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{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "20fce00f",
   "metadata": {},
   "source": [
    "### ML, Data Analysis\n",
    "#### Continuous random variables and their distirbutions\n",
    "In this notebook, we express about Continuous Random Variables with an example from *Continuous uniform distribution*.\n",
    "<br>**Definition:** *Random variables* are *continuous* when their range is **uncountably infinite**. In other words, when we measure things such as speed,voltage, temperature, profit, and etc.\n",
    "<br> **Reminder:** A set is *countable* if the number of its elements is not greater than that of the *natural numbers*. As a result, any interval of real numbers is infinite and uncountable.  \n",
    "<br>**Contents:**\n",
    "- Defining the *distribution function* for continuous uniform distribution..\n",
    "- Defining the *probability (density) function* for continuous uniform distribtuion.\n",
    "- An example to compute a probability for the continuous uniform distribution.\n",
    "<hr>\n",
    "https://github.com/ostad-ai/Machine-Learning\n",
    "<br> Explanation: https://www.pinterest.com/HamedShahHosseini/Machine-Learning/background-knowledge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "84c6d039",
   "metadata": {},
   "outputs": [],
   "source": [
    "# importing the required modules\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fdcf819d",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# continuous uniform distribution with paramters a and b:\n",
    "def CUD(x,a=0,b=1):\n",
    "    if x<a:\n",
    "        return 0\n",
    "    elif x>b:\n",
    "        return 1\n",
    "    else:\n",
    "        return (x-a)/(b-a)\n",
    "    \n",
    "#displaying the distribution function  \n",
    "a,b=0,1\n",
    "xs=list(np.linspace(a-1,b+1,100))\n",
    "ys=[CUD(x,a,b) for x in xs]\n",
    "plt.plot(xs,ys)\n",
    "plt.title(f'Continuous Uniform Distribution with parameters $a=${a}, $b=${b}')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5acd3169",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# probability density fucntion of continuous uniform distribution\n",
    "# with parameters a and b\n",
    "def CUP(x,a=0,b=1):\n",
    "    if x<a or x>b:\n",
    "        return 0\n",
    "    else:\n",
    "        return 1/(b-a)\n",
    "\n",
    "#display the probability function\n",
    "a,b=0,1\n",
    "xs=list(np.linspace(a-1,b+1,100))\n",
    "ys=[CUP(x,a,b) for x in xs]\n",
    "plt.plot(xs,ys)\n",
    "plt.title(f'Probability (Density) Function of Uniform Distr. with parameters $a=${a}, $b=${b}')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a41df24",
   "metadata": {},
   "source": [
    "**Example:** Find the probability $P(0.5<X<2)$ if random variable $X$ comes \n",
    "from a uniform distribution with parameters $a=0$ and $b=3$.  \n",
    "We know that $P(.5<X<2)=F(2)-F(0.5)$. So, let's use the Python function **CUD** defined above to compute it: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f174c0a3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability that X falls within 0.5 and 2 for Uniform Distri. with a=0 and b=3:\n",
      "P(0.5<X<2)=0.5\n"
     ]
    }
   ],
   "source": [
    "# Solving the example mentioned above:\n",
    "p_e=CUD(2,a=0,b=3)-CUD(0.5,a=0,b=3)\n",
    "print('The probability that X falls within 0.5 and 2 for Uniform Distri. with a=0 and b=3:')\n",
    "print(f'P(0.5<X<2)={p_e}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "74ae0061",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}