0011 Using the Probability Density Function.ipynb

{
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "'1.9.1'"
       ],
       "metadata": {}
      }
     ],
     "input": [
      "%matplotlib inline\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "import seaborn as sns\n",
      "from scipy import stats\n",
      "from __future__ import division\n",
      "\n",
      "sns.set_palette(['#00A99D', '#F5CA0C', '#B6129F', '#76620C', '#095C57'])\n",
      "np.version.full_version"
     ],
     "language": "python",
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Data"
     ]
    },
    {
     "cell_type": "code",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "array([ 182.69792418,  198.23020226,  157.56420921,  125.45396097,\n",
        "        195.21382698,  165.43823491,  183.35407068,  205.80912603,\n",
        "        147.99162148,  175.44291567,  186.29464374,  231.45285956])"
       ],
       "metadata": {}
      }
     ],
     "input": [
      "#We use a fictional data set of 10000 averge number of Facebook friends.\n",
      "facebook_mu = 190.0\n",
      "facebook_sigma = 36.0\n",
      "facebook_friends = np.random.normal(facebook_mu, facebook_sigma, 10000)\n",
      "\n",
      "# show first 12 samples\n",
      "facebook_friends[:12]"
     ],
     "language": "python",
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Using the Probability Density Function\n",
      "The total area under the Probability Density Function (pdf) is always 1.0. Roughly 68% of the values is within 1 standard deviation from the mean. About 95% falls within two standard deviations. We can determine the probability of finding a given value in the distribution by using the pdf. \n",
      "\n",
      "Let's say someone's got 227 Facebook friends. What is the probability of having this or less number of Facebook friends?"
     ]
    },
    {
     "cell_type": "code",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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ciWzdugWfz0dpack33uNyJWC365hDpKH00yLSTGqmex0y2OIkbYDNRnHvnlR4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\nbowxxnjAOnRjjDHGA9ahG2OMMR74D6tfYWdp5ykxAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3c12e10>"
       ],
       "metadata": {}
      }
     ],
     "input": [
      "# First take a look at the pdf and especially the green area under\n",
      "# the curve containing the probability of 227 Facebook friends or less.\n",
      "x = 227.0\n",
      "sns.distplot(facebook_friends, label='Facebook friends', kde=False, \n",
      "             fit=stats.norm, color='w')\n",
      "plt.text(x+5, .0003, '$x$='+str(x))\n",
      "\n",
      "x_plot = np.linspace(min(facebook_friends), x, 1000)\n",
      "y_plot = stats.norm.pdf(x_plot, facebook_mu, facebook_sigma)\n",
      "plt.fill_between(x_plot,  y_plot)\n",
      "c=plt.legend()"
     ],
     "language": "python",
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "1.0277777777777777"
       ],
       "metadata": {}
      }
     ],
     "input": [
      "# To calculate the probability, we need the z score.\n",
      "zscore = (x - facebook_mu) / facebook_sigma\n",
      "zscore"
     ],
     "language": "python",
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "0.84797281411763326"
       ],
       "metadata": {}
      }
     ],
     "input": [
      "# Calculate the probability by calling stats.norm.cdf\n",
      "# This is a computational z table lookup\n",
      "p = stats.norm.cdf(zscore)\n",
      "p"
     ],
     "language": "python",
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So this means the probability of people having 227 Facebook friends or less is about 85%. Since the area under the curve adds up to 1, we can say that the probability of people having a value more than 227 Facebook friends is $1-p$."
     ]
    },
    {
     "cell_type": "code",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "0.15202718588236674"
       ],
       "metadata": {}
      }
     ],
     "input": [
      "# Probability of having a value more than 227\n",
      "1 - p"
     ],
     "language": "python",
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## From probability back to the actual value\n",
      "Let's assume we have a 21% chance of having a certain number of Facebook friends or more. What is the minimum number of Facebook friends we have in this case?"
     ]
    },
    {
     "cell_type": "code",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "0.80642124701824036"
       ],
       "metadata": {}
      }
     ],
     "input": [
      "# We use the ppf function (inverse cdf) - from probability to z score\n",
      "p = 1 - .21\n",
      "z = stats.norm.ppf(p)\n",
      "z"
     ],
     "language": "python",
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "219.03116489265665"
       ],
       "metadata": {}
      }
     ],
     "input": [
      "# From z score to number of Facebook friends\n",
      "x = z * facebook_sigma + facebook_mu\n",
      "x"
     ],
     "language": "python",
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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c3Oynez2bog7tCDkcZK/VBDMiDUmFLtKAsrNXAZCZOdjiJJErHB9HYUZn/CdP\ncuTIYavjiMQMFbpIA1q9ehV2u52BA5vv7Wq1UdCjG/D1L0AiUn8qdJEG4vP52LJlM/369W/207zW\npKBn+eNkP5r/kcVJRGLHOR+fKiK1t3btGsrKyjTday2UpKUSTElmx47tBINBiooKv/Uet9uD3a59\nDpHa0t8WkQby9XSvoyxOEgVsNgp6dKM0EGDjxvXfmmkvGCzG7/dZnVIkqqjQRRpAOBxm9epVuN1u\n+vbtb3WcqFDQsxsAq1ZlfWOmvZSUFNxuj7XhRKKQCl2kARw6dJC8vEMMHz6C+HidyaqNgowuhG02\nlmYtszqKSExQoYs0gHXr1gLo/Pl3EEpKpLhjO44ezqOgoMDqOCJRT4Uu0gDWrl0DqNBrEg6FoLAI\nCguhsJCCLh0hHGbjxvVWRxOJejo2KFJPpaWlbNy4ns6du9CxY0er40S0YGER13foirNlCgC+0ji2\nrlzL0uVLmTr1MovTiUQ3FbpIPW3fvo2ioiJGjdLeeW04kxJxusvv00/t3xe7y8WGDRssTiUS/XTI\nXaSeNmwof2rYyJG6Xe27ssfH4+nZnVMnjnPgwH6r44hENRW6SD2tX7+WuLg4hg4dbnWUqOQ5rxcA\nq1attDiJSHRToYvUQ37+KXbt2kHfvv1p0aKF1XGiUvJ5PQFYtOQzi5OIRDcVukg9rFu3hnA4zNCh\nw6yOErVcrdNwpbVi86ZNlJaWWh1HJGqp0EXqYc2a8md6Dxumw+31kdLbIFBczJYtm62OIhK1VOgi\ndRQOh8nJWU1ycjI9e/ayOk5US+ld/v1bsUKzxonUlQpdpI727v2So0e/IjNzCHFxcVbHiWrJvXqA\n3c6S5Sp0kbpSoYvUUeXh9sGDh1qcJPrFJyaS3LM7+/bsxuv1Wh1HJCqp0EXqKCdnNQBDhqjQG0Lq\ngH4VpzGyrY4iEpVU6CJ1UFJSwsaN6+jWLYPWrdOtjhMTWvbvB8CSpYstTiISnVToInWwfv16AoEA\nw4ePtDpKzPB070Z8UhI5a7IJh8NWxxGJOip0kTrIysoCYPhwTffaUGx2Oy379eHUiRMcPHjA6jgi\nUUeFLlIHWVlZOBwOMjMHWx0lpqQOLD/srvPoIt+dCl3kOzpx4jjbtm1j4MBBJCYmWh0nplSeR1+u\n+9FFvrNzPj7VMAw78AwwEAgAt5mm+UW15dOAh4FSYLZpmi+cbR3DMNoAzwMtARtwk2maXzb8kEQa\nTygUYvl7EJYNAAAgAElEQVTypQAMGJCJ15uPz+fF6Uy1OFlsSGidRmL7dpjmdoLBoNVxRKJKTXvo\n0wGnaZpjgIeAJyoXGIbhAGYBk4GJwB0VpT0dcJ1hnceA10zTnAj8GujfkAMRaQp+v49163IAGDly\nJC6Xg2AwQCBQYnGy2JHavy/BkhK2b99qdRSRqFJToY8FPgEwTTMbqP4Eij7ALtM0803TDAIrgAkV\n63x8hnXGAJ0Nw/gU+AGwqKEGIdJUwuEwubkbSUtLY/DgIaSkpNCihdvqWDEldWD57/orV2ZZnEQk\nupzzkDuQDFSftqnMMAy7aZqhimX51Zb5gJSzrBMHdANOmKY52TCMh4FfAI/UFDA93VPjIKJVLI8N\nYnN8e/eanDhxgmnTppGSkgSA2+3C4XDg8SRUvS8WXvN4Ehpse0VFrhq/t5VSep+HLS6OlWtWNurP\nUCz+fFaK5bFB7I+vrmoqdC9Q/TtXWeZQXubVl3mAU2dZp8wwjOPABxWvzQV+X5uAR4/6avO2qJOe\n7onZsUHsjm/x4uUAjB07Fp+vGAC/P4DTGa76PBZe83gS8PmKG2x7BQWBGr+3leISEnD3yOD4jl3s\n3LmPli0b/vqEWP35hNgeGzSP8dVVTYfcs4CpAIZhjAJyqy3bDvQyDCPVMAwn5YfbV55jnRXA9yr+\nPBHQcxIl6qxfvxaA0aNHW5wktqX0MQBYuzbH4iQi0aOmQn8XKDYMI4vyi9t+ZhjG9YZh3F5x3vw+\nYD7lRf6iaZp5Z1qnYlv3AzdVvD4F+J+GH45I4ykqKmLz5k10796DNm3aWB0nprXs2xuA+Qs/sTiJ\nSPQ45yF30zTDwIzTXt5Rbfk8YF4t1sE0zX2UF7lIVNq4cT2lpUGGDx9hdZSYl9SpI6WJCWz8fCPh\ncBibzWZ1JJGIp4llRGopJ2cVgAq9Cdjsdgq6dSZQUMCXX+62Oo5IVFChi9RSdvYqEhMT6dtXUyg0\ntnAoRGHHdgAsWrQQrzcfrzefUChUw5oizZcKXaQWDh48wIED+8nMHIzD4bA6TswLFhZx0bDyIyGr\n16yqmMCnGL8/dq9uFqmvmm5bExEgJ2c1AEOGDKvhndJQ3O3bktSpI1/s3ElCQvn97YGApoMVORvt\noYvUQnZ2+flzFXrTSh3Ql9JgkM8/32B1FJGIp0IXqUEwGGTDhrV06dKVdu3aWx2nWUmtePra4iWL\nLU4iEvlU6CJnEQqF8Hrzyc5eSVFREYMGDcHn8xIO68KsppJs9MLmiCdr9Uqro4hEPBW6yFn4/T6C\nwWI2blwPwMiRo/RktSYW53KRYpzH4QMHOHHiuNVxRCKaCl3kHNxuD+vXr8XpdDJ+/Hg9Wc0ClYfd\n16zRNLAi56JCFzmHY8eOsWvXTgYPHkpCQqLVcZql1AF9AViyfIm1QUQinApd5BzWrl0DwOjRYyxO\n0nwlde6EIyWFrVu2aGIZkXNQoYucQ+XTvlTo1rHZbKQO6Euh38+XX+6xOo5IxFKhi5xFWVkZ69ev\npV27dnTrlmF1nGbt69vXFlmcRCRyqdBFzmLHDhOfz8fo0WP1tC+Ltexffh592aoVFicRiVwqdJGz\nWL++/Pz5qFE63G41Z0oyLbp25vjhPAoK/FbHEYlIKnSRs1i3bi1xcXEMHz7c6ihCxV56OMyqVZpk\nRuRMVOgiZ3Dq1Cl27jTp27c/brfH6jjC14fd3533rsVJRCKTCl3kDHJyVhEOhxk+fITVUaRCiy6d\nKU1KZPu2rbp9TeQMVOgiZ7BqVRYAo0aNtjiJVLLZ7RR070KwqIidO02r44hEHBW6yGlKS0vJzl5F\nenob3a4WYfzduwIw96O5FicRiTwqdJHTbN6ci9/vY8SIkbpdLcIUZHQhbLOxbOVyq6OIRBwVushp\nVlXc6zxs2EiLk8jpQgkuirp05NSRI5w6ddLqOCIRRYUucpqVK7NwuVwMHDjI6ihyBv7zugOwdOli\ni5OIRBYVukg1hw4dZO/ePQwdOhyXy2V1HDkDf6/yQn/3ow8sTiISWVToItVUHm4fPXqcxUnkbEra\ntCaYkszeL3ZRWlpqdRyRiKFCF6kQCoVYtmwJAAMGDMTn8xIO637niGOz4e+VQVlJCbm5G61OIxIx\nVOgiFY4e/YpNmz6ne/cedOzYgWAwQCBQYnUsOQN/754AvPXu2xYnEYkcKnSRChs3rqe0tJSJEy8g\nJSWFFi3cVkeSsyjs1oWQ08G6DWsJh8NWxxGJCCp0kQpr1qwGYOxYnT+PdGFHPP6eGRR7vezd+6XV\ncUQiggpdBCgrKyMnZzUtW7akX7/+VseRWvAbPQD4YO57FicRiQwqdBFg69YtnDp1ilGjxhAXF2d1\nHKkF/3k9CNtsfLZc96OLgApdBIAVK5YAOtweTUJJiRR16cjJw4c5ceK41XFELKdCl2YpFArh9ebj\n9eaTn3+KpUsX43IlMGjQYKujyVmEQyEoLILCwqoPX0YXAD788P2q/59eb74eryrNUrzVAUSs4Pf7\nCAaLcbs97N27l0OHDlY8+1wPY4lUwcIiru/QFWfLlKrXjheF2LVkJctXreD7378OKP9/6/dDcnLK\n2TYlEpNU6NJsud0eUlJSWL9+DQCjR4+1OJHUxJmUiNP99e2Ens6dSGzXll2micvlJCEhEYBAIGhV\nRBHLnLPQDcOwA88AA4EAcJtpml9UWz4NeBgoBWabpvlCLda5AbjLNM0xDT0YkbpYunQJcXFxDBky\nzOooUgct+/clb+FiVq5cyaRJF1odR8QyNZ1Dnw44K8r3IeCJygWGYTiAWcBkYCJwh2EYbSrWcZ1l\nncHArQ06ApF6OHr0K7Zs2czgwUPxeDxWx5E6SB3QF4D3P9TDWqR5q6nQxwKfAJimmQ1U34XpA+wy\nTTPfNM0gsAKYULHOx6evYxhGGvB74F50olIixLJlSwGYOPF8a4NInbm7dMaRksLG9ev0sBZp1moq\n9GTAW+3zsopD6pXL8qst8wEpZ1nHCbwI3Af465VYpAEtXboEUKFHM5vdTuthgykqKGD9+nVWxxGx\nTE0XxXmB6sch7aZpVt4Pkn/aMg9w6kzrAJlAT+BZIAHoaxjGLNM076spYHp67B4GjeWxQWSPz+kM\n4ff7WbduDX379qVXrwz27duHw+HA40kAwO12fePz6q8BtXpfNL/m8SQ02PaKihr32fJpw4eS99kS\n3p/3Hr8b9igeTwIpKef++Yvkn8/6iuWxQeyPr65qKvQsYBrwlmEYo4Dcasu2A70Mw0gFCig/3P44\nED59HdM01wD9AQzD6Aq8WZsyBzh61PcdhhM90tM9MTs2iPzxeb0+srKWEgwGGTduAj5fMX5/AKcz\njM9XDPCtz6u/BtTqfdH6mseTcMbvSV23V1AQOMv/iYbRsvd5xLvdrFy5kvz8QoLBMkpKzn4AMtJ/\nPusjlscGzWN8dVXTIfd3gWLDMLIov7jtZ4ZhXG8Yxu0V583vA+YDK4EXTdPMO9M6p23TRnnpi1iq\n8tnnkyZdZG0QqTdbXBythw2mwOtly5ZNVscRscQ599BN0wwDM057eUe15fOAebVYp/ryLwHdsiaW\nKiwsJCcnm+7de9C9ew+r40gDSBs+lMNLljP3w7ncf15fq+OINDlNLCPNUk7OaoLBIBdeONnqKNJA\nWvbtTXxSEjlr15Cff+pby91uD3a7ZruW2KWfbmmWVqxYBsCFF+pwe6ywx8fTakgmBfn57N69A5fL\nUfURDBbj98fueVcRUKFLM1RYWMC6dTl069ZNh9tjTOvhQwFYvHQpKSkpVR9ut66KltinQpdmJytr\nOcFgkAkTzrc6ijSw1P79sLucrFm3hnBY195K86JCl2ZnyZLPAFToMcjudJDSpze+kyfZvn2r1XFE\nmpQKXZqVwsICsrNX0aVLN7p27WZ1HGkELQf2B+Bfb//b4iQiTUuFLs1KVtZySkpKGDdugtVRpJEk\n9z6PuIQEli9fRigUqnkFkRihQpdmpfJwuwo9dtkdDlpl9sd36hQbNqy3Oo5Ik1GhS7Ph8/lYvXol\nGRnd6dKlq9VxpBGlDR0MwJtvvWlxEpGmo0KXZmPJks8IBoNMnnyp1VGkkSX36oEjJYXs1asIBoNW\nxxFpEip0aTYWLPgYgMmTL7Y4iTQ2m91O+qjhFBcWkpW13Oo4Ik1ChS4xLxQKsWvXDj7/fAMDBmSS\nmJiIz+clHNYFU7GszZiRALz5jq52l+ZBhS4xz+/3sWjRAgAmT55SMRVogECgxOJk0pjcGd1IaNuG\n3A0bKCoqtDqOSKNToUvMC4fDLFu2FKfTyfe+N42UlBRatHBbHUsamc1mo83okZSWlLB4yWKr44g0\nOhW6xLwvvtjFvn17GTduAh6P5vRuTtIrDrvP/XheDe8UiX56fKrElFAo9K2nai1Y8BEAl1461YpI\nYqGk9u1wZ3TlC3M7J0+eIDk5xepIIo1Ge+gSU/x+H8FgcdVjM+PjbWRlrcDj8TBmzDir44kF2o4f\nSzgU5g3dky4xToUuMcft9lQ9NtM0TfLzTzFu3EQcDofV0cQC6aNHYIuPZ9GSz/QENolpKnSJaR98\n8B4AkyZNsjiJWMXhdtNq0ACKvV42bfrc6jgijUaFLjHr5MkTLF26mE6dOmMYfayOIxZKHzMKgP+b\n/ZzFSUQajwpdYtZHH82jtLSUyZOnYLPZrI4jFko2ehFMdrMldyNFRUVWxxFpFCp0iUnhcJj33nsX\nh8PBxIkXWB1HLGaz28kf0IdwaSkfzH3P6jgijUKFLjFp48YN7N37JRdccCEeT7LVcSQC5A/oDcA/\n3/mXxUlEGocKXWLSe+/NAWD69KssTiKRIpiSTEH3LpzMO8SePXusjiPS4FToEnN8Ph+LFi2kc+fO\nDB06zOo4EkHyBw8A4I+zZlmcRKThqdAl5nz22acEAgEuv/xKXQwn3+Drcx6lSYlkrVhOIFBsdRyR\nBqVCl5gSDof5+OMPiYuL57LLLrc6jkSIcCgEhUWEgyWcGtiHsuIA78x5y+pYIg1KhS4xZevWLeze\n/QUTJ04kLS3N6jgSIYKFRVzfoSs3d+vFRdOmgc3Ga//6p2aOk5iiQpeY8v775RfDXXvtDRYnkUjj\nTErE6Xbj6dKZ1MwBFJw4Tm7uRqtjiTQYFbrEjMOH81i9OouePXsxaNBgq+NIBGs7sfxBPU8++5TF\nSUQajgpdYsacOW8RCoW46qprdDGcnFOy0YtAWipfbN/G8ePHrI4j0iBU6BITCgsLmTfvfVq2TNXM\ncFKzcJiTA3pDKMSTf3sSrzcfrzefUChkdTKROlOhS0yYP/8j/H4fU6dOw+l0Wh1HIlywsIgp519A\nXEICa7JXYbdDMFiM3++zOppInanQJeqFQiHeeedfOBwOLr30MqvjSJRITG1J24njKPT5WLhoIW63\nx+pIIvWiQpeol5Ozmn379jJp0mRSU1OtjiNRpOMlk7HFxfHKay/rcLtEPRW6RL033ngNgGuuuc7i\nJBJtElqnkT56JMePHGHp0iVWxxGpl/hzLTQMww48AwwEAsBtpml+UW35NOBhoBSYbZrmC2dbxzCM\nQcBTQFnF6zeZpvlVI4xJmpHc3I1s2LCOkSNHYxi98XrzrY4kUabzZZfw1YqVvPTaS4wePc7qOCJ1\nVtMe+nTAaZrmGOAh4InKBYZhOIBZwGRgInCHYRhtKtZxnWGdJ4G7TNO8AJgD/KIhByLN06uvzgbg\npptutTiJRKukjh1IGzqYvP37Wbt2jdVxROqspkIfC3wCYJpmNlD90VV9gF2maeabphkEVgATKtb5\n+AzrXGeaZm7Fnx1AUYOMQJqtrVs3k5OzmoEDB9G1aze83nx8Pi/hsM6FynfT6bJLAfjfF561OIlI\n3dVU6MmAt9rnZRWH1CuXVT++6QNSzraOaZqHAQzDGAPcCfylPsGleQmFQlX3Cld+PP98+T++N954\nEy6XA5fLQTAYIBAosTitRJvknt1JPq8Xxw8eYPPm3JpXEIlA5zyHTnkxV7+Xw26aZuXuT/5pyzzA\nqXOtYxjGtcBMYKppmsdrEzA9PXZvJYnlsUHDji8/P59gEDye8m3u3LmTdevW0K9fPy677JKqmeFC\noQAOhwOPJ6FqXbfbVafXzvUeoFbvi+bXPJ6EBtteUZGLSNfhkovw7tjJH598jPnvv291nHrRvy3N\nU02FngVMA94yDGMUUP1X1+1AL8MwUoECyg+3Pw6Ez7SOYRg3AncA55umebK2AY8ejc2JHtLTPTE7\nNmj48Xm9PlwuB3Z7eTG8/PKrQPmV7X5/oOp9fn8ApzOMz1dc79fO9R6gVu+L1tc8ngR8vuIG215B\nwdf/jyJVcu/zKOzQjn07drBw4TIyM6PzeQD6tyW61eeXlZoOub8LFBuGkUX5xW0/MwzjesMwbq84\nb34fMB9YCbxommbeWdaJA/4KuIE5hmEsNgzj0Tqnlmbtiy92sWjRQnr06MnQocNqXkGkFmw2G0fP\nHw3Ab//03xanEfnuzrmHbppmGJhx2ss7qi2fB8yrxToAeji1NIinn36ScDjMtdfeoIewSIMJh0IU\npaXiz+gCe/Yxf/7HjB49Brfbg92uKTsk8umnVKJKTk42K1dmMWzYCIYMGWp1HIkhwcIiru/QlVHX\nfx+AF15+jpKSIs3vLlFDhS5RIxQK8fTTTwJwzz33au9cGpwzKZHUPr1pPXI4Rw4eZNXqVVZHEqk1\nFbpEjUWLFmKa27nkkqn07t3H6jgSw7pdMx3sdp6f/TxlZWVWxxGpFRW6RIWSkhJeeulFHA4HM2bc\naXUciXGJ7drS7vzxnDp2jNkVsxGKRDoVukSFuXPf46uvjnDttdfTvn0Hq+NIM9D1qiuIS0zkgw/m\ncOJErabNELGUCl0i3pEjR3jjjdfweJL54Q9/ZHUcaSacKcl0unwq4WApD/7XL74xS6EetSqRSIUu\nEe+vf32c4uJi7rhjBsnJyVbHkWYkdcggEju0Z8fmXLZt21QxvXCxrnyXiKRCl4i2fPkSVqxYRv/+\nA7j44kusjiPNjM1uJ+PaqwB4/C9/pkWLFrjdmnZUIpMKXSJWYWEBTz75ZxwOB3feqdvUxBqebl1p\nO3EcXx06xPMvPmd1HJGzUqFLxHrhhb9z9OhX/OAHN9O5cxer40gz1u37VxPfIonXXn2ZAwf2Wx1H\n5IxU6BKRtmzZxJw5/6Zz5y784Ac3Wx1HmjlnsoceN/+A0mCQ/3r0v3RvukQkFbpEnIICP7/97cOE\nw2EeeGAmLlfkP3pTYl+b0SNpPXI4B/fu5ZnnnrE6jsi3qNAl4vzlL4+Tl3eIG2+8mUGDhlgdR6RK\nzx/+AEdKCvM/msvWrVusjiPyDSp0iSgLFnzMggUf07dvf2655Q6r44h8g8PtpvtN10E4zH0P/YxA\nIPKf8y7NhwpdIsbBgwd44ok/kZSUxH33PUhhYUHVRB4+n5dwWJN5iPVa9u3DycH9KTx1ivt+eR/h\ncNjqSCKACl0iRCBQzG9+8yuKigqZMeNu0tJScbkcVR/BYIBAoMTqmCIAfHXBWIrbt2HT2jW89MqL\nVscRAVToYrFQKER+/il++9tfs337Ni666GKGDRtBixYtSElJqfpo0cJtdVSRKmFHPAeum05pUiIv\nv/Q869atsTqSiApdrOX3+3j99ZdZvnwJ/fr152c/u1974xIVSlumcOj7lxMGHvjl/Xz11RGrI0kz\np0KXRhEKhb7xMIuzPdRi2bIlvPnmP2nfvgOzZv2V9PR07Y1LRAuHQlBYBIWFFLZtzVeTxlJaXMyP\nZvyIwsJCq+NJMxZvdQCJTT6fj2Cw+BvzXvv9Pvx+SE5OAWDz5lyefPJxkpKSmDXrr6SmtrIqrkit\nBQuLuL5DV5wty3+Ow117sstbxIk167j1J7fwyvOvau4EsYT20KXRuN2eb5wHr17uW7du4YEHfkpp\naSkzZz5Mjx49LUwq8t04kxJxut043W5cHg89b74BX68MDn25hxk//QmlpaVWR5RmSIUuTc40t/Hz\nn99DUVER99//ECNHjrY6kki92OLiOHT5FAq6d2HX1i389Of36Jnp0uRU6NKkdu/exX333U1BgZ+Z\nMx9l4sQLrI4k0iDC8fEcuO5Kijq1Z9P6tdzz83u0py5NSoUuTSY393NmznwQv9/HQw89zJQper65\nxIbKC+XCZaXsv2oqRe3bkLs2hx/95BaKioqsjifNhC6Kkybx8ccf8rvfPUo4HObeex9g7NjxVTPA\nOZ2pVscTqZfTL5Qre/A8zGdfYM8Okxtuvo6nnnialJTyZW63B7td+1LS8PRTJY0qHA7z3HP/xyOP\n/BdOp4uHHvoVU6dO1QxwEnOqXyiX2DqNHrf+B6mDBnL8cB53/fQnHDq0n2CwGL/fZ3VUiVEqdGk0\nXq+Xhx76OS+88Hfat+/AH/7wGKNGjdEMcNIs2OLi6HXzDXS67BJOHjvGf975Y5YvX2p1LIlhOuQu\njWLdunU88sgjHDt2jMGDh/CHPzxOQUG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       "text": [
        "<matplotlib.figure.Figure at 0x3f45048>"
       ],
       "metadata": {}
      }
     ],
     "input": [
      "# The green area under the curve containing the probability \n",
      "# of (roughly) 206 Facebook friends or more.\n",
      "sns.distplot(facebook_friends, label='Facebook friends', kde=False, \n",
      "             fit=stats.norm, color='w')\n",
      "plt.text(x+5, .0003, '$x$='+str(int(x)))\n",
      "\n",
      "x_plot = np.linspace(x, max(facebook_friends), 1000)\n",
      "y_plot = stats.norm.pdf(x_plot, facebook_mu, facebook_sigma)\n",
      "plt.fill_between(x_plot,  y_plot)\n",
      "c=plt.legend()"
     ],
     "language": "python",
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Calculate probability in between two values\n",
      "What is the probability of people having between 120 and 170 Facebook friends?"
     ]
    },
    {
     "cell_type": "code",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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kJSXRrFkzXRgnUs9U6CL1qOKhKa6+SRYnCV0xMQ4GDRrMjh3b2L9/n9VxRCKG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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3f453c8>"
       ],
       "metadata": {}
      }
     ],
     "input": [
      "# We want to know the proportion of the green area under the curve.\n",
      "x1 = 120.0\n",
      "x2 = 170.0\n",
      "sns.distplot(facebook_friends, label='Facebook friends', kde=False, \n",
      "             fit=stats.norm, color='w')\n",
      "plt.text(x1+5, .0003, '$x_1$='+str(x1))\n",
      "plt.text(x2+5, .0003, '$x_2$='+str(x2))\n",
      "\n",
      "x_plot = np.linspace(x1, x2, 1000)\n",
      "y_plot = stats.norm.pdf(x_plot, facebook_mu, facebook_sigma)\n",
      "plt.fill_between(x_plot,  y_plot)\n",
      "c=plt.legend()"
     ],
     "language": "python",
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "-1.9444444444444444"
       ],
       "metadata": {}
      }
     ],
     "input": [
      "# First we need the z score of x1\n",
      "z1 = (x1 - facebook_mu) / facebook_sigma\n",
      "z1"
     ],
     "language": "python",
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "0.025920939357842999"
       ],
       "metadata": {}
      }
     ],
     "input": [
      "# Then we calculate the probability for value x1 or less\n",
      "p1 = stats.norm.cdf(z1)\n",
      "p1"
     ],
     "language": "python",
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "-0.5555555555555556"
       ],
       "metadata": {}
      }
     ],
     "input": [
      "# Now we calculate the z score for x2\n",
      "z2 = (x2 - facebook_mu) / facebook_sigma\n",
      "z2"
     ],
     "language": "python",
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "0.28925736075397196"
       ],
       "metadata": {}
      }
     ],
     "input": [
      "# and agian the probabilty for value x2 or less\n",
      "p2 = stats.norm.cdf(z2)\n",
      "p2"
     ],
     "language": "python",
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "0.26333642139612895"
       ],
       "metadata": {}
      }
     ],
     "input": [
      "# So the probability of having between x1 and x2 Facebook friends is\n",
      "# the probability having x2 minus the probability having x1\n",
      "p2 - p1"
     ],
     "language": "python",
     "prompt_number": 15
    }
   ]
  }
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