Created
June 13, 2018 16:03
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Probability density
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{ | |
"cells": [ | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"import numpy as np" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 6, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"import matplotlib.pyplot as plt" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 26, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"N = int(1e8)\n", | |
"phi = np.random.random(N) * np.pi\n", | |
"x = np.cos(phi)\n", | |
"modx = np.abs(x)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 29, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"(values, edges, patches) = plt.hist(modx, bins=50, density=True)\n", | |
"x_plot = np.linspace(0, 1, 600, endpoint=False)\n", | |
"plt.plot(x_plot, 2/(np.pi * np.sqrt(1-x_plot**2)), lw=6, alpha=0.7)\n", | |
"plt.xlabel(\"$x$\")\n", | |
"plt.ylabel(r\"f_|x|(x)\")\n", | |
"plt.savefig('rozklad.png', transparent=False)" | |
] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python 3", | |
"language": "python", | |
"name": "python3" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython3", | |
"version": "3.6.5" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 2 | |
} |
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