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@kiwidamien
Last active May 14, 2019 05:45
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{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"Z = np.linspace(-3,3,100)\n",
"pdf = np.exp(-Z**2/2)/np.sqrt(2*np.pi)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"def shade(lower=-3, upper=+3, color='blue'):\n",
" Z_range=np.linspace(lower, upper, 100)\n",
" pdf = np.exp(-Z_range**2/2)/np.sqrt(2*np.pi)\n",
" plt.fill_between(Z_range, pdf, color=color)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We want \n",
"$$P(18\\% < p < 20\\%) = P(p < 20\\%) - P(p < 18\\%)$$\n",
"where the mean is 19%=0.19 and $\\sigma = 0.0127$.\n",
"\n",
"How to figure out, if we can only look up $P(z < A)$ for positive $A$?\n",
"\n",
"First, we look at \n",
"$$P(18\\% < p < 20\\%) = P(p < 20\\%) - P(p < 18\\%)$$\n",
"Getting $P(p<18\\%)$ is the tricky part\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Visualizing P(p<18%)\n",
"\n",
"First do the z-score thing:\n",
"$$\n",
"z = (0.18 - 0.19)/0.0127 = -0.787\n",
"$$\n",
"\n",
"Let's visualize this:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(Z, pdf)\n",
"shade(upper=-0.787)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"How do we get this? If we have a table that lists [negative z-values](https://www.math.arizona.edu/~jwatkins/normal-table.pdf), we can look it up and be done ($P(z < -0.787) = 0.2148$). \n",
"\n",
"If not, we need some tricks. The rest of this is the \"if not\" section. We know that $P(z < 0) = 0.5$"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(Z, pdf)\n",
"shade(upper=0, color='grey')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can redraw this area as two pieces"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(Z, pdf)\n",
"shade(lower=-0.787, upper=0, color='grey')\n",
"shade(upper=-0.787)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If we can find the grey area, we are done. Note that the grey area is the same as "
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(Z, pdf)\n",
"shade(lower=0, upper=0.787, color='grey')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"That is because the left and the right sides are the same. This grey area is the area less that 0.787 minus the left half. \n",
"$$\\text{grey area} = P(z < 0.787) - P(z < 0) = 0.7852 - 0.5 = 0.2852$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we have\n",
"$$\\text{blue area} + \\text{grey area} = 0.5 \\Rightarrow \\text{blue area} + 0.2852 = 0.5 \\Rightarrow \\text{blue area} = 0.5 - 0.2852 = 0.2148$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"i.e. the answer is 0.2148 (just as it was if we had the other table)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## P(p < 20%)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we have\n",
"$$z = (0.2 - 0.19) / 0.0127 = + 0.787$$\n",
"\n",
"And $P(z < 0.787) = 0.7852$ from the table.\n",
"\n",
"This gives us this area:"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(Z, pdf)\n",
"shade(upper=0.787, color='red')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Altogether"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We want $P(-0.787 < z < 0.787)$. This is the following area"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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Q5pus9I1jXvxyH7HRHq45dYjTUULOrWclcqS0mve2HXQ6igkwVvrGEQeLK3lv2yFmnh5PTJRfl4uYE3BeUhzD+8bwgp3QNU1Y6RtHvLI6C1Xl5qmJTkcJSS6XcMtZiWzOKWJDdqHTcUwAsdI3na6qtp75KTlcNKY/8b27Oh0nZF1z6hBiozzMXZXpdBQTQKz0Tad7e/MBCspruOXMRKejhLRuUR6uSx7Csq0HOVJS5XQcEyCs9E2nUlVeWpXJqP7dmDqij9NxQt7NUxOprVfm2fBN42OlbzrV+qxC0g6UMOvMRERsmGZHG9Y3hgtGx/HaumwbvmkAK33TyV5alUn3aA9XT/q3WTNNB5l1ZiJ5NnzT+Fjpm05zuKSK97cd4rvJ8XSNtGGaneXcpDiG9Y3hJTuha/Cz9EVkmojsEpF0Ebm/mdd/JiLbRWSLiHwsIkMbvVYvIpt8X0ubbmvCx7w1WdTbMM1O53IJs6YOZWN2EZtzipyOYxzWYumLiBt4ErgMGAvcICJjm6y2EUhW1fHAIuDRRq9VqupE39f0dsptgkx1XT2vrcvmW6P7kdDHhml2tmtPG0JMpJu5qzOdjmIc5s+e/mQgXVUzVLWGhonPZzReQVVXqGqF7+kaGiZAN+Zr7209xNGyGmbZME1HxEZHcO1pQ3hn80G7+2aY86f0BwM5jZ7n+pYdy+3Ae42eR4tIqoisEZGrWpHRhIC5qzMZHhfD2SP7Oh0lbN08NZGaei/zU3JaXtmELH9Kv7lxddrsiiI3AcnAY40WJ6hqMnAj8DcRGdHMdnf5fjGk5uXl+RHJBJMtuUVszC7i5jOG2t00HTSyXzfOHtmXV9dkUVdvwzfDlT+lnwvEN3o+BDjQdCURuQj4NTBdVb/++1FVD/j+NwP4FJjUdFtVna2qyaqaHBdn91UPNXNXZRET6eba0+yon9NmnZnIweIqPtx+2OkoxiH+lH4KkCQiw0QkEpgJfGMUjohMAp6lofCPNFreS0SifI/7AmcB29srvAl8+WXVvL3lANeeNoTY6Ain44S9b53UjyG9utjwzTDWYumrah1wD7Ac2AEsUNU0EXlYRL4ajfMY0A1Y2GRo5hggVUQ2AyuAR1TVSj+MzE/JoabOa8M0A4TbJXz/jKGs3VfAzkMlTscxDvDrChlVXQYsa7LswUaPLzrGdquAU9oS0ASvunov89ZkcdbIPozs183pOMbnu8nxPP7hbuauyuLP19g/z3BjV+SaDvPRjsMcKK5ilu3lB5ReMZHMmDiItzbup7ii1uk4ppNZ6ZsO89KqTAb37MKFY/o7HcU0cfPURCpr61m43oZvhhsrfdMhdh0qZU1GAd+fOhS3DdMMOOMG9yB5aC9eXp2F19vsCGwToqz0TYeYuzqTKI+L65PjW1zXOGPWmYlkF1Tw6e4jLa9sQoaVvml3xZW1/GvDfmZMHESvmEin45hjuPTkAfSLjWLuqiyno5hOZKVv2t3C1Bwqa+ttmGaAi/S4uHFKAp/tziMjr8zpOKaTWOmbduX1Kq+syeK0ob0YN7iH03FMC26ckkCEW3h5te3thwsrfdOuPt19hKz8Cpv0PEj0i43m8lMGsmh9LmXVdU7HMZ3ASt+0q5dWZdG/exTTxg1wOorx06wzEymrruPNDblORzGdwErftJu9eWV8vjuP700ZSoTbfrSCxaT4nowf0oO5qzJRteGboc7+ZZp288rqLCLdLm6YnOB0FHMCRIRZUxPZm1fOyvSjTscxHcxK37SL0qpaFqbmcMX4gcTFRjkdx5ygKycMpE9MJHPt7pshz0rftIvF63Mpr6m3E7hBKsrj5sYpCXy88wjZ+RUtb2CClpW+aTOvV3l5dRYT43syIb6n03FMK31vylDcIry8OtPpKKYDWembNvtsTx4ZR8u59axEp6OYNhjQI5pp4wbwRmoO5TZ8M2RZ6Zs2e/HLTPrFRnHZuIFORzFtdOtZwyitsuGbocyv0heRaSKyS0TSReT+Zl7/mYhsF5EtIvKxiAxt9NosEdnj+5rVnuGN89KPNAzT/P4ZQ4n02D5EsDs1oScThvTgxVWZdvfNENXiv1IRcQNPApcBY4EbRGRsk9U2AsmqOh5YBDzq27Y38BAwBZgMPCQivdovvnHaS6v2fX0PFxP8RIRbzxpGRl45n+/JczqO6QD+7JpNBtJVNUNVa4D5wIzGK6jqClX96pT/GmCI7/GlwIeqWqCqhcCHwLT2iW6cVlxRy+L1+5k+YRB9utkwzVBx+SkNw25f/DLT6SimA/hT+oOBxtPr5PqWHcvtwHut3NYEkQW+u2naCdzQEulxcdOUoXy2O4+9dvfNkONP6Tc37VGzB/tE5CYgGXjsRLYVkbtEJFVEUvPy7E/KYFBX7+WlVZlMHtabkwfZ3TRDzY1TEoh0u3jJ9vZDjj+lnws0nv5oCHCg6UoichHwa2C6qlafyLaqOltVk1U1OS4uzt/sxkEfbD/M/qJKbjtrmNNRTAeIi41i+sRBLFqfS1FFjdNxTDvyp/RTgCQRGSYikcBMYGnjFURkEvAsDYXfeO615cAlItLLdwL3Et8yE+TmrNxHQu+uXDzWJj0PVbedNYzK2npeX2eTp4eSFktfVeuAe2go6x3AAlVNE5GHRWS6b7XHgG7AQhHZJCJLfdsWAH+g4RdHCvCwb5kJYptyilifVcgtZybapOchbOyg7pw5og9zV2VSW+91Oo5pJx5/VlLVZcCyJssebPT4ouNs+wLwQmsDmsAzZ+U+YqM8fPd0m/Q81N1+9jBun5vKsq0HmTHRxmCEAruaxpyQA0WVLNt6kOtPj6dblF/7DCaIXTC6H8P7xvDCyn12r/0QYaVvTsjc1Q0Tbcyyu2mGBZdLuPWsRDbnFrM+q9DpOKYdWOkbv5VX1/H62mwuPXkA8b27Oh3HdJJrTxtCjy4RPP/FPqejmHZgpW/8tiA1h5KqOu48d7jTUUwn6hrp4aYzEli+/RBZ+eVOxzFtZKVv/FJX72XOyn0kD+3FqQl2+6RwM2tqIhEuF3NW2t5+sLPSN355P+0QuYWVtpcfpvp1j+aqSYNYkJpDYbldrBXMrPRNi1SV5z7PYFjfGC4aYxdjhas7zhlOVa2XV9dkOR3FtIGVvmnRun0FbM4t5vazh9nFWGFsVP9YLhgdx9zVmVTV1jsdx7SSlb5p0XNfZNA7JpJrTx3S8sompN157nCOltXw1sb9TkcxrWSlb45rz+FSPtpxhO+fMZQukW6n4xiHTR3eh3GDuzP78wzqbWatoGSlb47rmc8y6BLhtouxDNAws9bd540g42g5H24/5HQc0wpW+uaY9hdVsmTTfmZOjqd3TKTTcUyAuGzcQIb26crTn+61WzMEISt9c0xzfFdg3nGODdM0/8/tEv7j3BFszi1mdUa+03HMCbLSN80qLK/h9XXZTJ84iME9uzgdxwSYa04dTFxsFE9/utfpKOYEWembZs1dnUllbT13nzfC6SgmAEVHuLn97GF8seco2/YXOx3HnAArffNvyqvreGlVJheN6c+o/rFOxzEB6sYpCcRGeWxvP8j4VfoiMk1EdolIuojc38zr54rIBhGpE5HrmrxW75tN6+sZtUxgm7c2i6KKWn54ge3lm2PrHh3B96cOZdm2g6QfKXU6jvFTi6UvIm7gSeAyYCxwg4iMbbJaNnAL8Fozb1GpqhN9X9Obed0EkKraemZ/vo+zR/a1G6uZFt1+9jCiPW6eWmF7+8HCnz39yUC6qmaoag0wH5jReAVVzVTVLYBNpBnk5q/L5mhZNfd8a6TTUUwQ6NMtiu9NSWDJ5gN22+Ug4U/pDwZyGj3P9S3zV7SIpIrIGhG56oTSmU5VXVfPs59nMDmxN2cM7+N0HBMk7jp3OG6X2LH9IOFP6Td3h60TuSIjQVWTgRuBv4nIvx0oFpG7fL8YUvPy8k7grU17Wrx+PweLq2wv35yQft2jmXl6PIs35LK/qNLpOKYF/pR+LhDf6PkQ4IC/30BVD/j+NwP4FJjUzDqzVTVZVZPj4uL8fWvTjmrrvTz1aToT4ntyTlJfp+OYIPMfvqG9z9jefsDzp/RTgCQRGSYikcBMwK9ROCLSS0SifI/7AmcB21sb1nScf23YT25hJT++YCQidvtkc2IG9+zCdacN4Y2UHA4W295+IGux9FW1DrgHWA7sABaoapqIPCwi0wFE5HQRyQW+AzwrImm+zccAqSKyGVgBPKKqVvoBpqbOyxOf7GHCkB5cOKaf03FMkPrRBSNRlCdXpDsdxRyHx5+VVHUZsKzJsgcbPU6h4bBP0+1WAae0MaPpYIvW55JbWMkfrxpne/mm1Yb06sr1p8fzRkoOd583giG9ujodyTTDrsgNc9V19fzzkz2cmtCT80bZ+RTTNj+6YCSC2N5+ALPSD3MLUnI4UFzFzy4ebXv5ps0G9ujCjVMSWJiaS3Z+hdNxTDOs9MNYVW09/1yRzuTE3pw10sblm/bxg/NH4HYJT3yyx+kophlW+mHs1TVZHC6p5j8vHmV7+abd9O8ezU1nDOXNDbmkHylzOo5pwko/TJVU1fLPFemcOyqOqSNsL9+0rx+eP4KukR7+Z/kup6OYJqz0w9Rzn2dQVFHLLy4d7XQUE4L6dIviznOG837aITblFDkdxzRipR+GjpRW8fwX+/j2hEGMG9zD6TgmRN1xzjD6dovkL+/ttLl0A4iVfhj6x8fp1NZ7+fnFo5yOYkJYTJSHH38ridUZ+Xy+56jTcYyPlX6Yycov5/V12cycHE9i3xin45gQd8PkBOJ7d+Ev7+3E67W9/UBgpR9mHnlvJ5EeF/demOR0FBMGIj0u7rtkNNsPlvCvjfudjmOw0g8razPyeW/bIX5w3gj6xUY7HceEiW+PH8SE+J48unwnFTV1TscJe1b6YcLrVf747g4G9YjmznOHOx3HhBGXS3jwyjEcLqlm9ucZTscJe1b6YeKtTfvZur+YX0w7iegIt9NxTJg5bWhvrhg/kGc/y+BQcZXTccKalX4YqKip49H3dzFhSA+mTxjkdBwTpu6fdhL1XuUxu2DLUVb6YeCZT/dyqKSK31w5FpfLbrdgnBHfuyu3np3I4g25dsGWg6z0Q1xWfjnPfJ7BjImDOD2xt9NxTJi754KR9IuN4sEl26i3IZyO8Kv0RWSaiOwSkXQRub+Z188VkQ0iUici1zV5bZaI7PF9zWqv4MY/v397OxEu4VeXj3E6ijHERkfw6yvGsCW3mDdScpyOE5ZaLH0RcQNPApcBY4EbRGRsk9WygVuA15ps2xt4CJgCTAYeEpFebY9t/PHR9sN8svMIP71oFP272xBNEximTxjElGG9eXT5TgrLa5yOE3b82dOfDKSraoaq1gDzgRmNV1DVTFXdAnibbHsp8KGqFqhqIfAhMK0dcpsWVNXW8/t30kjq141bzkp0Oo4xXxMRHp4xjtKqOh61k7qdzp/SHww0/jss17fMH35tKyJ3iUiqiKTm5eX5+dbmeJ5akU5OQSW/n3EyEW47dWMCy+gBsdxyZiLzU7LZkF3odJyw4k8bNDfcw98zMH5tq6qzVTVZVZPj4mye1rbadaiUpz/by9WTBnPmiL5OxzGmWf958SgGdI/mgcVbqalrepDAdBR/Sj8XiG/0fAhwwM/3b8u2phXqvcr9b24hNjqC317Z9NSLMYGjW5SHP8wYx67Dpcz+fK/TccKGP6WfAiSJyDARiQRmAkv9fP/lwCUi0st3AvcS3zLTQV5dk8XG7CJ+e+UYesdEOh3HmOO6aGx/rjhlIE98nM7ePJtasTO0WPqqWgfcQ0NZ7wAWqGqaiDwsItMBROR0EckFvgM8KyJpvm0LgD/Q8IsjBXjYt8x0gANFlTz6/k7OHRXHVRP9Pe1ijLMemj6W6AgXD7y51W6/3Ak8/qykqsuAZU2WPdjocQoNh26a2/YF4IU2ZDR+UFXuf3MrXoU/XTXOJjo3QaNfbDS/vmIMv1y8lVfXZnHz1ESnI4U0G9YRIuatzebz3Xn86vKTiO/d1ek4xpyQ7ybHc96oOP572Q72HS13Ok5Is9IPAZlHy/nTuzs4J6kvN50x1Ok4xpwwEeEv144n0u3i5ws2UVdvo3k6ipV+kKv3Kvct3IzHLTzlQFD6AAAPjElEQVR63Xg7rGOC1oAe0fzhqnFsyC7iWbvvfoex0g9ysz/PIDWrkN9PP5mBPbo4HceYNpk+YRCXnzKAv320m237i52OE5Ks9IPYhuxC/veDXVx+ygCunmSjdUzwExH+eNUp9I6J5N7XN1JebdMrtjcr/SBVXFnLva9vZECPaP58jR3WMaGjd0wkf7t+Epn55fx2yTan44QcK/0gpKrcv3gLh4qr+McNk+jRJcLpSMa0q6kj+vDjbyXx5ob9LF6f63SckGKlH4ReXZvNe9sO8V+XjmZSgt2p2oSmey9MYsqw3vx2yTbSj9jVuu3FSj/IrM8q5OG30zh/dBx3njPc6TjGdBi3S/j7zEl0iXDzH6+kUlpV63SkkGClH0SOlFTxg1fXM7BHF/5+/SSb79aEvAE9ovnnjaeSmV/Bzxdstts0tAMr/SBRU+flB/M2UFpVx+ybT6NHVzuOb8LD1BF9+PXlY/hg+2GeXJHudJygZ6UfBFSVh5amsT6rkMe+M56TBnR3OpIxnerWsxK5etJgHv9oNx9uP+x0nKBmpR8EZn+ewevrsvnh+SO4cvwgp+MY0+lEhD9fcwqnDO7Bva9vZGuuXbjVWlb6Ae7dLQf583s7uXL8QO67ZLTTcYxxTHSEm+dnJdM7JpLb5qaQW1jhdKSgZKUfwNZnFfCfCzaRPLQX//OdCXbi1oS9frHRvHTr6VTV1nPriykUV9qInhPlV+mLyDQR2SUi6SJyfzOvR4nIG77X14pIom95oohUisgm39cz7Rs/dO06VMrtc1MZ3LMLs29OJjrC7XQkYwJCUv9Ynr3pNDLzy7ljbgqVNfVORwoqLZa+iLiBJ4HLgLHADSLSdPLV24FCVR0J/BX4S6PX9qrqRN/X3e2UO6TtO1rO955fS5THxcu3TbZpD41p4syRffnr9RNZn1XIXa+kUl1nxe8vf/b0JwPpqpqhqjXAfGBGk3VmAHN9jxcBF4rdDKZV9hdV8r3n1uBVZd4dU2xCFGOO4crxg3jkmvF8seco976+0e7B7yd/Sn8wkNPoea5vWbPr+ObULQb6+F4bJiIbReQzETmnjXlD2v6iSm58bg2l1XW8fNtkRvaLdTqSMQHtu6fH8+CVY1medpifvrGJWiv+FvkzR25ze+xNL4s71joHgQRVzReR04C3RORkVS35xsYidwF3ASQkJPgRKfRk5Zdz43NrKamqZe5tkxk3uIfTkYwJCredPYyaei+PvLeTmjov/7hxElEeOwd2LP7s6ecC8Y2eDwEOHGsdEfEAPYACVa1W1XwAVV0P7AVGNf0GqjpbVZNVNTkuLu7EP0WQSz9SyneeWU1FTR2v33kGp9pN1Iw5IXefN4LffXssH2w/zF0vr6eq1o7xH4s/pZ8CJInIMBGJBGYCS5ussxSY5Xt8HfCJqqqIxPlOBCMiw4EkwOZBa2RDdiHffXYNXoX5d021PXxjWumWs4bxyDWn8PmePG6es46iihqnIwWkFkvfd4z+HmA5sANYoKppIvKwiEz3rTYH6CMi6cDPgK+GdZ4LbBGRzTSc4L1bVQva+0MEq/e3HeKG2WvoFuVhwX+cwegBdgzfmLaYOTmBJ2ZOYlNOEdc8vYrsfLuAqyl/jumjqsuAZU2WPdjocRXwnWa2WwwsbmPGkKOqvPhlJn94dzsThvRkzqxk+nSLcjqWMSHh2xMG0b97NHe+nMo1T3/Jczcn27wTjdgVuZ2sqrae+xZu4eF3tnPJ2P68fucZVvjGtLPJw3qz+Adn0iXSzfWz17AgJafljcKElX4nyimo4NqnV7F4Qy4/uTCJp793Gl0ibZSBMR1hZL9uLPnR2UxO7M0vFm/hgTe32kVc+Hl4x7Td+9sOcv+bW6n3KnNmJXPhmP5ORzIm5PWOiWTubZP53w928dSne9m2v5i/z5zI8LhuTkdzjO3pd7Dy6jp+uWgLd7+6gYTeXXn7nrOt8I3pRG6X8ItpJ/Hs908jp7CCK55YyevrslENz1m4bE+/A63JyOf+xVvIKqjgRxeM4KcXjSLCbb9njXHCpScPYMKQnty3cDMPvLmVj3cc5o9XncKAHtFOR+tU1kAdoLiilvsXb2Hm7DXUqzL/zjP4r0tPssI3xmEDekTz8m2T+c0VY1iZfpSLHv+MV1ZnhtXcu7an347qvcri9bk8unwnhRW13H3eCH5yYZKdrDUmgLhcwh3nDOfisf35zVvb+O2SNBZv2M9D3x4bFkM7rfTbyaq9R/njOzvYfrCEUxN6Mve2cZw8yK6uNSZQDe0Tw8u3TeatTfv572U7ufqpVUyfMIhfTBvNkF6he3dbK/02Wp9VwN8+2sMXe44yuGcX/nHDJK4cPxC7s7QxgU9EuHrSEC4ZO4BnP9vLs59nNFwpPzmeH5w/MiSP91vpt4KqsnpvPk9/tpcv9hylT0wkv7r8JG6emmgzXBkThGKiPPzsktHMnJzAPz7Zw7y12by+LofrT4/njnOGMbRPjNMR242V/gmoqq3nnS0HmbNyHzsOltC3W0PZ33TGULpG2v+VxgS7QT278OdrxvPD80fy1KfpzE/J5tW1WVwytj+3nz2c0xN7Bf1f8dZUfthxsIQ3UnJ4a9N+iipqGd0/lkevHc/0iYNsz96YEBTfuyt/vmY8P71oFC+vzmTe2myWpx1mZL9uXJ8cz9WnDqZvkN4+xUr/GLLzK3hn6wHe2XyQ7QdLiHS7uHTcAGaeHs+ZI/oE/W97Y0zL+neP5r8uPYl7Lkji7c0HeCM1hz8t28Ff3t/JOUl9uXL8IC4+uT/doyOcjuo3K30fr1fZsr+YT3Yc5uOdR0g70DC516kJPfndt8cyY+JgetkE5caEpS6Rbr57ejzfPT2ePYdLWbQhl3c2H+TnCzcT+aaLqSP6cOGYflwwul/Az2sdtqXv9SrpeWWs3VfA6r1HWb03n8KKWlwCpw3txQOXncQV4weG9NAtY8yJS+ofywOXjeH+aSexMaeIZVsO8vHOIzy4JA1IY3jfGKaO6MPUEX2YnNibft0DawRQWJS+qnKguIpt+4tJO1DCppwiNmYXUlpVB8CgHtF866T+nJPUl/NGxdkevTGmRSLCqQm9ODWhF7+5ciwZeWV8svMIq/bm89bG/cxbmw3A4J5dOHVoLyYM6cHYQd05eVAPenRx7nCQX6UvItOAvwNu4HlVfaTJ61HAy8BpQD5wvapm+l57ALgdqAfuVdXl7Za+ieq6enIKKsnKL2ff0XL25pWz53Ape46UUVxZ68sKo/rFcuX4gUxK6MXpib1J7NPVjtEbY9pkeFw3hsd1445zhlNb72Xr/mI2ZBWyIbuQlH0FvL35/6cWH9yzCyP7dSOpXzdG9OvG0D5dSewTw4Du0bhcHdtFLZa+b47bJ4GLaZgAPUVElqrq9kar3Q4UqupIEZkJ/AW4XkTG0jCn7snAIOAjERmlqu1+U+uDxZWc+cgnNL5xXq+uEST1j+WK8QMZMyCWsYN6MGZgrA2vNMZ0qAi36+u/Ar6SV1pN2oGGow1f7Yyuycinus779TqnDO7B2z8+u0Oz+dN+k4F0Vc0AEJH5wAygcenPAH7ne7wI+Kc07DrPAOarajWwzzeH7mRgdfvE/3/9YqO591tJJPZt+I05tE8Mve0wjTEmQMTFRnH+6H6cP7rf18vqvcqhkiqyjpaTmV9BpKfjb8roT+kPBhrPNZYLTDnWOqpaJyLFQB/f8jVNth3c6rTH4XYJ/3nxqI54a2OM6RBulzC4ZxcG9+zCmSM753v6U/rNHWBqeh/SY63jz7aIyF3AXQAJCQl+RDKhqEtEF3pF96KspszpKEHrpL4nOR3BBDh/Sj8XiG/0fAhw4Bjr5IqIB+gBFPi5Lao6G5gNkJycHD43tjbf0DWiKwfvO+h0DGNCmj8HkFKAJBEZJiKRNJyYXdpknaXALN/j64BPtGEusqXATBGJEpFhQBKwrn2iG2OMOVEt7un7jtHfAyynYcjmC6qaJiIPA6mquhSYA7ziO1FbQMMvBnzrLaDhpG8d8KOOGLljjDHGPxJokwMnJydramqq0zGMMSaoiMh6VU1uaT2btNUYY8KIlb4xxoQRK31jjAkjVvrGGBNGrPSNMSaMBNzoHRHJA7La8BZ9gaPtFMdJofI5wD5LoAqVzxIqnwPa9lmGqmpcSysFXOm3lYik+jNsKdCFyucA+yyBKlQ+S6h8Duicz2KHd4wxJoxY6RtjTBgJxdKf7XSAdhIqnwPsswSqUPksofI5oBM+S8gd0zfGGHNsobinb4wx5hhCrvRF5A8iskVENonIByIyyOlMrSUij4nITt/n+ZeI9HQ6U2uJyHdEJE1EvCISdCMtRGSaiOwSkXQRud/pPG0hIi+IyBER2eZ0lrYQkXgRWSEiO3w/Wz9xOlNriUi0iKwTkc2+z/L7DvteoXZ4R0S6q2qJ7/G9wFhVvdvhWK0iIpfQMDdBnYj8BUBVf+lwrFYRkTGAF3gWuE9Vg+ZWqiLiBnYDF9MwMVAKcIOqbj/uhgFKRM4FyoCXVXWc03laS0QGAgNVdYOIxALrgauC8b+Lb07xGFUtE5EIYCXwE1Vd08KmJyzk9vS/KnyfGJqZnjFYqOoHqlrne7qGhpnHgpKq7lDVXU7naKXJQLqqZqhqDTAfmOFwplZT1c9pmPciqKnqQVXd4HtcCuygg+bg7mja4Kt5QiN8Xx3SXSFX+gAi8icRyQG+BzzodJ52chvwntMhwtRgIKfR81yCtFxClYgkApOAtc4maT0RcYvIJuAI8KGqdshnCcrSF5GPRGRbM18zAFT116oaD8wD7nE27fG19Fl86/yahpnH5jmXtGX+fJYgJc0sC9q/IEONiHQDFgM/bfKXflBR1XpVnUjDX/STRaRDDr35MzF6wFHVi/xc9TXgXeChDozTJi19FhGZBVwJXKgBfgLmBP67BJtcIL7R8yHAAYeymEZ8x78XA/NU9U2n87QHVS0SkU+BaUC7n2wPyj394xGRpEZPpwM7ncrSViIyDfglMF1VK5zOE8ZSgCQRGSYikTTMAb3U4Uxhz3fycw6wQ1UfdzpPW4hI3Fej80SkC3ARHdRdoTh6ZzEwmoaRIlnA3aq639lUreObaD4KyPctWhPEI5GuBv4BxAFFwCZVvdTZVP4TkcuBvwFu4AVV/ZPDkVpNRF4Hzqfhjo6HgYdUdY6joVpBRM4GvgC20vDvHeBXqrrMuVStIyLjgbk0/Hy5gAWq+nCHfK9QK31jjDHHFnKHd4wxxhyblb4xxoQRK31jjAkjVvrGGBNGrPSNMSaMWOkbY0wYsdI3xpgwYqVvjDFh5P8A3UKfOsDca/sAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(Z, pdf)\n",
"shade(lower=-0.787, upper=0.787, color='green')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can subtract red and blue:"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(Z, pdf)\n",
"shade(upper=0.787, color='red')"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(Z, pdf)\n",
"shade(upper=-0.787, color='blue')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"i.e 0.7852 - 0.2148 = 0.5704"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "metis",
"language": "python",
"name": "metis"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.8"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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