Coursera Data Analysis -- in Python

Simulation Basics

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     "metadata": {},
     "source": [
      "Simulation Basics -- equivalent in Python"
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    {
     "cell_type": "code",
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     "input": [
      "import numpy as np\n",
      "import scipy.stats as s"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
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     "input": [
      "# normal distribution\n",
      "# normal(mean, stdev, size)\n",
      "heights = np.random.normal(188, 3, 10)\n",
      "print heights"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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       "stream": "stdout",
       "text": [
        "[ 190.15026626  187.20390227  187.95763008  187.25140845  191.62472211\n",
        "  190.08039721  186.44935175  184.17754141  192.08413107  190.014875  ]\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# binomial distribution\n",
      "# binomial(n, p, size)\n",
      "coinFlips = np.random.binomial(10, 0.5, 10)\n",
      "print coinFlips"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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        "[4 2 4 4 5 5 7 6 7 7]\n"
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     "prompt_number": 3
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     "input": [
      "# normal density\n",
      "x = np.linspace(-5, 5, num=10)\n",
      "normalDensity = s.norm.pdf(x, 0, 1)\n",
      "print np.around(normalDensity, decimals=2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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        "[ 0.    0.    0.01  0.1   0.34  0.34  0.1   0.01  0.    0.  ]\n"
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     "prompt_number": 4
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    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# binomial density\n",
      "x = np.arange(0, 11, 1) # note that it's (0, 11, 1) instead of (0, 10, 1)\n",
      "binomialDensity = s.binom.pmf(x, 10, 0.5)\n",
      "print np.around(binomialDensity, decimals=2)"
     ],
     "language": "python",
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     "outputs": [
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       "stream": "stdout",
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        "[ 0.    0.01  0.04  0.12  0.21  0.25  0.21  0.12  0.04  0.01  0.  ]\n"
       ]
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     "prompt_number": 5
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     "input": [
      "## 'sample' draws a random sample with and without replacement --> numpy.random.choice in numpy 1.7\n",
      "## not available in my installed version of numpy\n",
      "#\n",
      "# heights = np.random.normal(188, 3, 10)\n",
      "#\n",
      "## with replacement\n",
      "# np.random.choice(heights, size=10, replace=True, p=None)\n",
      "#\n",
      "## without replacement\n",
      "# r.choice(heights, size=10, replace=False, p=None)\n",
      "#\n",
      "## sample according to a set of probability\n",
      "# probs = [0.4, 0.3, 0.2, 0.1, 0, 0, 0, 0, 0, 0]\n",
      "# sum(probs)\n",
      "# np.random.choice(heights, size=10, replace=True, p=probs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# setting a seed\n",
      "np.random.seed(12345)\n",
      "print np.random.normal(0, 1, 5)\n",
      "print '-------------------------------------------------------------'\n",
      "\n",
      "np.random.seed(12345)\n",
      "print np.random.normal(0, 1, 5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[-0.20470766  0.47894334 -0.51943872 -0.5557303   1.96578057]\n",
        "-------------------------------------------------------------\n",
        "[-0.20470766  0.47894334 -0.51943872 -0.5557303   1.96578057]\n"
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