time in the future"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 51
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The Black-Scholes model is given by\n",
      "\n",
      "$X\\sim N(0,1)$\n",
      "\n",
      "$S(T,X) = S_0 \\exp\\left(\\left(\\mu-\\sigma^2/2\\right)T + \\sigma\\sqrt{T}X\\right)$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def f_ST(x):\n",
      "    return S0 * np.exp((mu-.5*sigma**2) * T + sigma * sqrt(T) * x)\n",
      "R = 10\n",
      "E_ST = expectedValue(f_ST, norm.pdf, -R, R) # note that norm.pdf has default parameters of mean = 0, sigma = 1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 52
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Sample mean"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "B   = 10000;\n",
      "M   = 200;\n",
      "X   = np.random.randn(M,B);\n",
      "ST  = f_ST(X);\n",
      "\n",
      "# B estimates of the sample mean\n",
      "E_ST_MC  = mean(ST, axis = 0); #Each estimate is over a sample of size M"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 53
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Monte Carlo error"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "error_MC = np.std(ST) / np.sqrt(M)\n",
      "error_MC"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 54,
       "text": [
        "5.3069481020105558"
       ]
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def modelPDF(x):\n",
      "    return norm.pdf(x, E_ST, error_MC)\n",
      "\n",
      "graphicalComparisonPdf(E_ST_MC, modelPDF)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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czMxMDh8+THFxMatWrSImJsaqTkxMDMuXLwcgNTUVb29vfH19uXDhAoWFhQCc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\nbFB9+vRRBoNBLVy4sMY6Dz30kDIYDGr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       "text": [
        "<matplotlib.figure.Figure at 0xc0f7110>"
       ]
      }
     ],
     "prompt_number": 55
    }
   ],
   "metadata": {}
  }
 ]
}