{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Statistik\n",
    "\n",
    "Dieses Kapitel umfasst die grafische Darstellung und Analyse von empirischen Daten."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Zufallszahlen\n",
    "\n",
    "Obwohl streng gesprochen keine Statistik,\n",
    "sind Zufallszahlen in Computerprogrammen immer wieder notwendig\n",
    "und ein praktisches Hilfsmittel um diverse Statistiken zu illustrieren.\n",
    "\n",
    "Python's internes `random` modul hat einige praktische Funktionen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import random"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fließkommazahl in [0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.36461328514232505"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random.random()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "zufällige Ganzzahl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random.randint(-10, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "mischen einer Liste (hier, die Zahlen von 0 bis 9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 5, 1, 4, 9, 3, 8, 2, 6, 7]\n"
     ]
    }
   ],
   "source": [
    "x = list(range(10))\n",
    "random.shuffle(x)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gauß'sche Normalverteilung, wobei `mu` der Mittelwert und `sigma` die Standardabweichung ist."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.790115275319303"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random.normalvariate(mu = 1, sigma = 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Da Zufallszahlen in Programmen unvorhersebar sind,\n",
    "jedoch mit einer deterministischen Methode berechnet werden,\n",
    "gibt es die Möglichkeit den internen Status des Zufallszahlengenerators zu setzen.\n",
    "Dies passiert mit der `seed` Funktion und ist für Tests oder das reproduzieren bestimmter Ergebnisse nützlich."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6394267984578837 -1.2479729469788396\n",
      "0.6394267984578837 -1.2479729469788396\n"
     ]
    }
   ],
   "source": [
    "# zweimal genau dieselbe Zufallszahl!\n",
    "random.seed(42)\n",
    "print(random.random(), random.normalvariate(mu = 1, sigma = 2))\n",
    "random.seed(42)\n",
    "print(random.random(), random.normalvariate(mu = 1, sigma = 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Abzählstatistiken\n",
    "\n",
    "Mittels der Klasse [`Counter` in den `collections`](https://docs.python.org/2/library/collections.html#collections.Counter)\n",
    "([Counter in Python 3](https://docs.python.org/3/library/collections.html#collections.Counter)) können Listen abgezählt werden."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from collections import Counter\n",
    "from random import randint"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Multipliziere 10000 mal zwei zufällig von 1 bis 4 gewählte Ganze Zahlen.\n",
    "Welche Häufigkeiten gibt es und was sind die drei häufigsten Zahlen?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Counter({1: 638,\n",
       "         2: 1264,\n",
       "         3: 1227,\n",
       "         4: 1901,\n",
       "         6: 1224,\n",
       "         8: 1261,\n",
       "         9: 599,\n",
       "         12: 1240,\n",
       "         16: 646})"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numbers = [randint(1, 4) * randint(1, 4) for i in range(10000)]\n",
    "c = Counter(numbers)\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(4, 1901), (2, 1264), (8, 1261)]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c.most_common(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Einfaches Balkendiagramm, mit Skalierung.\n",
    "Beachte, dass einige Zahlen überhaupt nicht vorkommen.\n",
    "\n",
    "**Frage**: warum kommt die 4 am häufigsten vor?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "can't multiply sequence by non-int of type 'float'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0mTraceback (most recent call last)",
      "\u001b[1;32m<ipython-input-16-604a169dfc9a>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m17\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m     \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"%2d: \"\u001b[0m \u001b[1;33m%\u001b[0m \u001b[0mi\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;34m\"-\"\u001b[0m \u001b[1;33m*\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mc\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;36m30\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m: can't multiply sequence by non-int of type 'float'"
     ]
    }
   ],
   "source": [
    "for i in range(1, 17):\n",
    "    print(\"%2d: \" % i + \"-\" * (c[i]/30))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot Normal-/Exponential verteilter Punkte"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f00f5b47588>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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mQyna29vR6XSEh4cTGhrKvn37KC0txc3NjQMHDuDn50dQUBC2trY8+eSTNDc3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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0110432cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 1000 # Anzahl der Punkte\n",
    "xx = [ random.expovariate(.5)      for _ in range(N)]\n",
    "yy = [ random.normalvariate(10, 2) for _ in range(N)]\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.scatter(xx, yy, marker=\".\", color=\"black\", alpha=.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## NumPy/SciPy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Es lassen sich leicht einfache Statistiken über Arrays or Matrizen berechnen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = np.array([\n",
    "[ 3.1, 3.3, 3.2, 3.0 ],\n",
    "[ 0.1, 11, 9999,    0],\n",
    "[  31, -33,  11,   51],\n",
    "[-5.1, -.6,   1,  9.1]\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "630.44375000000002"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([    7.275,    -4.825,  2503.55 ,    15.775])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Spaltenweise\n",
    "data.mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  3.15000000e+00,   2.50252500e+03,   1.50000000e+01,\n",
       "         1.10000000e+00])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Zeilenweise\n",
    "data.mean(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9999.0"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  3.15,   5.55,  21.  ,   0.2 ])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Zeilenweiser Median\n",
    "np.median(data, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   36.1,    44. ,  9998. ,    51. ])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Spaltenweise die range von Minimum bis Maximum\n",
    "np.ptp(data, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1.11803399e-01,   4.32809417e+03,   3.11126984e+01,\n",
       "         5.13176383e+00])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Standardabweichung\n",
    "np.std(data, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Zufallszahlenarrays\n",
    "\n",
    "NumPy liefert in [numpy.random](http://docs.scipy.org/doc/numpy/reference/routines.random.html) eine Fülle von Funktionen für das effiziente Sampeln verschiedener Verteilungen in Arrays."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die vorhergehenden `xx` und `yy` listen lassen sich viel effizienter als NumPy Vektoren erzeugen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f00f3277c18>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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D2tpatFotWq0WnU5HfX09Hh4euLu74+3tjcPhwM3NDYfDQWNjIzU1NZSUlHDt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\nFxEJCSV0EZGQUEIXEQmJ/wdLMZyDAkBiWAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00f334fd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx = np.random.exponential(scale = 5, size = N)\n",
    "yy = 10 + 2 * np.random.randn(N)\n",
    "plt.scatter(xx, yy, color=\"black\", marker=\".\", alpha=.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "SciPy beinhaltet in [scipy.stats](http://docs.scipy.org/doc/scipy-dev/reference/stats.html) eine Sammlung von statistischen Verteilungen, Methoden und Tests.\n",
    "Viele alltägliche Anwendungen sind damit abgedeckt.\n",
    "\n",
    "Das allgemeine Schema ist hierbei so,\n",
    "dass für jede der diskreten oder kontinuierlichen Verteilungen jeweils eine Liste bestimmter Funktionen implementiert sind.\n",
    "\n",
    "* `pdf` und `cdf` sind beispielsweise die Dichte- und kumulierten Dichteverteilungen,\n",
    "* `rvs` zum Sampeln zufälliger Werte,\n",
    "* und schließlich `fit` zum Anpassen an gegebene Daten und\n",
    "* `stats` für generelle Daten über die Verteilung."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import scipy.stats as sps"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "10 Bernulli-verteilte Zahlen, mit Wahrscheinlichkeitsparameter `p = 0.2`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 0, 0, 0, 0, 0, 1, 0, 1])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sps.bernoulli.rvs(.2, size = 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rekonstruktion unserer Parameter der Normalverteilung (siehe `yy` oben)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10.04454503926571, 2.0309183722908273)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sps.norm.fit(yy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Es gibt in `scipy.stats` auch eine Reihe von statistischen Funktionen und Tests.\n",
    "Beispielsweise gibt es den berühmten [T-Test](http://en.wikipedia.org/wiki/Student's_t-test),\n",
    "um herauszufinden ob zwei unterschiedliche Samples den gleichen Mittelwert haben."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sierpinsky Dreieck\n",
    "\n",
    "Als visuelles Ergebnis eines Zufallsprozesses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f00e629db70>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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XBHJ1pioY8/Nj6o9SlIDQ9y8dIUQHgAtE9FGLz+4GcICI7hFC3Argy0R0a47j\nULmuiZkZotEo7rxzGx59dABPPPFEWcsjM5WFaKLBz7Vr18pe3pqZGYQQIKLiW9ChTJ3FhBABAP8D\nQI8Q4j0hxENCiIeFEPsBgIi+DeDHQoh3AfwVgM+W47xMbTA2Noaf//xfsWrVKgBAKBRCNBoFK/Pa\nJ5FIYOvW7di8+V6sWbMGV65cmZG2m0ztUBYlQER/REROIrqRiFYS0d8Q0V8R0YvKNgNEtJqI+ogo\nWo7zMtVFziJ1bPjJT36CZ599Fvv2/QnuuusPy962kSk/fX19cLv345e/fB+XLl3CPffswLPPPluR\ntptMbVI2c1C5YHNQ/RCPx7F9+z6cPfsKvvOd7+D06RchhMDAwH/Cpk2bYLPZpt0onZk5NE3D2bNn\nsXr1atx1132YO/dGfOlLXuzatYufXZ1QijmIlQAzLeQqgIgghEBfX58xc+zv70cikcD27fvg9X6e\nhUmNoa7gVCWtPlNAFyysxOuDqvsEmMYjkUhgx44HcO3atcxq4Cz6+/sNBdDb2wuv9/N48sk/w8jI\nCNuXawQiwpkzZ7Bly73YunU74vH4JMEvhMC99+7Gtm072CTUAPBKgCkYIr1xe19fHwAYwuOdd96B\n230Izz//HNavX2+sAHp6enD16lUcPvw5nDp1Art37+ZZZZWJx+PYunU7kskU/vzPfXjvvffw4ouv\n4Pz5YYyPj+PIkS/g/Hm/sT2vBOoDXgkwM4I08SQSCWPGuHPnf8Rbb72Ff/3XX+LAgT8FAPh8x3Ho\n0DHce+9OCCFw/fqHeOyxYzyrrDIyLvzVV8/i4sVvwGaz4dgxDx5++EEAwNGjT8PnO47+/n5s3LgR\nGzduZAXQAPBKgCkIKzuyXBl85CMfwalTp7Bp0ybccsstAGBsq/oK+vr6cOXKFfT19bFwqQKxWAzb\ntu3ChQsj2Lhxo+EQ3rlTV9Zylac+G3X1x8+sduGVAFNxYrEYtmy5z3AEAxOOwzlz5uDJJ5/Exz72\nMWOFoM4k5XZXrlzh0MMqoGkazpw5A03TQJTG2NgYYrEYhBDYvXs3bDabpROYiDAyMoL77/8jnDlz\nBrFYjH07s5HpphpX6gUuG1GT6EXVFlIgECh4H1mfR9a34Rr21UHWFAoGg0YdJKu+DGZkRdihoSFy\nOruM0tpM7YESykbwSoApiLVr12LJksVYu3Zt1swyF5SJQnn00Sfh8XzOMCewo3Hm2blzJ4aH/9oI\n1X3//d8D5kg6AAAgAElEQVQgmfxt3n2kgDh79hWsXLkSJ09+ETfcMG+GrpiZUaarPSr1Aq8EaoZc\nxcryVf+URKPRTCnn5Tx7rCFkR7OpWnXK6qOysJyslppOpy37NzDVBbVQRbRcL1YCtYO5cbtEFSS5\negLIev1+vz9vJU+msuS657KxjLnrmqxEKtt6Xr9+PasyaSwWo7a2lWSzzSu4bzRTeUpRAnOquQph\nahciwtWrV3H9+u9w8OAREOkOYVllct26ddi6dTs++OAD/PKX/wYA2LNnD4j0KKJLly7hV7/6MCvq\nRIaYnj/vR39/f5VHOLsh0qN6iAg7djxgmbmdTKbwp3/6JIjSeOONC+jv78fJkydx7JgHn/3s/8Bf\n/uXfAAAef/xxAHrEV29vL7785SE88sgThhBh816dM13tUakXeCVQdWSnrPb2DvJ6veT3+8lud5LN\nNp/8fn/WKsDj8VBrq95hi0ifKTqdndTaupzcbjeNjo4aDdLN5iU2K1QO2WAnHA7T0NAQrVq1Nquh\njtqBzensIq/XS4FAwGguk0wms/aLRqNZDn69R/Hk3sZMdQCbg5hyIjtlLV7sJKezk4LBILW2ttOi\nRUvJ6/VSU1MLtbY6M52+9Gbl0sYs2xe2tjqprW0lBQIBo/WjqgT0HrnLqKmpmRuZVABdCXRlWmpu\nILfbbbTGVLuTRaNR8vl8ZLPNJ4djhdE3Wdr/ZXSX2p+ZqLC+yczMwUqAKRtW3bnS6bQhMFKplBFq\nOBE+qLdodLm6jBmibAsZiUQs20tGo1Fqb+8gn8/HK4EKoHYUC4VC1N7eMan9pZzdyxWZfKaFhvVG\no1FqbXWS3b7UWAky1YGVAFM25AxyqogeVcioM0JzY/N8bRQLbRvJFIdZcOdqf2m1Xa5nZ3WOYDBI\nixYtJSHmFZU/wpQfVgJMyUgBEIlEDPNNpZF2a91kNDkKiSkcs6mtEEVeCjKRzOv1UlvbSl4JVJlS\nlAAnizEAJorDXb16FSdPPg0iqmibQU3TcPHiRVy//ltomoYPPvgVHn30KJedngZEemLePfdsN5L4\nkslURe9jb28vfL7jOHz4ME6ffhZ9fX3ckrJema72qNQLvBKoCjLiQ7fvu8jlWp1lGy4X0katl6GY\nT4sXO42VgM/nM2zSvCIoHN2R3012u4OcTn1FZfbHlBO1HIj6k59d9QCbg5hyYI74qIStPhgMUlNT\nC3k8HgoEAhSJRLL8CJVQPLMdq+cWjUYz4Z+dZVcGMtFMhvfys6s+pSgBNgcxIJooE71x40bccsst\n6Ovrw9mzZ9Hb21vWZKA1a9ZgwYI5eP75/4qf/vSnACaqkdpsNuzatQtnz76CsbGxvLWJGB1Zx4mI\nsiq3jo+P4/DhzyGZTGF8fLws1VvT6TR8Ph++/e1vg0hg7dq1Rh9p+ezOn/cbTYeYOmG62qNSL/BK\nYEawciSqM0Z9xt5c9tIAshSF2+02zEFmB6asTTQ0NMSmhSkIhULU1NRCDofTMMXoM/VuY6U1OjpK\nPp+PUqlUSefy+XwEzCch5hmhvRzVVRuAVwJMsUhHcDwex9WrVwEIvPHGG7j77j/EmTNnsGbNGixe\nvEhVztOGiBCLxRCLxdDX14cLF87iU5/6FE6c+Bzmzbtx0vY7duzAZz/7EL761b/h3gN5ICJ0d3fj\nP//nB/HII5/FkSNfQCwWw8WLF5FMfmjM1O+++34cO+bBqVOnpvUsKbNSvOOOO9DSshA339yMzZs3\nI5FIGH2K5Tby+Ob3TA0zXe1RqRd4JVBx1JINkUhESfrqJLt9Gblc3RSNRieVBphuAbhIJEJ2+zJq\nb++gWCyWlbFqdTz5uSxcxrNNa2KxGDkcLrLZmsnhWE6hUIiCwWDWCks+a6/XS05nZ9Fho+l02sgM\nl7kG8rgyxFfNQpb/K+b3TGUBO4aZYpDRJA6HyzABmZO+zOWjpYlIKohCSafTNDAwQELMo4GBAUqn\n01MqE3O2K9eoySadTlMgECC/30+jo6OG2UfTNKPCq3wviUQitGSJy3DIF5qlrZubmi1Nc7lKjctr\nDIVCRgkKVuKVhZUAUxCqcA0Gg+R0Fi7Q9cJw3UV3lwoGgwTcQAsX2snl6i5KmKsJScUIrtmKObzW\nZrMWzlbotZqWks22kGy2eQXXa5LnTKfTWb9PhVwJBAIBcjhWcDJZhWElwBSEFKpyhlboF5poYvYp\nhXGhpqFIJEIOxwry+/0FFRszl6MIBoPU1raSmpoWNHyhOekwl6uAgYEBWrVqXd7YfHk/U6kUBQIB\nGh4epoGBAUomkwWds9hmQhKpMPx+f0UCDJhsWAkwUyJtuMFgMCvJp9CZuW5CWk0uV5dRfCxfaYJU\nKmWUJLYqIJfvPOr1SRMVl5zOnpXLWH2fz5f3nprvp+wU5vf7jYqhZlTBrz6z6awEIpFIUZMNZnpU\nXQkAuBPAGIBxAE9YfP5JAO8DiGZex/Icq1L3qWGZsOd3ZfkActlz1f2sCr5JZ2O+mjEynNDn81ke\nL9d1clG5wlD7BVj5ACRm27ysAjswMEDAfBocHMzpmDdXEZXPXfVBmCmmCB1TPqqqBADYALwLYBWA\nuQDiANaZtvkkgFcLPF6FblPjEo1GyeFYbpQSlkihKzNLzQXc1OgPFVWpWK0ENE2j4eFhammx0+jo\nqOU1WVWwlE7gYDA4ZcXLRkcKZJ/PR+3tnZOerUQ1Acp7F4vFqKNjHe3du5c6OzdkfZavT0AsFqPW\nVhcJMY+WLFk2yQwl/y/MvqZcVUyZ8lFtJXArgNeV90+aVwMZJXChwONV5CY1ImplUCshL008DofT\nCA1Vu0+pgl6d4QUCAWptXW74B9QvuAwpVOvXm6/HHF4or0X2IXA4lk9yIjeiecFKeFrZ6N1uN7W3\nd1hWYVXr/Mj7qfaI1pvOTERfmc1H6jPQNI28Xi/ZbM00MDCQtVqQpkans4vsdoexQpyoSdVJLtfq\nKXsUMNOj2kpgO4AXlfcPADht2uaTAH6eWSW8BmBDnuNV6j41HFPF42uaZrSIHB4eJr/fbyiLaDRK\nHR3rjK5hUlgEg0Gy25eREDdSIBCgYDBIS5a4yOHQC8Hpnceayev1Ws4kpeDQHcb6PqpJKhwO05Il\n7eT1erPCC+XnwWCwYOdkvaOv4FzkdHYZzyQcDhuhvdLUI1tBdnZmm3DUuj6qmU1vMtNJixc7jY5w\ncuYvAwZko/lUKpV1POmfSaVSNDo6SgMDAzQ8PExOZ7fho3A6u4wG9rJxjQwqiEQiFA6Hufx0makH\nJdAMYEHm97sAjOc5Hh0/ftx4Xb58uTJ3rQEoZMYl48AdjhVGJI5MKgqFQkY+gVwl6P0G9Iqf8ne7\nvY0WL3aSw+GkJUtcOTtNmVcCejey7Bm/+ner2Wgxzsl6Jp1OG6YevUtbN7lcXeTz+aipqSUr2sZs\n8rGazZv/Jst2BIPBzIqwK6tyrHQgh0KhnKuDwcFBAuZTS8sSQ0nJ5yOvV05AZCCBy7XaaGfp8/l4\nNTBNLl++nCUnq60EbgVwUXk/yRxksc+PASzO8VlFblqjkUqljCbx+QSmmlxkNu1Y2YetnMWyFaXa\nknKqL3cuO3EhzuFGsDFLU8/g4CClUqms9p5mJWjlX8nl/Jd/U49jdc/Nn1s5e5PJJLndbhodHc35\nDM2+hmg0SslkkgYHB42VC1M61VYCTYpj+IaMyWe9aZulyu8fB/CTPMer1H1qKPTonBsIaJp1My41\nXHW21a9X4/p1E8/sy5aWKxerAABmepSiBOZYlBMqCiJKCyEGAFyCHin0NSJ6RwjxcObCXgSwQwjx\nGQBJAL8FsLvU8zK5ISKsWLECCxYsRFOTXrZZCIHDhw/DZqv/moG9vb04deqL0DQNBw8eQU9PDzZu\n3FjtyyoL8Xgc27btwIUL53D48GF0dHSgt7e32pdVFogmisqdP+8HAOzY8QC83s9j165dZS1ZzhTB\ndLVHpV7glUDJxGIxam/vILt9Kfn9/owdubnunalyliydjXr00sz0Q54JNE2jQCBAS5a4yO/3Zzqu\nVa5D2Eyj/19ORA+pYcGzbbUz06DayWLlfLESKJ2J8M5uw46cKzu0XlBDHaWzUbVR17vDeCKUsovs\n9qXU1raSHA4ntbWtNCKz6tX0pfqO9OixCcd2I/h3ZgJWAoyBlRNvNpT1lQlOQ0NDlk7Reg8dVQuu\nBQIBCofDWc52We6jHp+h9OG0t3dYFgNU21WyIpgerAQYA3O44GyZaVmtBCaSzrooHA7Xdelis6lL\nCnurrm/1hnxO0iwpK5+qyYxW4cJM4ZSiBEp2DDPVh2iiR3BfXx88ns/B7T6E7u5ufPe738VXvvIC\n/vzPh9Df31/lKy0edWw7d+7E2rVrkUqlsHnzVly69C28++67AASuXbuG3bt3Gx3Tzp/31/x45dg0\nTcP4+Dh6enoAACdOHIOmacaX9Pr1JMbGxrB+/XoQERKJBPr6+urCkaper6Zp+Od//md89at/i46O\nDvT09GDHjgfg8XwOFy9+A0II9Pb2Ih6P1834ZgXT1R6VeoFXAkVjrvCp15tfSJs2bSKbbSG1tCzJ\nmmXVU9q+TGRyOidKWsjidG63mzo712diztfXXUkCmRi3aNFSstnmkd2+jFpbl5Pdvoyczk5jZeBw\nuKitbaUREltPZiE10Ux/jl1GjkAwGLQsW7Fq1VojP4IpDLA5qLExm3wikQjddJODgBuppWUx+f3+\nLHNQPfkI1Lo08prVMtWhUIg6OtZlmb/qQQnISKDWVhcNDw8bfgA9IqjbsI+bE/ZkiYjr16/XhSNc\n9VHJ5yjbmXZ2rp9U0kTTtEwm8gIaGhqq8tXXD6wEGphc2Zn5Sv7mygCtJXJlweYai/y77mTsrnkn\no77C6Sa7fVlWiY18SkwWcBNiIe3evZtstoUFdxarFfL978nPkslkQdnuzASsBBoMqxo80nxQDLW6\nIjDHjxc6u5eza7u9readjDKMN1f1Tyv0FpFOAmzU2rqC3G530T2fZwJzS8p8/Q7UfbxeL7W2thuV\nYus52mumYSXQQKgCUi6vVfNBIftP1Uym2qh2ZClEphJ28r60t3dRa6uTBgYGKBwO19zYiLLj5gsN\n/ZRKw25vI2A+eb3eTAG/rppb9QSDQbLZ9GuUBe/s9qV5n5++z0ISYp4RQloP5q5agZVAAyE7eslS\nvTIcNJ9pRzUZmUMQa4lcOQ5OZyc5HMuNMZvHKHsYSGejrFLZ1rayJsepOvKlTTxfz2ep4Do61hnl\nu2Vht1rMuI1EIpmqssupvb2D3G43LVu2Kufzk/vY7Utp0aLWSRVoa3WyUkuwEmgQZGRMU9MCY/ZX\nSEKYWirYqrdAreQS6DHx3VnCQnUMO53WHbTkLFL2MJAtFKUJolaEiLoCMFdbDQaDORuyy9wPc6Kc\nesxqPzui7FaWqjNbruZkmXKr/9F846hVs2UtwUqgQVCzZs0NV3KVX1a7SOUSFKqSqOYXTfo3HA5n\n1rXI8QUCAWpv7yCfz2cIQ+kHcDiW0yuvvEJ2+zIKh8NZx622EMlWZN1GKK+KTJiymgWbo6Pk32st\nIzyXHV+astRmM8UorFpR4rUMK4EGwewQVs0JMpNWftnkSkGdYeaKuJEdo/I1EJ+JcckwwtHRUfJ6\nvYZNXx2f2uyEaCKjNhgMktfrzWpuL/c1rwxmemzBYNBomamac6zGrgpI1cxlrpekmvVqRUiqNarM\n/6tOZ6cx9lwKS52wyG525vtU7THWKqwEGhDpG5CCbSL9fjk1Ny+i9vYuo2CXw7HcKDtg1YEqFotV\ndTWgCnk12c3hWG4IRmlCkbH0altEl2s1RSIRo93hW2+9ZQj9iUSlbnI4VtDo6OiMFtOTPo3W1uVG\n/Xxp2pF+ANnsXQp2eR+kAlfDQGVvZnk/qqW4JaoSkyY7dWIiFZbLtZqCweCk+k+qAzgUCpEQC2jB\ngpvo5pvbjMmL/N+Wkx5mMqwEZjlWsyB1JaD+Ta8+6TKyMc21WtSMU3OkkOxhq87AZgIpAKTQluYd\naTqYEOQTjWTMPg55PxyOFWS3L8sSIKqAcrvdBCygwcHBGRGcH374Id122230ve99z7jPcjUjE6bM\niVNyzDJU0lxsTT53vTVoCzkcrqqtCLIzgnVFK1cz5ig0+ZzVlYBqQkqn0+R2u6mpqYU8Hk+WIi82\nCq7RYCUwy7Gy+Vp94c3ONaswu6kEhfxSVjoJyUowWJWItjKXWJlOVKerlSLTNI3C4TCdOHGCDhw4\nQB0d6yq+4tE0jW677TYCbqDbbrsty8yjFrsz+3GmShiTn5lj8GfaN6BpE0mJsurpVPZ+89jM/6Pm\n95NXGrWXF1ELsBKY5czkDE/aodVSDJVAteV3dKwzGtdX6nzpdJr27NljxNjPRESNnty1lG644aZp\nJfMVgzk4YKbGp9Y1qvT4VHMTk00pSqD+ew3OUogmWvEREa5evSqVZEURQmDz5s3w+Y7j6NGnkUgk\nyn4OIsLY2BiSyRTS6TT2738Qzz13GnfeeZ9RMbTc5zt58iRCoW9iwYK5uOOOO3Dp0iVs376vIuNT\nz9vUNBdf//pfwu3ej49+9KMVO8/IyAi2b9+H8fFxJBIJbNu2A9u27arY84vFYhgbG8PcuTfiy18e\nwoUL54wKoJX4P43H43jssaNwu/ejr6+v7MdvaKarPSr1Aq8EiGjCBBSJRGhwcJBstoUzkkJvdtKW\neyYpZ3StrS5atKg1ExLqIrt9meHoLvd5dYf4BnK73YapaCZMXjLvYc+ePRUtgaDmEXR2ZjemKfdq\nQPqVnM7OrMquRBPjrYTdXvq71BUHRwxNADYHzR5U27YM+Zwzp4UGBwdnxFlrDhstt5N4wnm93Ihs\nMXfQKmcGrBpnL487UyUJpBPYZltYsecn7fLBYNCINpK5CJUoOy0nCTLSSbXtezweWrBgES1b1lGW\nc5pDfFWlJpVRpc2W9QIrgVmCOstyuboN56EUWDM584nFYuRwrCh7g/pwOEyLFrWR3++f5NRWwyXL\nNUY1Rt3sSC73vbRSLmYncKVn5WrOx+joaNlDSNVJgjqeUChENttCAuaS2+0uy/mk32hgYICamprJ\n5/MZx5Xh0F6vtyYS5aoNK4FZglo2waq5eLmjP9ToEnNETiQSoeHhYfJ6vWWNqZdhq4FAIEuImHMY\nyoXMQpZKNde9LIdSyFf5Uj1fuRSQOiuXfQikGc/p7MzU73GWJffDHHlmHk84HCaPx0Mej4eSyWTJ\n45Nmw7a2lbRkyTJqaVlMTmeX8Qxz/R81KqwEZgly1ipNMDIaQtrJpaAuVx8APc58Ad10U1vWjEoK\nziVL2rPivkuJOJGC4/r16+R2u2l4eDinEC7nLF1edyAQyIosUc0ocvbscLgmlW0oBnPIptr8RjXx\nqbkP072X5pwOOWuWfxseHqbWVhd5PJ6yrAR0xdJFdvvSrEQ9eQ9l9zezQpou+oqx1Wi4I7PInc5O\nCofD5Pf7yePx0OjoaEGhqbMdVgKzBHMyl5ppqQpM1WlcrG3bbPMfGBggIW6k1tblhlCSKxKv1ztp\ndmlVwG0qUqkUDQ4OGtmiTU0LyOFYkVMIluqctqphL++leu3qzF2fWbZYFnArBnWGPDQ0ZCSmSaEv\nx1VK9U+ppFVHqXyu0ofk8/nI4XAZfRVKUeLyfno8HsMsoybwyYmLTOhqbV1ODoerJCWgtxBdQG63\n2ziX/P+bKE/tMJIj29u7LAvsNQqsBOoYs401V6KUVTKR/MIXY7OXwnB4eJjs9qX09ttvTxKYVufV\nNI38fj/Z7W2TCrRNhSoMC6njozpzizV/SWdsU1MzORwr8pp7VBt+MpmkwcFBSiaTRY3N6vzyPOpK\noNBnOxWy+cqSJcsmtQ1VxyQrearmG5lRXUz0jqZphtD1+/2TktzUc6hBDeprOopHPo/r169POpfq\nKJbn8Pl8Dd2EhpVAHaOm3Rcr8IqNctE0WXHTSQcOHMgqtlbIvrowsC53nI/r16/T3r176fr16wXv\nM10fgdzP4/HQiRMnCmpRODG2ySW6p9qvVPNcMX4eqeCEWEgtLXYKBAJFCXO9kJ2zqK5rE2YgR1Gm\nMl3pdBuz9WJXBbmqqlohfRI+n68s/oh6hJVAnWLO8iz0n3e6NnOZ4TmdQmpqLHoxSqfYFUupglXu\nHwgESIj5JMS8vOeVinHRIgfZ7U7jvkxlqpmIZtLvyXTNV8U8S2mmGxgYMMJsCxGu6j0t1CQ0nX3M\n+weDQVqyxEUtLfYpV4/mCU2+/gpmpMKRq5xGjBZiJVCnWBWBK8R2q+5XTAiiFCLmevyFCKGp6t1Y\nIWe54XC4YIWjroyKFUCqLyAcDpPDsYIGBgbynlcPhV1OQuj2Z7/fT01NzXTgwAGjzWG+65QlNoaG\nhigSiUy5epmOAk+lUuTz+Wh4eNgIFCikhII8l+qILjS4QPXLmE0++fZThbmmaeT1eslmW0iBQCDv\nGM2F5Px+f0GRafKZ+/1+am/vII/HQ4FAoCIhubVM1ZUAgDsBjAEYB/BEjm1OA7gGIA6gP8+xKnSb\nag8rZ6U+q1ltWYslWxh0Gw5Gmf061QxInb3K7ayuQd1eFQKq2SoQCFBb20oKh8M5v2xmITTV7Ez1\nBUhhqt6LXAJICp5AIGBU1ZT3ZqoZeiqVIq/XSx6Phzo712ca1S+lm29eQk1NuVcv6kxZ7fmcy6wn\nt89VEjmfaU93ks4nu73NUDCFKBN99baBfD4fBQIB454WYn5Un51aYjyf+SqdTtPg4GDWqq9Qs465\npHRT0wIjgzyfD0lfMSygQCBgBB20ta2sSKJcLVNVJQDABuBdAKsAzM0I+XWmbe4C8Frm998D8L08\nx6vYjao1cjkrZdq/WSDowuAGstvbDWFQbDKS+ZxWqxGJmqpvrvDp9/vJZltAAwMDk75s5m5mhawa\npPlA7T5lXgnkKksgFaHX681KjpL3ZnR01BAo6vmi0Sh5PB6y2ZrJ7/dnRU298sordODAARodHc06\nl9UzKyS8VY3pzzUGGXljTmobHh6m5mY7DQ8PTzpvvpWS6iRXy2rL8NLh4WHyeDxG8x6r8ZlNllbn\nk8/b6/VSU1Mz7d2715jBF7KyNZsA1eABvXVoM9ntDsv/UbWvhjnvZSaK6NUK1VYCtwJ4XXn/pHk1\nAOAFALuV9+8AWJrjeBW6TbWH1RdERnFYJfiEw2FavNg5KdvW6riFKgT1/GpnKKLJeQuqkPR4PLRo\nUSstW9Y5yfwh69zb7Y5JbSJzCUvZnHzRIgc5nd2TlEooFMqYeJZTa2u2LVytfKruJ1c5ukliflbG\nqbQjL1y4iISYRwMDA4bS1U1EKyyb1eeaCctVmipQrZ6JunKQ74PBII2OjpLP55tUk1+vs2Qdcpnr\nf8UqQkk1q0jfUEtLKwHzqKVliXHsfDN9sxlSFdT6CsyZaSrfmaXk1NWm1YrHKjhCjkHeVzXvwPx/\nlKu8STFO93qn2kpgO4AXlfcPADht2uYCgH+nvP8ugFtyHK9Ct6n2sDL9mAWz+n6q8Eor84s5Zl79\nAqlfkolSywuMiCH1C6vOZBctWko220RJZivzjN/vnxSdo0b86GaRiRmxXNbLZiLqF1qd6cuEIbNA\nlPfJ3Nzc6eyk0dFRcrvdWauMVCpFHo+Hbr7ZQZs2bcoqjyGjTdQWl+bzqONOp9O0d+9eAubTTTdN\nnrFaza5lNIv0QUiTic/no/b2DmPlpSsFZ5YiVoWfVVkI9blKAawmHEpT3vDwMB04cCBrlZRvAhGN\nRqm9vcswn9lszUYNKLUOlMxPkGPQlbfLGLMQ87IUshyLXJnIBDFZQkSWTpGr3Wg0apjuZHKaNImq\nK4BkMjmjXeSqCSuBOsBqRmYWXOYvnrThu1wTBcFy+QuI5My9O6tOjmpfNdt01S98KBQiYD4tWHAT\njY6OTlImqk27tbWdbropf76A+bzqeKQycThcxqxfKhzZScq8EhgaGiKns4uczuyVh1mpqd3H5OxS\n3hcZrig/dziWZ9pYugwBUogiNc8wpSlny5YthgA3Pxez30XmTni9XuPYqt/FPAEwnzffilG9J3L2\nLqNmZNKVVDq5HMy5zF66eamFFi1qpUWL9Exz1cdk5UfSTWCrDVPYTTc5yOnM/h/Waw8tICEWkBDz\nyeFwGlFaZj+G9BvZ7W2G01luK0tNuFxd5PP5yGbLrjk0W6m2ErgVwEXlfSHmoLF85qDjx48br8uX\nL1fmrs0w8ks/NDQ06bNcy1Y5c5YVG6eyc8plvhoHnm8loKJuJ7+8Vg7VCdt9/sgUq6xdub9qmzaP\nJdf15bItm5WaVcitqmzVlYLVTFqNilEVZL42jlP5Zaz8LrkmBfnMeGYzSCE2b7O9Xb3vZqWjkut/\nshh/T65zW0165ApleHiY/H5/Vj0rq4gmc6SbOkmRJsxwOJwxSRaeF1EvXL58OUtOVlsJNCmO4Rsy\njuH1pm3uVhzDtzaiY9jqSy/JJ/gKse2r25fDGVaMMKo25b4Wq+PlUmjVusZyke+6avWaJYV8Z8r1\nfagHSlECQt+/NIQQdwL4CvRIoa8R0ZAQ4uHMhb2Y2eZ56KGkvwHwEBFFcxyLynFNDMMwjYIQAkQk\nprVvrQlcVgIMwzDFUYoS4B7DDMMwDQwrAYZhmAaGlQDDMEwDw0qAYRimgWElwDAM08CwEmAYhmlg\nWAkwDMM0MKwEGIZhGhhWAgzDMA0MKwGGYZgGhpUAwzBMA8NKgGEYpoFhJcAwDNPAsBJgGIZpYFgJ\nMAzDNDCsBBiGYRoYVgIMwzANDCsBhmGYBoaVAMMwTAPDSoBhGKaBYSXAMAzTwLASYBiGaWBYCTAM\nwzQwrAQYhmEaGFYCDMMwDQwrAYZhmAaGlQDDMEwDw0qAYRimgZlTys5CCDuAMwBWAfgJgF1E9EuL\n7X4C4JcANABJIvp4KedlGIZhykOpK4EnAXyXiNYC+AcAR3JspwG4nYg2NrICePPNN6t9CRWFx1ff\n8Hr5/soAAARJSURBVPgak1KVwH0AXsr8/hKA/5BjO1GGc9U9s/2fkMdX3/D4GpNSBXMbEf0MAIjo\nXwC05diOAHxHCDEqhPh0iedkGIZhysSUPgEhxHcALFX/BF2oH7PYnHIc5hNE9L+EEA7oyuAdIvp/\nir5ahmEYpqwIolxyu4CdhXgHuq3/Z0KIZQAuE9H6KfY5DuDfiOhLOT6f/gUxDMM0KEQkprNfSdFB\nAF4F8McAngHwKQDfNG8ghFgAwEZEvxZCLASwGcAXch1wugNhGIZhiqfUlcBiACMAVgD4KfQQ0feF\nEO0A/pqItgohOgH8N+imojkA/EQ0VPqlMwzDMKVSkhJgGIZh6puqhm0KIexCiEtCiKtCiDeEEDfn\n2O4nQoiEECImhHh7pq+zWIQQdwohxoQQ40KIJ3Jsc1oIcU0IERdC9M/0NZbCVOMTQnxSCPG+ECKa\neVkFEdQkQoivCSF+JoS4kmeben52ecdX589uuRDiH4QQPxBCfF8IMZhju7p8foWMb1rPj4iq9oLu\nS3g88/sTAIZybPcjAPZqXmsRY7IBeBd6FvVcAHEA60zb3AXgtczvvwfge9W+7jKP75MAXq32tU5z\nfL8PoB/AlRyf1+2zK3B89fzslgHoz/zeDODqLPvuFTK+op9ftRO4ZmOy2ccBXCOinxJREkAI+jhV\n7gPwMgAQ0VsAbhZCLEV9UMj4AP2Z1R2khy7/a55N6vnZFTI+oH6f3b8QUTzz+68BvAPAZdqsbp9f\ngeMDinx+1RasszHZzAXgfyrv/z9MflDmbf7JYptapZDxAcBtmeX2a0KIDTNzaTNCPT+7Qqn7ZyeE\n6IC+4nnL9NGseH55xgcU+fxKDRGdEk42a0giAFYS0QdCiLsAfANAT5WviSmMun92QohmAOcAPJKZ\nMc8qphhf0c+v4isBItpERL3K66OZn68C+JlcimWSzf7/HMf4X5mf/xt6uGktF6H7JwArlffLM38z\nb7Niim1qlSnHR0S/JqIPMr+/DmBuJpx4NlDPz25K6v3ZCSHmQBeQrxDRpLwl1Pnzm2p803l+1TYH\nyWQzIE+yWUbzQUk2+8eZusBpMApgtRBilRDiBgB7oI9T5VUADwKAEOJWAO9Ls1gdMOX4VBurEOLj\n0EORfzGzl1kSArntqvX87CQ5xzcLnt3XAfyQiL6S4/N6f355xzed51dxc9AUPANgRAjxJ8gkmwGA\nmmwG3ZT03zLlJGSy2aVqXfBUEFFaCDEA4BJ0Jfs1InpHCPGw/jG9SETfFkLcLYR4F8BvADxUzWsu\nhkLGB2CHEOIzAJIAfgtgd/WuuDiEEAEAtwNYIoR4D8BxADdgFjw7YOrxob6f3ScA7APwfSFEDLp5\n+Sj0SLa6f36FjA/TeH6cLMYwDNPAVNscxDAMw1QRVgIMwzANDCsBhmGYBoaVAMMwTAPDSoBhGKaB\nYSXAMAzTwLASYBiGaWBYCTAMwzQw/xftaFYz8Wqw5gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00e62d7fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "N = 2000\n",
    "edges = np.array([[0, 0], [2, 0], [1, 2]], dtype=np.float)\n",
    "sierp = np.empty((N, 2))\n",
    "point = edges[0]\n",
    "\n",
    "for i in range(3, N):\n",
    "    edge = edges[random.randint(0, 2)]\n",
    "    point = (point + edge) / 2\n",
    "    sierp[i] = point\n",
    "\n",
    "plt.scatter(*sierp.T, s=1, marker=\".\", c=\"b\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (Welch's) T-Test\n",
    "\n",
    "`male` und `female` sind (halbwegs normalverteilte) Prüfungsergebnisse.\n",
    "Gibt es einen signifikanten Unterschied?\n",
    "Die $H_0$ [Nullhypothese](http://en.wikipedia.org/wiki/Null_hypothesis) wäre, dass die Mittelwerte gleich sind.\n",
    "Die Ergebnisse des Tests liegen aber über der 1% bzw. 5% Schranke ($\\sim 55.2\\%$)\n",
    "und daher kann die Nullhypothese nicht verworfen werden.\n",
    "In der Tat sind die Mittelwerte jedoch nicht gleich,\n",
    "jedoch kann der Test dies aufgrund der kleinen Datenmenge bzw. großen Streuung dies nicht erkennen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "male = [3, 4, 1, 2, 2, 1, 3, 4, 2, 3, 2, 3, 3, 4, 4, 3, 3, 5, 1, 4,\n",
    "        2, 3, 3, 2, 1, 5, 3, 3, 1, 2]\n",
    "female = [3, 3, 2, 3, 4, 3, 1, 4, 1, 2, 1, 3, 2, 3, 4, 1, 3, 3, 3, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.7333333333333334, 1.1234866364235143, 3.0)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(male), np.std(male), np.median(male)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.5499999999999998, 0.97339611669658921, 3.0)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(female), np.std(female), np.median(female)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=0.59990642797746641, pvalue=0.55161451342571177)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sps.ttest_ind(male, female, equal_var = False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Statsmodels\n",
    "\n",
    "Eine mächtigere Bibliothek für statistische Modellierung und Rechnung ist [Statsmodels](http://statsmodels.sourceforge.net/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
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