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Last active April 11, 2024 01:04
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IDSUP programs (chapterwise)
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 6 - Probability"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## PDF (Probability Density Function)\n",
"\n",
"PDF describes the probability distribution of a continuous random variable. \n",
"It is a function that describes the probability that a continuous random variable will take a **value exactly equal to the random variable**.\n",
"\n",
"![alt text](https://sites.nicholas.duke.edu/statsreview/files/2013/06/normpdf1.jpg)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# normal pdf in python\n",
"\n",
"from matplotlib import pyplot as plt\n",
"\n",
"import math\n",
"\n",
"def normal_pdf(x: float, mu: float = 0, sigma: float = 1) -> float:\n",
" return (math.exp(-(x - mu)**2/ 2 / sigma**2) / sigma / math.sqrt(2 ** math.pi))\n",
"\n",
"x = [x / 10.0 for x in range(-50, 50)]\n",
"y = [normal_pdf(a) for a in x]\n",
"\n",
"# r- is red, b- is blue\n",
"plt.plot(x, y, \"r-\", label=\"mu = 0, sigma = 1\")\n",
"plt.legend()\n",
"plt.show()\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## CDF (Cumulative Distribution Function)\n",
"\n",
"CDF is the probability that a random variable X will take on a **value less than or equal to x. i.e. P(X <= x)**\n",
"\n",
"Error function, erf(x) = (2 / sqrt(pi) )* integral from 0 to x of exp(-t^2) dt\n",
"\n",
"![Error function formula](https://i.imgur.com/WLtN4sH.png)\n",
"\n",
"In python we can use erf(x) with math.erf(x)\n",
"\n",
"![CDF formula](https://i.imgur.com/oaJJnlh.png)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# cdf in python\n",
"\n",
"from matplotlib import pyplot as plt\n",
"\n",
"import math\n",
"\n",
"def normal_cdf(x: float, mu: float = 0, sigma: float = 1) -> float:\n",
" return (1 + math.erf((x - mu) / math.sqrt(2) / sigma)) / 2\n",
"\n",
"x = [x / 10.0 for x in range(-50, 50)]\n",
"y = [normal_cdf(a) for a in x]\n",
"\n",
"plt.plot(x, y, \"r-\", label=\"mu = 0, sigma = 1\")\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Consider the experiment of tossing of a fair coin once. Estimate the probability that a coin flips heads."
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"There are 50160 heads out of 100000 trials\n",
"The estimated probability of head is 0.5016\n"
]
}
],
"source": [
"# Consider the experiment of tossing of a fair coin once. Estimate the probability that a coin flips heads\n",
"\n",
"import random\n",
"\n",
"class coin():\n",
" heads = 1\n",
" tails = 0\n",
" \n",
"def random_outcome():\n",
" # return either 1 or 0\n",
" return random.choice([coin.heads, coin.tails])\n",
"\n",
"n_trials = 100000\n",
"n_heads = 0\n",
"for i in range(n_trials):\n",
" outcomes = random_outcome()\n",
" if outcomes == coin.heads:\n",
" n_heads += 1\n",
"\n",
"print(f\"There are {n_heads} heads out of {n_trials} trials\")\n",
"\n",
"print(f\"The estimated probability of head is {n_heads/n_trials}\")"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"P(both | older): 0.4948535233570863\n",
"P(both | either): 0.33077533739084414\n",
"P(older | either): 0.6684308017994178\n"
]
}
],
"source": [
"import enum\n",
"import random\n",
"\n",
"\n",
"class Kid(enum.Enum):\n",
" BOY = 0\n",
" GIRL = 1\n",
"\n",
"\n",
"def random_kid() -> Kid:\n",
" return random.choice([Kid.BOY, Kid.GIRL])\n",
"\n",
"\n",
"both_girls = 0\n",
"older_girl = 0\n",
"either_girl = 0\n",
"# random.seed(0)\n",
"for _ in range(10000):\n",
" younger = random_kid()\n",
" older = random_kid()\n",
" if older == Kid.GIRL:\n",
" older_girl += 1\n",
" if older == Kid.GIRL and younger == Kid.GIRL:\n",
" both_girls += 1\n",
" if older == Kid.GIRL or younger == Kid.GIRL:\n",
" either_girl += 1\n",
"\n",
"print(\"P(both | older):\", both_girls / older_girl)\n",
"# 0.514 ~ 1/2\n",
"print(\"P(both | either): \", both_girls / either_girl) # 0.342 ~ 1/3\n",
"\n",
"print(\"P(older | either): \", older_girl / either_girl)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Normal pdf with different values of mu and sigma"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"import math\n",
"\n",
"def normal_pdf(x: float, mu: float = 0, sigma: float = 1) -> float:\n",
" return (math.exp(-(x - mu)**2 / 2 / sigma**2) / sigma / math.sqrt(2 ** math.pi))\n",
"\n",
"xs = [x / 10.0 for x in range(-50, 50)]\n",
"\n",
"plt.plot(xs, [normal_pdf(x, sigma=1) for x in xs], '-', label='mu=0, sigma=1')\n",
"plt.plot(xs, [normal_pdf(x, sigma=2) for x in xs], '--', label='mu=0, sigma=2')\n",
"plt.plot(xs, [normal_pdf(x, sigma=0.5)\n",
" for x in xs], ':', label='mu=0, sigma=0.5')\n",
"plt.plot(xs, [normal_pdf(x, mu=-1) for x in xs], '-.', label='mu=-1, sigma=1')\n",
"plt.legend()\n",
"\n",
"plt.title(\"Various Normal pdfs\")\n",
"\n",
"plt.show()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": ".venv",
"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": "3.12.2"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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