normal_distrubition.ipynb

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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm\n",
    "\n",
    "xs = np.arange(-10, 10, 0.001)\n",
    "\n",
    "mean = 0\n",
    "for standard_deviation in range(1, 4):\n",
    "    plt.plot(\n",
    "        xs,\n",
    "        norm.pdf(xs, mean, standard_deviation),\n",
    "        label = 'standard deviation = {0}'.format(standard_deviation)\n",
    "    )\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "probability to fall between -2 and 2 : 0.9544997361036417\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm\n",
    "import scipy.integrate as integrate\n",
    "\n",
    "mean = 0\n",
    "distribution_function = lambda x: norm.pdf(x, mean)\n",
    "x1 = -2\n",
    "x2 = 2\n",
    "\n",
    "print('probability to fall between {0} and {1} :'.format(x1, x2), integrate.quad(distribution_function, x1, x2)[0])\n",
    "step = 0.001\n",
    "whole_x = np.arange(-4, 4, step)\n",
    "whole_y = distribution_function(whole_x)\n",
    "\n",
    "needed_x = np.arange(x1, x2, step)\n",
    "needed_y = distribution_function(needed_x)\n",
    "plt.plot(whole_x, whole_y)\n",
    "plt.fill_between(needed_x, needed_y, color='r')\n",
    "plt.show()"
   ]
  }
 ]
}