ML_Probability.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Machine Learning Probability"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "Understanding Probability "
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "def P1_win_prob_weighted_coin_game(num_games, prob_heads=.5): \n",
        "  player_one_wins = 0 \n",
        "  for n in range(0,num_games): \n",
        "    num_flips = 0 \n",
        "    win = 0\n",
        "    while win == 0: \n",
        "      turn = np.random.uniform(0,1) \n",
        "      num_flips += 1 \n",
        "      if turn <= prob_heads: \n",
        "        if num_flips % 2 != 0: \n",
        "          player_one_wins += 1 \n",
        "        win += 1 \n",
        "  return float(player_one_wins)/float(num_games)\n",
        "\nP1_win_prob_weighted_coin_game(50, prob_heads=.5)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 1,
          "data": {
            "text/plain": [
              "0.52"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 1,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import random\n",
        "\n",
        "def flip(p): # p for probability\n",
        "    return 'H' if random.random() < p else 'T'\n",
        "\n",
        "N = 100\n",
        "flips = [flip(0.2) for i in range(N)]\n",
        "float(flips.count('T'))/N"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 2,
          "data": {
            "text/plain": [
              "0.84"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 2,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def coin_flip(p): # p for probability \n",
        "    if random.random() < p:\n",
        "        return 'H'\n",
        "    else:\n",
        "        return 'T'\n",
        "\nflip(0.9)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 3,
          "data": {
            "text/plain": [
              "'H'"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 3,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def flip():\n",
        "    toss = random.randint(0,1)\n",
        "    if toss == 0:\n",
        "        print('Heads')\n",
        "    else:\n",
        "        print('Tails')\n",
        "    return\n",
        "\nflip()"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Tails\n"
          ]
        }
      ],
      "execution_count": 4,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Simple 52 cards of class\n",
        "# 52 Cards\n",
        "class Card:\n",
        "    def __init__(self, value, color, shape):\n",
        "        self.value = value\n",
        "        self.color = color\n",
        "        self.shape = shape\n",
        "\n",
        "value = ['2', '3', '4', '5', '6', '7', '8', '9', '10', 'J', 'Q', 'K', 'A']\n",
        "color = ['Black', 'Red']    \n",
        "shape = ['Heart', 'Diamonds', 'Spades', 'Clubs']\n",
        "\n",
        "deck = [Card(value, color, shape) for value in range(1, 13) for colors in color for shapes in shape]\n"
      ],
      "outputs": [],
      "execution_count": 5,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Library\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "from numpy import mean, median, std, var, cov, corrcoef\n",
        "from scipy.stats import kurtosis, skew\n",
        "from scipy.stats import mode\n",
        "from scipy import stats\n",
        "import matplotlib.pyplot as plt\n",
        "import random"
      ],
      "outputs": [],
      "execution_count": 6,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "samples = [8, 22, 11, 2, 6, 3, 14, 99, 44, 77, 31, 100, 44, 8, 23, 55, 88, 66, 7, 20, 8]"
      ],
      "outputs": [],
      "execution_count": 7,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "sorted(samples)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 8,
          "data": {
            "text/plain": [
              "[2, 3, 6, 7, 8, 8, 8, 11, 14, 20, 22, 23, 31, 44, 44, 55, 66, 77, 88, 99, 100]"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 8,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "len(samples)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 9,
          "data": {
            "text/plain": [
              "21"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 9,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Statistics \n",
        "# convert list to dataframe\n",
        "df = pd.DataFrame(samples) \n",
        "df.describe()"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 10,
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>0</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>21.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>35.047619</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>33.100568</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>2.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>8.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>22.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>55.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>100.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                0\n",
              "count   21.000000\n",
              "mean    35.047619\n",
              "std     33.100568\n",
              "min      2.000000\n",
              "25%      8.000000\n",
              "50%     22.000000\n",
              "75%     55.000000\n",
              "max    100.000000"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 10,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Mode, Median, Mean\n",
        "# Mode is the most frequently occuring number\n",
        "# Median is the middle number of the order\n",
        "# Mean is the sum of the numbers divided by the length of the list\n",
        "print('Mode: {}'.format(mode(samples)))\n",
        "print('Median: {}'.format(median(samples)))\n",
        "print('Mean: {}'.format(round(mean(samples),2)))"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mode: ModeResult(mode=array([8]), count=array([3]))\n",
            "Median: 22.0\n",
            "Mean: 35.05\n"
          ]
        }
      ],
      "execution_count": 11,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Variance\n",
        "# Numeric value used to describe how widely the numbers distribution vary\n",
        "print('Variance: {}'.format(round(np.var(samples),2)))"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Variance: 1043.47\n"
          ]
        }
      ],
      "execution_count": 12,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Standard Deviation \n",
        "# The square root of the variance\n",
        "print('Standard Deviation: {}'.format(round(np.std(samples),2)))"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Standard Deviation: 32.3\n"
          ]
        }
      ],
      "execution_count": 13,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Standard Error\n",
        "print('Standard Error with first axis:')\n",
        "print(stats.sem(samples))\n",
        "print('Standard Error with Degrees of freedom:')\n",
        "print(stats.sem(samples, axis=None, ddof=0))"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Standard Error with first axis:\n",
            "7.22313617102\n",
            "Standard Error with Degrees of freedom:\n",
            "7.04905911622\n"
          ]
        }
      ],
      "execution_count": 14,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Skewness and Kurtosis\n",
        "print('Skewness: {}'.format(round(kurtosis(samples),6)))\n",
        "print('Kurtosis: {}'.format(round(skew(samples),6)))"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Skewness: -0.708744\n",
            "Kurtosis: 0.835358\n"
          ]
        }
      ],
      "execution_count": 15,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Covariance\n",
        "# 2x2\n",
        "X = np.array([[2, 8], [4,6]])\n",
        "print(\"Covariance:\")\n",
        "print(np.cov(X))"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Covariance:\n",
            "[[ 18.   6.]\n",
            " [  6.   2.]]\n"
          ]
        }
      ],
      "execution_count": 16,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Diagonal elements\n",
        "print(np.var(X, axis=1, ddof=1)) # N-1 degree of freedom"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 18.   2.]\n"
          ]
        }
      ],
      "execution_count": 17,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Correlation Coefficient\n",
        "x = np.array([[3, 8], [2,7]])\n",
        "y = np.array([[6, 8], [14,12]])\n",
        "print(\"Correlation Coefficient:\")\n",
        "print(np.corrcoef(x, y))"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Correlation Coefficient:\n",
            "[[ 1.  1.  1. -1.]\n",
            " [ 1.  1.  1. -1.]\n",
            " [ 1.  1.  1. -1.]\n",
            " [-1. -1. -1.  1.]]\n"
          ]
        }
      ],
      "execution_count": 18,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "n = [2, 69, 78, 2, 24, 3, 16, 99, 21, 25, 31, 100, 2, 4, 23, 56, 225, 64, 6, 19]\n",
        "n = sorted(n)\n",
        "range = n[-1] - n[0]\n",
        "\n",
        "print(\"mean:\",mean(n))\n",
        "print(\"median:\",median(n))\n",
        "print(\"mode:\",mode(n)[0])\n",
        "print(\"range:\",range)\n",
        "print(\"std:\", std(n))\n",
        "print(\"var:\", var(n))\n",
        "print(\"Negative skew: mean < median < mode\")\n",
        "print(\"Positive skew: mode < median < mean\")"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "mean: 43.45\n",
            "median: 23.5\n",
            "mode: [2]\n",
            "range: 223\n",
            "std: 52.2335859386\n",
            "var: 2728.3475\n",
            "Negative skew: mean < median < mode\n",
            "Positive skew: mode < median < mean\n"
          ]
        }
      ],
      "execution_count": 19,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Probability Distributions"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "Uniform Distribution"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "s = np.random.uniform(-1,0,1000)\n",
        "s"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 20,
          "data": {
            "text/plain": [
              "array([-0.41578025, -0.61374558, -0.75922468, -0.88297531, -0.78360309,\n",
              "       -0.94184362, -0.97820378, -0.44493557, -0.51560485, -0.6219762 ,\n",
              "       -0.7352949 , -0.57023561, -0.52132866, -0.68013107, -0.84036425,\n",
              "       -0.77827933, -0.00430933, -0.42904777, -0.32752206, -0.68329582,\n",
              "       -0.0799335 , -0.80417075, -0.60709341, -0.03293452, -0.69104945,\n",
              "       -0.33020035, -0.04341611, -0.42222185, -0.64957873, -0.94716461,\n",
              "       -0.57833222, -0.01340972, -0.36668767, -0.68399738, -0.19883179,\n",
              "       -0.60620804, -0.1778494 , -0.05564482, -0.02178811, -0.13487289,\n",
              "       -0.39361164, -0.02135098, -0.79272488, -0.59671515, -0.82720423,\n",
              "       -0.70099259, -0.1096216 , -0.98445498, -0.74215742, -0.76058273,\n",
              "       -0.29301625, -0.11161005, -0.48129555, -0.31931465, -0.34479385,\n",
              "       -0.96135717, -0.9343455 , -0.86960088, -0.0220046 , -0.95000546,\n",
              "       -0.20659024, -0.30740344, -0.22125661, -0.13098213, -0.72014202,\n",
              "       -0.22361692, -0.84592456, -0.05058615, -0.3455576 , -0.46239842,\n",
              "       -0.7184056 , -0.77973895, -0.35287059, -0.13255893, -0.37441765,\n",
              "       -0.9307513 , -0.2927454 , -0.26884287, -0.42677565, -0.64475228,\n",
              "       -0.57603019, -0.45879937, -0.75780469, -0.46965387, -0.2362616 ,\n",
              "       -0.52268868, -0.1179776 , -0.31892031, -0.3228403 , -0.92922091,\n",
              "       -0.61567606, -0.09411299, -0.17442831, -0.85685173, -0.82683982,\n",
              "       -0.7189731 , -0.1670325 , -0.75441365, -0.59994011, -0.62367717,\n",
              "       -0.36652966, -0.29279648, -0.38573284, -0.80767621, -0.68815925,\n",
              "       -0.63086681, -0.54639633, -0.15762374, -0.35678128, -0.71344154,\n",
              "       -0.31014702, -0.66037352, -0.17483628, -0.22871459, -0.29440772,\n",
              "       -0.92981476, -0.09305393, -0.92861557, -0.38552717, -0.44090837,\n",
              "       -0.47102798, -0.58224211, -0.52651907, -0.8175911 , -0.36876489,\n",
              "       -0.38387194, -0.42774252, -0.26499228, -0.60800579, -0.70329105,\n",
              "       -0.10065157, -0.3638692 , -0.6392418 , -0.34429089, -0.15115274,\n",
              "       -0.75025308, -0.51002737, -0.16355354, -0.03685824, -0.86357922,\n",
              "       -0.46878703, -0.22873775, -0.64020585, -0.17297979, -0.35003371,\n",
              "       -0.46893688, -0.70797242, -0.26041129, -0.44193281, -0.1654657 ,\n",
              "       -0.08389035, -0.57827742, -0.18649687, -0.63929549, -0.90871198,\n",
              "       -0.09606862, -0.88151064, -0.15423699, -0.43094929, -0.62523865,\n",
              "       -0.89117588, -0.30399866, -0.88597942, -0.49568822, -0.54568377,\n",
              "       -0.96086129, -0.45720281, -0.7317262 , -0.11876264, -0.82058583,\n",
              "       -0.9095975 , -0.65397662, -0.41265426, -0.2031593 , -0.36785035,\n",
              "       -0.93468287, -0.92988776, -0.17699857, -0.32521839, -0.82677403,\n",
              "       -0.62802377, -0.59062286, -0.18075029, -0.83473101, -0.13981361,\n",
              "       -0.07738009, -0.87525289, -0.01298733, -0.84495814, -0.7076854 ,\n",
              "       -0.5673242 , -0.42473858, -0.69981099, -0.17323341, -0.55239224,\n",
              "       -0.00813064, -0.87728796, -0.22158828, -0.20182744, -0.7425593 ,\n",
              "       -0.65759088, -0.59010651, -0.32985336, -0.9264881 , -0.27439593,\n",
              "       -0.96162657, -0.32388546, -0.240847  , -0.63700124, -0.46103523,\n",
              "       -0.14177427, -0.87432923, -0.34325985, -0.7602909 , -0.30563057,\n",
              "       -0.75638532, -0.55723745, -0.31558208, -0.00749195, -0.72130463,\n",
              "       -0.95927785, -0.61060506, -0.38061546, -0.42030273, -0.97934126,\n",
              "       -0.82357078, -0.9102244 , -0.06868281, -0.4295916 , -0.04285129,\n",
              "       -0.83830125, -0.0745931 , -0.71814164, -0.39194381, -0.4151048 ,\n",
              "       -0.45714127, -0.42235409, -0.09209223, -0.5105109 , -0.06022502,\n",
              "       -0.11901768, -0.61652337, -0.15499321, -0.63283585, -0.48956455,\n",
              "       -0.75375506, -0.16993104, -0.32956891, -0.43895996, -0.93056892,\n",
              "       -0.05706803, -0.21267326, -0.99819859, -0.55051529, -0.08586921,\n",
              "       -0.81272614, -0.26431939, -0.57324216, -0.90752616, -0.060436  ,\n",
              "       -0.27693099, -0.47539836, -0.05031803, -0.1803839 , -0.01796805,\n",
              "       -0.55784739, -0.99911491, -0.67839432, -0.7591997 , -0.62970339,\n",
              "       -0.6488856 , -0.62767047, -0.14062457, -0.05464797, -0.23107761,\n",
              "       -0.53159215, -0.06983409, -0.420059  , -0.22695509, -0.93030551,\n",
              "       -0.04170992, -0.14858455, -0.92634119, -0.48203613, -0.1543665 ,\n",
              "       -0.44530587, -0.54160633, -0.76501585, -0.65679274, -0.7756837 ,\n",
              "       -0.61766143, -0.12038081, -0.92748428, -0.1764147 , -0.39647477,\n",
              "       -0.61240645, -0.93134017, -0.25225957, -0.1636752 , -0.05273717,\n",
              "       -0.90315538, -0.77027134, -0.15725507, -0.39037255, -0.42159633,\n",
              "       -0.34032957, -0.7230071 , -0.67697886, -0.34982063, -0.57816191,\n",
              "       -0.09693998, -0.27997128, -0.9099354 , -0.58473949, -0.37138877,\n",
              "       -0.859893  , -0.77266674, -0.24782371, -0.57437219, -0.53820397,\n",
              "       -0.13023712, -0.1069509 , -0.80813138, -0.7975912 , -0.01096781,\n",
              "       -0.13700753, -0.63071451, -0.93492522, -0.93761843, -0.34705301,\n",
              "       -0.52852858, -0.32144131, -0.79057206, -0.08924473, -0.66838279,\n",
              "       -0.77382437, -0.02491001, -0.59100511, -0.87120704, -0.39490942,\n",
              "       -0.81286504, -0.6433059 , -0.26962315, -0.84032977, -0.9806618 ,\n",
              "       -0.43752638, -0.39284   , -0.44339505, -0.81186655, -0.49202024,\n",
              "       -0.47558813, -0.2454098 , -0.11448052, -0.69983998, -0.633762  ,\n",
              "       -0.44198025, -0.85473165, -0.33406312, -0.29668819, -0.46367602,\n",
              "       -0.54164034, -0.24570799, -0.11954915, -0.53376349, -0.00199476,\n",
              "       -0.07955178, -0.29412303, -0.56411083, -0.70321358, -0.2615129 ,\n",
              "       -0.73948954, -0.00504067, -0.35178888, -0.59648345, -0.07585968,\n",
              "       -0.75934169, -0.41973206, -0.95054386, -0.69074991, -0.00826368,\n",
              "       -0.33668231, -0.83350321, -0.66087176, -0.46317077, -0.73388712,\n",
              "       -0.04689255, -0.47097137, -0.11440674, -0.71993276, -0.85218628,\n",
              "       -0.77585306, -0.73944091, -0.47135249, -0.00269932, -0.47586942,\n",
              "       -0.28889169, -0.80028062, -0.7267047 , -0.35822857, -0.3437264 ,\n",
              "       -0.74135036, -0.45108045, -0.74962558, -0.87038806, -0.98069867,\n",
              "       -0.64524627, -0.35644567, -0.89106542, -0.59069025, -0.59477296,\n",
              "       -0.10917522, -0.99598461, -0.81976017, -0.55330875, -0.48973362,\n",
              "       -0.01023487, -0.19457868, -0.75717941, -0.26753518, -0.21605367,\n",
              "       -0.77464522, -0.0686905 , -0.38402261, -0.42647531, -0.33349382,\n",
              "       -0.34547066, -0.34388397, -0.59329509, -0.66990739, -0.49264108,\n",
              "       -0.79901454, -0.27149026, -0.34952898, -0.04805799, -0.24805105,\n",
              "       -0.09092897, -0.17286857, -0.22569545, -0.88246664, -0.11350877,\n",
              "       -0.29217211, -0.98922974, -0.56963436, -0.90650033, -0.66788487,\n",
              "       -0.78419422, -0.07176729, -0.48435184, -0.0062835 , -0.3715466 ,\n",
              "       -0.25982108, -0.68396769, -0.83634091, -0.43168337, -0.94338806,\n",
              "       -0.91084302, -0.76849339, -0.10587535, -0.78162923, -0.29593666,\n",
              "       -0.99412341, -0.48963323, -0.24076661, -0.90163749, -0.19399671,\n",
              "       -0.65313807, -0.36360833, -0.59688185, -0.06085403, -0.83389646,\n",
              "       -0.50436176, -0.09858749, -0.81910641, -0.90885963, -0.17834998,\n",
              "       -0.81463232, -0.70597952, -0.94715376, -0.71002307, -0.87844632,\n",
              "       -0.06761145, -0.82563739, -0.15259831, -0.48571921, -0.28018472,\n",
              "       -0.73831107, -0.13404111, -0.9150777 , -0.51270821, -0.40735672,\n",
              "       -0.69671194, -0.18960808, -0.2546675 , -0.14205627, -0.29638729,\n",
              "       -0.3401529 , -0.5543964 , -0.56912368, -0.67170041, -0.80534179,\n",
              "       -0.07624884, -0.93978821, -0.35028919, -0.91593757, -0.23160111,\n",
              "       -0.56596268, -0.60893244, -0.66953929, -0.07319529, -0.12896392,\n",
              "       -0.0491774 , -0.70093664, -0.38991686, -0.42027569, -0.63943369,\n",
              "       -0.75444587, -0.39553445, -0.51602483, -0.35000328, -0.45145845,\n",
              "       -0.96521708, -0.07198838, -0.41843012, -0.99373155, -0.89449336,\n",
              "       -0.95866889, -0.9055617 , -0.72389121, -0.79012423, -0.9025967 ,\n",
              "       -0.16333774, -0.60094587, -0.37760012, -0.04055098, -0.77951331,\n",
              "       -0.63937669, -0.64942453, -0.96729655, -0.65567679, -0.46617681,\n",
              "       -0.56080756, -0.34184494, -0.49270752, -0.15228927, -0.80670676,\n",
              "       -0.57970456, -0.9387581 , -0.50966079, -0.76616906, -0.46062539,\n",
              "       -0.69155645, -0.68745808, -0.20550561, -0.82389683, -0.88822459,\n",
              "       -0.2069826 , -0.39055423, -0.05269651, -0.12010452, -0.69592076,\n",
              "       -0.28829137, -0.99406376, -0.47607395, -0.60235016, -0.13811782,\n",
              "       -0.69922914, -0.63514819, -0.44298649, -0.32428152, -0.91907553,\n",
              "       -0.91517903, -0.39591939, -0.51688846, -0.06821448, -0.06337276,\n",
              "       -0.308898  , -0.70513378, -0.28365309, -0.79378251, -0.50189751,\n",
              "       -0.23081047, -0.40212499, -0.10004652, -0.99892397, -0.77702988,\n",
              "       -0.76121684, -0.79465512, -0.46795876, -0.92140819, -0.14435631,\n",
              "       -0.23956859, -0.84068969, -0.56777691, -0.66220022, -0.58566513,\n",
              "       -0.68969433, -0.59328523, -0.39118144, -0.8439322 , -0.35437261,\n",
              "       -0.78596297, -0.3859687 , -0.9069391 , -0.50124595, -0.25939466,\n",
              "       -0.03040267, -0.18434345, -0.16095273, -0.50838596, -0.33673796,\n",
              "       -0.56510135, -0.96856379, -0.24870762, -0.25047997, -0.49109216,\n",
              "       -0.10784503, -0.92102206, -0.72057431, -0.75583266, -0.77152961,\n",
              "       -0.02174826, -0.73660484, -0.63887545, -0.89557934, -0.74549359,\n",
              "       -0.72712589, -0.77327037, -0.55416518, -0.54562991, -0.24759312,\n",
              "       -0.68634611, -0.30937008, -0.67732689, -0.02862134, -0.98519994,\n",
              "       -0.68914606, -0.02322105, -0.06202404, -0.49960748, -0.44110508,\n",
              "       -0.47572579, -0.16657735, -0.75182471, -0.8260666 , -0.16138912,\n",
              "       -0.77504657, -0.31327022, -0.80787625, -0.63779058, -0.41614792,\n",
              "       -0.93528472, -0.25579954, -0.1338216 , -0.10280407, -0.80638344,\n",
              "       -0.63914422, -0.88874791, -0.92585594, -0.17531764, -0.58020922,\n",
              "       -0.25637537, -0.14328502, -0.43580867, -0.15971166, -0.03994391,\n",
              "       -0.29299671, -0.85183985, -0.45368365, -0.90343663, -0.3917395 ,\n",
              "       -0.18486383, -0.91725039, -0.05712314, -0.08551241, -0.03331944,\n",
              "       -0.41618542, -0.31626116, -0.98266547, -0.2323946 , -0.48838254,\n",
              "       -0.50558603, -0.72137104, -0.40983882, -0.0071357 , -0.11722453,\n",
              "       -0.39521597, -0.5387926 , -0.80503686, -0.37859463, -0.41643054,\n",
              "       -0.59137474, -0.81620156, -0.40644827, -0.6353721 , -0.45962961,\n",
              "       -0.8721326 , -0.82267778, -0.08941185, -0.58313966, -0.67413808,\n",
              "       -0.12519009, -0.81473994, -0.47059923, -0.02157067, -0.93317361,\n",
              "       -0.13853927, -0.44632828, -0.28086669, -0.34082959, -0.13885826,\n",
              "       -0.80578611, -0.9837855 , -0.73537489, -0.84989413, -0.78152587,\n",
              "       -0.90862508, -0.69145423, -0.22683871, -0.58120515, -0.35323567,\n",
              "       -0.34035737, -0.42274515, -0.12992362, -0.5053823 , -0.94748081,\n",
              "       -0.57246746, -0.13628185, -0.70756547, -0.80911322, -0.85533508,\n",
              "       -0.23626578, -0.46797284, -0.69683159, -0.92221688, -0.25757943,\n",
              "       -0.74574885, -0.0969914 , -0.56339838, -0.55970746, -0.71536053,\n",
              "       -0.81744932, -0.30248413, -0.88981957, -0.90050026, -0.42468673,\n",
              "       -0.59887678, -0.0239991 , -0.7460865 , -0.49651923, -0.24003445,\n",
              "       -0.71046715, -0.56231592, -0.29622578, -0.23527777, -0.24482888,\n",
              "       -0.92193213, -0.44838059, -0.56857573, -0.07662915, -0.74225828,\n",
              "       -0.82957736, -0.13027376, -0.16317911, -0.65593859, -0.53501375,\n",
              "       -0.1517804 , -0.50621483, -0.00584639, -0.94631545, -0.60158831,\n",
              "       -0.340367  , -0.0332892 , -0.8976488 , -0.27756651, -0.90256485,\n",
              "       -0.16938316, -0.41284721, -0.51583474, -0.89042306, -0.48633376,\n",
              "       -0.71540258, -0.75049472, -0.8716347 , -0.87406602, -0.50172039,\n",
              "       -0.55077772, -0.48912574, -0.30985852, -0.30107876, -0.8725051 ,\n",
              "       -0.43051912, -0.96829168, -0.79153036, -0.18074109, -0.18092998,\n",
              "       -0.85641024, -0.21270905, -0.38643142, -0.27232142, -0.33574816,\n",
              "       -0.5314743 , -0.05597589, -0.58917852, -0.04623735, -0.82357364,\n",
              "       -0.89856405, -0.07337006, -0.07188322, -0.35976525, -0.05954569,\n",
              "       -0.40519641, -0.64984604, -0.19711563, -0.80900527, -0.52459138,\n",
              "       -0.69314425, -0.35510167, -0.75369125, -0.69970896, -0.7389115 ,\n",
              "       -0.73213707, -0.85573078, -0.92407925, -0.92430137, -0.93423658,\n",
              "       -0.09284955, -0.79566484, -0.63072344, -0.89574597, -0.60985619,\n",
              "       -0.52293843, -0.07918915, -0.08501091, -0.57535039, -0.4230885 ,\n",
              "       -0.63863943, -0.59802563, -0.86006057, -0.75310393, -0.54193169,\n",
              "       -0.12813023, -0.01704255, -0.90863408, -0.48695115, -0.5775421 ,\n",
              "       -0.85601553, -0.2382218 , -0.17594882, -0.1572351 , -0.77503163,\n",
              "       -0.59964781, -0.89063947, -0.32877553, -0.29235346, -0.70695996,\n",
              "       -0.37121139, -0.9326223 , -0.84097035, -0.7938635 , -0.32661146,\n",
              "       -0.21826729, -0.39396604, -0.84571682, -0.12487543, -0.95323954,\n",
              "       -0.62632351, -0.15755964, -0.8386254 , -0.22848867, -0.68429725,\n",
              "       -0.68700122, -0.51816461, -0.86766409, -0.3578037 , -0.62521327,\n",
              "       -0.2297638 , -0.63337049, -0.230396  , -0.46351415, -0.34445757,\n",
              "       -0.6332508 , -0.38176854, -0.58125216, -0.11086056, -0.69674284,\n",
              "       -0.54489458, -0.75316369, -0.50382072, -0.4525829 , -0.2357315 ,\n",
              "       -0.44271003, -0.92780287, -0.2123215 , -0.48218906, -0.92365424,\n",
              "       -0.819031  , -0.66761442, -0.39808892, -0.64244964, -0.33052485,\n",
              "       -0.12292802, -0.10570587, -0.65844484, -0.41746474, -0.8545494 ,\n",
              "       -0.18728141, -0.98935775, -0.51913465, -0.83865061, -0.42216021,\n",
              "       -0.70089266, -0.34025887, -0.24921613, -0.45616966, -0.1598879 ,\n",
              "       -0.23573784, -0.19746361, -0.90854932, -0.83324921, -0.0126697 ,\n",
              "       -0.64447863, -0.10142956, -0.76726458, -0.08969188, -0.53120467,\n",
              "       -0.07425867, -0.88875941, -0.76331792, -0.57191494, -0.95574308,\n",
              "       -0.19342065, -0.03257887, -0.57095742, -0.95452193, -0.97077904,\n",
              "       -0.38233225, -0.2763309 , -0.45804204, -0.04640843, -0.01468303,\n",
              "       -0.70281623, -0.8137347 , -0.59306611, -0.094036  , -0.95149028,\n",
              "       -0.32906207, -0.37378258, -0.82803019, -0.38401555, -0.50113405,\n",
              "       -0.63380544, -0.86277489, -0.89305262, -0.83828598, -0.99385967,\n",
              "       -0.65190907, -0.27766099, -0.19891865, -0.14831108, -0.04455828,\n",
              "       -0.65795187, -0.57240963, -0.61196812, -0.29215847, -0.63515747,\n",
              "       -0.52757709, -0.59440017, -0.91933068, -0.88571396, -0.19103843,\n",
              "       -0.79723411, -0.7876785 , -0.01787078, -0.02705377, -0.21254146,\n",
              "       -0.12739143, -0.9871713 , -0.13291009, -0.28297826, -0.74028422,\n",
              "       -0.9245054 , -0.63686333, -0.88852824, -0.23116407, -0.75554899,\n",
              "       -0.26228536, -0.01487818, -0.5520133 , -0.68962705, -0.96906136,\n",
              "       -0.88071906, -0.95431752, -0.13101721, -0.75514448, -0.4885677 ,\n",
              "       -0.55323397, -0.86507064, -0.95060648, -0.06239321, -0.69979868])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 20,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "np.all(s >= -1)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 21,
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 21,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "np.all(s < 0)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 22,
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 22,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "count, bins, ignored = plt.hist(s, 15, normed=True)\n",
        "plt.plot(bins, np.ones_like(bins), linewidth=2, color='r')\n",
        "plt.grid()\n",
        "plt.title(\"Uniform Distribution\")\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              "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\n"
            ],
            "text/plain": [
              "<matplotlib.figure.Figure at 0x260b55eb208>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 23,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Normal Distribution"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "samples = np.random.normal(1, 100, 50)\n",
        "samples"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 24,
          "data": {
            "text/plain": [
              "array([ -70.73268231,  139.34310783,   73.26574497,   57.52956191,\n",
              "        141.32558109,   89.70434524,   90.35260385,    7.93326925,\n",
              "        112.25490894,   59.04475528,  -60.27653175,   18.26157234,\n",
              "         75.04801267,  -64.32224422,   28.65900041,  -29.91546654,\n",
              "        154.52006115,    2.79293182,  -87.06865817,  -64.82502711,\n",
              "        -65.56191754, -268.39188052,  138.87285545,  -64.73415747,\n",
              "         -7.54940022,   13.37897833,  -90.98543039,  -19.49906152,\n",
              "        122.22044924, -166.54250473,   62.57791413,  120.17583276,\n",
              "         49.15151357,   49.05191329, -105.94825192,   37.66318874,\n",
              "        -76.87847743,   31.57858474,  -32.50330922,  -51.58407535,\n",
              "         73.20208188,  -13.96298688,  -56.41886833,   59.06613704,\n",
              "       -138.47200754,   84.58020093,  -44.12457155,  156.09725098,\n",
              "        178.90771988,  -79.75124079])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 24,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mu = np.mean(samples)\n",
        "sigma = np.std(samples)\n",
        "s = np.random.normal(mu, sigma, len(samples))\n",
        "s"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 25,
          "data": {
            "text/plain": [
              "array([ -23.80973217,  160.42752189, -109.55838177,   30.69676199,\n",
              "         96.19629418,   53.16643095,  -92.54456411,  -95.90625864,\n",
              "         59.34827033,   -1.4556773 ,   64.58716514,  -54.10276204,\n",
              "         36.3596223 ,  113.03253577,   45.29550505,   24.48846825,\n",
              "        -42.62062409,   17.78715797, -129.92190837,    3.01943001,\n",
              "         63.03814456,   17.83872291,   54.06623689,    6.8452103 ,\n",
              "         15.81852139,   21.16839183,  149.34300927,   21.70174219,\n",
              "         43.81738636,  -21.5609433 ,  -25.18806003,   78.6316852 ,\n",
              "       -101.9759564 ,   31.2381579 ,   48.9686271 ,  145.33248288,\n",
              "         61.28084646,   24.53613555,   33.96441985,   42.24319164,\n",
              "        132.39116049,  -50.02707596,   30.0010136 ,   64.56813558,\n",
              "         84.35460433,   34.9957701 ,  110.38767418,   82.69660499,\n",
              "        -38.15741302,  -65.99748715])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 25,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "abs(mu - np.mean(samples)) < 0.01"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 26,
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 26,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "abs(sigma - np.std(s, ddof=1)) < 0.01"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 27,
          "data": {
            "text/plain": [
              "False"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 27,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "count, bins, ignored = plt.hist(s, 30, normed=True)\n",
        "plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) *\n",
        "         np.exp( - (bins - mu)**2 / (2 * sigma**2) ),\n",
        "         linewidth=2, color='r')\n",
        "plt.title(\"Normal Distribution\")\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              "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\n"
            ],
            "text/plain": [
              "<matplotlib.figure.Figure at 0x260b57383c8>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 28,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Multivariate Normal Distribution"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import multivariate_normal\n",
        "x = np.linspace(0, 5, 10, endpoint=False)\n",
        "y = multivariate_normal.pdf(x, mean=2.5, cov=0.5)\n",
        "y"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 29,
          "data": {
            "text/plain": [
              "array([ 0.00108914,  0.01033349,  0.05946514,  0.20755375,  0.43939129,\n",
              "        0.56418958,  0.43939129,  0.20755375,  0.05946514,  0.01033349])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 29,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(x, y)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 30,
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x260b5f0d908>]"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              "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\n"
            ],
            "text/plain": [
              "<matplotlib.figure.Figure at 0x260b5773be0>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 30,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Bernoulli Distribution"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import bernoulli\n",
        "import seaborn as sns\n",
        "\n",
        "data = [1,8,10,11,25,37]\n",
        "p = .5\n",
        "\n",
        "data_bern = bernoulli.rvs(size=1000,p=p)\n",
        "ax = sns.distplot(data,\n",
        "                  kde=True,\n",
        "                  color='blue',\n",
        "                  hist_kws={\"linewidth\": 1,'alpha':1})\n",
        "ax.set(xlabel='Bernouli', ylabel='Frequency')"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 31,
          "data": {
            "text/plain": [
              "[<matplotlib.text.Text at 0x260b6213ef0>,\n",
              " <matplotlib.text.Text at 0x260b620a860>]"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              "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\n"
            ],
            "text/plain": [
              "<matplotlib.figure.Figure at 0x260b5edff98>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 31,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "R = bernoulli.rvs(p, size=100)\n",
        "R"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 32,
          "data": {
            "text/plain": [
              "array([1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1,\n",
              "       1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0,\n",
              "       0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0,\n",
              "       0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1,\n",
              "       1, 0, 1, 1, 1, 1, 0, 0])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 32,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Bionomial Distribution"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "n = 10\n",
        "p = 0.3\n",
        "k = np.arange(0,21)\n",
        "binomial = stats.binom.pmf(k, n, p)\n",
        "binomial"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 33,
          "data": {
            "text/plain": [
              "array([  2.82475249e-02,   1.21060821e-01,   2.33474440e-01,\n",
              "         2.66827932e-01,   2.00120949e-01,   1.02919345e-01,\n",
              "         3.67569090e-02,   9.00169200e-03,   1.44670050e-03,\n",
              "         1.37781000e-04,   5.90490000e-06,   0.00000000e+00,\n",
              "         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
              "         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
              "         0.00000000e+00,   0.00000000e+00,   0.00000000e+00])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 33,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(k, binomial, 'o-')\n",
        "plt.title('Binomial: n=%i, p = %.2f' % (n,p), fontsize=15)\n",
        "plt.xlabel('Number of successes')\n",
        "plt.ylabel('Probability of successes', fontsize=15)\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              "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\n"
            ],
            "text/plain": [
              "<matplotlib.figure.Figure at 0x260b5f25198>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 34,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "binom_sim = data = stats.binom.rvs(n=10, p=0.3, size=10000)\n",
        "print('Mean: %g' % np.mean(binom_sim))\n",
        "print('SD: %g' % np.std(binom_sim, ddof=1))\n",
        "plt.hist(binom_sim, bins=10, normed=True)\n",
        "plt.xlabel(\"x\")\n",
        "plt.ylabel(\"density\")\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean: 2.9866\n",
            "SD: 1.44666\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              "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\n"
            ],
            "text/plain": [
              "<matplotlib.figure.Figure at 0x260b7276080>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 35,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Poisson Distribution"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "rate = 2\n",
        "n = np.arange(0, 10)\n",
        "y = stats.poisson.pmf(n, rate)\n",
        "y"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 36,
          "data": {
            "text/plain": [
              "array([  1.35335283e-01,   2.70670566e-01,   2.70670566e-01,\n",
              "         1.80447044e-01,   9.02235222e-02,   3.60894089e-02,\n",
              "         1.20298030e-02,   3.43708656e-03,   8.59271640e-04,\n",
              "         1.90949253e-04])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 36,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(n, y, 'o-')\n",
        "plt.title('Poisson: $\\lambda$ =%i' % rate)\n",
        "plt.xlabel('Number of accidents')\n",
        "plt.ylabel('Probability of number of accident')\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              "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\n"
            ],
            "text/plain": [
              "<matplotlib.figure.Figure at 0x260b5ed1470>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 37,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "data = stats.poisson.rvs(mu=2, loc=0, size=10000)\n",
        "print('Mean: %g' % np.mean(data))\n",
        "print('SD: %g' % np.std(data, ddof=1))\n",
        "plt.hist(data, bins=9, normed=True)\n",
        "plt.xlabel(\"Number of accidents\")\n",
        "plt.ylabel(\"Simulating Poisson Random Variables\")\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean: 2.006\n",
            "SD: 1.41243\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              "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\n"
            ],
            "text/plain": [
              "<matplotlib.figure.Figure at 0x260b5f2ca58>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 38,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Maximum Likelilhood Estimate"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import norm\n",
        "\n",
        "# Example\n",
        "samples = 4\n",
        "mu = 2\n",
        "sd = 1\n",
        "norm.pdf(samples, mu, sd)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 39,
          "data": {
            "text/plain": [
              "0.053990966513188063"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 39,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Compare the likelihood of the random samples of two distributions\n",
        "x = [1,2,3,4,5,6,7,8,9,10]\n",
        "\n",
        "def compare_dist(x, mu_1=4, mu_2=8, sd_1=3, sd_2=3):\n",
        "    ll_1 = 0\n",
        "    ll_2 = 0\n",
        "    for i in x:\n",
        "        ll_1 += np.log(norm.pdf(i, mu_1, sd_1))\n",
        "        ll_2 += np.log(norm.pdf(i, mu_2, sd_2))\n",
        "    \n",
        "    print(\"The Likelihood of x for mu = %d and sd = %d is: %.4f\" % (mu_1, sd_1, ll_1))\n",
        "    print(\"The Likelihood of x for mu = %d and sd = %d is: %.4f\" % (mu_2, sd_2, ll_2))\n",
        "    if ll_1 > ll_2:\n",
        "        print(\"The first Likelihood is the better answer.\")\n",
        "    else:\n",
        "        print(\"The second Likelihood is the better answer.\")\n",
        "        \n",
        "compare_dist(x)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The Likelihood of x for mu = 4 and sd = 3 is: -26.0088\n",
            "The Likelihood of x for mu = 8 and sd = 3 is: -28.2311\n",
            "The first Likelihood is the better answer.\n"
          ]
        }
      ],
      "execution_count": 40,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Hypothesis Testing & p-value"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy import stats\n",
        "\n",
        "data1 = [0,1,2,3,4,5,6]\n",
        "data2 = [1,8,9,6,4,3,2]\n",
        "\n",
        "beta, alpha, r_value, p_value, std_err = stats.linregress(data1, data2)\n",
        "print(beta, alpha)\n",
        "print(\"R-squared=\", r_value**2)\n",
        "print(\"p-value =\", p_value)\n",
        "\n",
        "if p_value < alpha:  # null hypothesis: x comes from a normal distribution\n",
        "    print(\"The null hypothesis can be rejected\")\n",
        "else:\n",
        "    print(\"The null hypothesis cannot be rejected\")"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-0.428571428571 6.0\n",
            "R-squared= 0.0927835051546\n",
            "p-value = 0.506540486632\n",
            "The null hypothesis can be rejected\n"
          ]
        }
      ],
      "execution_count": 41,
      "metadata": {}
    }
  ],
  "metadata": {
    "kernelspec": {
      "name": "python3",
      "language": "python",
      "display_name": "Python 3"
    },
    "kernel_info": {
      "name": "python3"
    },
    "language_info": {
      "file_extension": ".py",
      "version": "3.5.5",
      "codemirror_mode": {
        "version": 3,
        "name": "ipython"
      },
      "name": "python",
      "pygments_lexer": "ipython3",
      "mimetype": "text/x-python",
      "nbconvert_exporter": "python"
    },
    "nteract": {
      "version": "0.12.2"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 4
}