{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# IntroStat Week 3 \n",
    "\n",
    "Welcome to the third lecture in IntroStat\n",
    "\n",
    "During the lectures we will present both slides and notebooks. \n",
    "\n",
    "This is the notebook used in the lecture in week 3.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 1: Stochastic variable following a uniform distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the standard form, the distribution is uniform on [0, 1]. Using the parameters loc and scale, one obtains the uniform distribution on [loc, loc + scale]. For more, read: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.uniform.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# lets plot pdf:\n",
    "x = np.arange(start=-5, stop=35, step=0.1) # range from -5 to 35\n",
    "plt.plot(x, stats.uniform.pdf(x, loc=0, scale=30))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# lets also plot cdf:\n",
    "plt.plot(x, stats.uniform.cdf(x, loc=0, scale=30))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.33333333333333337\n"
     ]
    }
   ],
   "source": [
    "# Probability P(20 <= X <= 30):\n",
    "print(stats.uniform.cdf(30, loc=0, scale=30) - stats.uniform.cdf(20, loc=0, scale=30))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualise the probability:\n",
    "xint = np.arange(start=20, stop=30, step=0.1) # range from 20 to 30\n",
    "plt.plot(x, stats.uniform.pdf(x, loc=0, scale=30))\n",
    "plt.fill_between(xint, stats.uniform.pdf(xint, loc=0, scale=30), color='peachpuff') # color the area\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n"
     ]
    }
   ],
   "source": [
    "# Probability P(x >=30)\n",
    "print(1 - stats.uniform.cdf(30, loc=0, scale=30))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualise the probability\n",
    "xint = np.arange(start=30, stop=35, step=0.1)\n",
    "plt.plot(x, stats.uniform.pdf(x, loc=0, scale=30))\n",
    "plt.fill_between(xint, stats.uniform.pdf(xint, loc=0, scale=30), color='peachpuff')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2: Stochastic variable following a standard normal distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(start=-5, stop=5, step=0.01) # Again the range by smaller steps\n",
    "plt.plot(x, stats.norm.pdf(x, loc=0, scale=1)) # loc = mean, scale = standard deviation\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.022750131948179195\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Probability P(x <= -2)\n",
    "print(stats.norm.cdf(x=-2, loc=0, scale=1))\n",
    "\n",
    "xint = np.arange(start=-5, stop=-2, step=0.01)\n",
    "plt.plot(x, stats.norm.pdf(x, loc=0, scale=1))\n",
    "plt.fill_between(xint, stats.norm.pdf(xint, loc=0, scale=1), color='peachpuff')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Probability P(x >= 2)\n",
    "print((1-stats.norm.cdf(2, loc=0, scale=1))*100)\n",
    "\n",
    "xint = np.arange(2, 5, .01)\n",
    "plt.plot(x, stats.norm.pdf(x, loc=0, scale=1))\n",
    "plt.fill_between(xint, stats.norm.pdf(xint, loc=0, scale=1), color='peachpuff')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Probability P(-1 <= x <= 1)\n",
    "print((stats.norm.cdf(1, loc=0, scale=1) - stats.norm.cdf(-1, loc=0, scale=1))*100)\n",
    "\n",
    "xint = np.arange(-1, 1, .001)\n",
    "plt.plot(x, stats.norm.pdf(x, loc=0, scale=1))\n",
    "plt.fill_between(xint, stats.norm.pdf(xint, loc=0, scale=1), color='peachpuff')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 3: Stochastic variable following a normal distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(270, 310, .1)\n",
    "plt.plot(x, stats.norm.pdf(x, loc=290, scale=4))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Probability P(x > 300)\n",
    "print(1 - stats.norm.cdf(300, loc=290, scale=4))\n",
    "\n",
    "xint = np.arange(300, 310, .1)\n",
    "plt.plot(x, stats.norm.pdf(x, loc=290, scale=4))\n",
    "plt.fill_between(xint, stats.norm.pdf(xint, loc=290, scale=4), color='peachpuff')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 95% interval around mean = 290\n",
    "\n",
    "# we need 2.5% on either side of the interval\n",
    "\n",
    "# lower bound should be where cdf = 0.025\n",
    "# upper bound should be where cdf = 0.975\n",
    "\n",
    "plt.plot(x,stats.norm.cdf(x, loc=290, scale=4))\n",
    "plt.axhline(0.025, linestyle='--', color=\"black\", xmin=0, xmax=.32)\n",
    "plt.axhline(0.975, linestyle='--', color=\"black\", xmin=0, xmax=(1-.32))\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"cdf(x)\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To find the corresponding values of x we need the inverse of cdf(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# in Python (Scipy.stats package) the inverse of \"cdf\" is called \"ppf\" (\"percent point function\") - The quantile function (percentile)\n",
    "# scale is the standard deviation, \n",
    "\n",
    "# lower bound where cdf = 0.025:\n",
    "lower_bound = stats.norm.ppf(0.025, loc=290, scale=4)\n",
    "print(lower_bound)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# upper bound where cdf = 0.975:\n",
    "upper_bound = stats.norm.ppf(0.975, loc=290, scale=4)\n",
    "print(upper_bound)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# lets also plot these values:\n",
    "plt.plot(x,stats.norm.cdf(x, loc=290, scale=4))\n",
    "plt.axhline(0.025, linestyle='--', color=\"black\", xmin=0, xmax=.32)\n",
    "plt.axhline(0.975, linestyle='--', color=\"black\", xmin=0, xmax=(1-.32))\n",
    "plt.axvline(lower_bound, linestyle='--', color=\"black\", ymin=0, ymax=.07)\n",
    "plt.axvline(upper_bound, linestyle='--', color=\"black\", ymin=0, ymax=1-.07)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# lets also plot pdf with interval:\n",
    "xint = np.arange(lower_bound, upper_bound, .1)\n",
    "plt.plot(x, stats.norm.pdf(x, loc=290, scale=4))\n",
    "plt.fill_between(xint, stats.norm.pdf(xint, loc=290, scale=4), color='peachpuff')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 4: Stochastic variable following an exponential distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# X ~ exp(lambda)\n",
    "\n",
    "# mean = 2\n",
    "# lambda = 1/2 = 0.5\n",
    "\n",
    "x = np.arange(0, 5, .01)\n",
    "plt.plot(x, stats.expon.pdf(x, loc=0, scale=2))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# X ~ exp(lambda)\n",
    "# a) Probability P(X > 2)\n",
    "print(1 - stats.expon.cdf(2, loc=0, scale=2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# lets also plot this probability:\n",
    "xint = np.arange(2, 5, .01)\n",
    "plt.plot(x, stats.expon.pdf(x, loc=0, scale=2))\n",
    "plt.fill_between(xint, stats.expon.pdf(xint, loc=0, scale=2), color='peachpuff')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### b) Using poisson distribution to answer the same question\n",
    "\n",
    "Poisson - count of events per time-interval.\n",
    "\n",
    "We want zero events (zero customers) in a time interval of 2 minutes. Average waiting time is 2 minutes, so the average count per two minutes (average rate) is 1\n",
    "\n",
    "We no use the poisson distribution with fixed time interval of 2 minutes and calculate the probability of zero events P(X=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# b) Using poissondistribution to answer the same question\n",
    "\n",
    "print(stats.poisson.pmf(0,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we can also plot the pdf for number of customers within next two minutes:\n",
    "plt.bar(np.arange(0,10,1), stats.poisson.pmf(np.arange(0,10,1), 1), width=0.1, color=\"red\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 5: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# simulate 1000 realisations of the random variable X:\n",
    "x = stats.norm.rvs(loc=4, scale=np.sqrt(6), size=1000)\n",
    "plt.hist(x, density=True)\n",
    "plt.plot(np.arange(4-20,4+20,0.01), stats.norm.pdf(np.arange(4-20,4+20,0.01), loc=4,scale=np.sqrt(6)), color=\"red\")\n",
    "plt.xlim(-40,30)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# calsulate corresponding values of the stochastic variable Y:\n",
    "y = -3*x + 2\n",
    "plt.hist(x, density=True)\n",
    "plt.plot(np.arange(4-20,4+20,0.01), stats.norm.pdf(np.arange(4-20,4+20,0.01), loc=4,scale=np.sqrt(6)), color=\"red\")\n",
    "\n",
    "plt.hist(y, density=True)\n",
    "plt.plot(np.arange(4-50,4+50,0.01), stats.norm.pdf(np.arange(4-50,4+50,0.01), loc=-10,scale=np.sqrt(54)), color=\"red\")\n",
    "plt.xlim(-40,30)\n",
    "plt.show()"
   ]
  }
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