From e60345f24997d5d7c0640128cefd0480049315a3 Mon Sep 17 00:00:00 2001 From: Roberto Ugalde <94400091+rober12345@users.noreply.github.com> Date: Wed, 20 Nov 2024 18:24:09 -0600 Subject: [PATCH] Add files via upload probability exercise 1 20 nov24 --- .../problems_solved_rober_ugalde201124.ipynb | 329 ++++++++++++++++++ 1 file changed, 329 insertions(+) create mode 100644 notebook/problems_solved_rober_ugalde201124.ipynb diff --git a/notebook/problems_solved_rober_ugalde201124.ipynb b/notebook/problems_solved_rober_ugalde201124.ipynb new file mode 100644 index 00000000..fe21442b --- /dev/null +++ b/notebook/problems_solved_rober_ugalde201124.ipynb @@ -0,0 +1,329 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "b967ebc8", + "metadata": {}, + "source": [ + "# Probability distribution problems" + ] + }, + { + "cell_type": "markdown", + "id": "c9b71587", + "metadata": {}, + "source": [ + "## Binomial distribution\n", + "\n", + "In probability theory and statistics, the binomial distribution is the discrete probability distribution that gives only two possible results in an experiment; for example, when you flip a coin, it can be either head or tails." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "4eb16d6e", + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.stats import binom\n", + "\n", + "# Define all the probability functions related to this distribution\n", + "\n", + "def dbinom(x, size, prob = 0.5):\n", + " \"\"\"\n", + " Calculates the point estimate of the binomial distribution\n", + " \"\"\"\n", + " result = binom.pmf(k = x, n = size, p = prob, loc = 0)\n", + "\n", + " return result\n", + "\n", + "def pbinom(q, size, prob = 0.5):\n", + " \"\"\"\n", + " Calculates the cumulative of the binomial distribution\n", + " \"\"\"\n", + " result = binom.cdf(k = q, n = size, p = prob, loc = 0)\n", + "\n", + " return result\n", + "\n", + "def qbinom(p, size, prob = 0.5):\n", + " \"\"\"\n", + " Calculates the quantile function from the binomial distribution\n", + " \"\"\"\n", + " result = binom.ppf(q = p, n = size, p = prob, loc = 0)\n", + "\n", + " return result\n", + "\n", + "def rbinom(n, size, prob = 0.5):\n", + " \"\"\"\n", + " Generates random variables from the binomial distribution\n", + " \"\"\"\n", + " result = binom.rvs(n = size, p = prob, size = n)\n", + "\n", + " return result" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "6cf6313a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Probability that a Binomial(10, 0.2) takes the value 2: 0.30198988800000004\n", + "Probability that a Binomial(10, 0.2) will take a value less than 2: 0.6777995263999999\n", + "Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? 4.0\n", + "Generate 2000 random values from a Binomial(10, 0.2) distribution: [1 4 3 ... 0 0 1]\n" + ] + } + ], + "source": [ + "# Binomial(10, 0.2) distribution, where n = 10 is the number of trials and p = 0.2 is the probability of success in a single trial\n", + "import numpy as np\n", + "\n", + "np.random.seed(42)\n", + "\n", + "print(f\"Probability that a Binomial(10, 0.2) takes the value 2: {dbinom(2, size = 10, prob = 0.2)}\")\n", + "print(f\"Probability that a Binomial(10, 0.2) will take a value less than 2: {pbinom(2, size = 10, prob = 0.2)}\")\n", + "print(f\"Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? {qbinom(0.9, size = 10, prob = 0.2)}\")\n", + "print(f\"Generate 2000 random values from a Binomial(10, 0.2) distribution: {rbinom(2000, size = 10, prob = 0.2)}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "69fd07da", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "np.random.seed(42)\n", + "\n", + "size = 10\n", + "prob = 0.2\n", + "data = rbinom(2000, size = 10, prob = 0.2)\n", + "\n", + "pmf = dbinom(data, size = size, prob = prob)\n", + "cdf = pbinom(data, size = size, prob = prob)\n", + "ppf = qbinom(data, size = size, prob = prob)\n", + "\n", + "fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n", + "\n", + "axis[0].stem(data, pmf, \"r-\")\n", + "axis[1].stem(data, cdf, \"b-\")\n", + "axis[2].stem(data, ppf, \"g-\")\n", + "\n", + "# Adjust the layout\n", + "plt.tight_layout()\n", + "\n", + "# Show the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "8aa7eaa0", + "metadata": {}, + "source": [ + "## Exercise 1\n", + "\n", + "Write the above functions but for both normal and uniform distributions." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "98d5f012", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.stats import binom, norm, uniform\n", + "\n", + "# Binomial Distribution Functions\n", + "def dbinom(x, size, prob=0.5):\n", + " return binom.pmf(k=x, n=size, p=prob, loc=0)\n", + "\n", + "def pbinom(q, size, prob=0.5):\n", + " return binom.cdf(k=q, n=size, p=prob, loc=0)\n", + "\n", + "def qbinom(p, size, prob=0.5):\n", + " return binom.ppf(q=p, n=size, p=prob, loc=0)\n", + "\n", + "def rbinom(n, size, prob=0.5):\n", + " return binom.rvs(n=size, p=prob, size=n)\n", + "\n", + "\n", + "# Normal Distribution Functions\n", + "def dnorm(x, mean=0, sd=1):\n", + " return norm.pdf(x, loc=mean, scale=sd)\n", + "\n", + "def pnorm(q, mean=0, sd=1):\n", + " return norm.cdf(q, loc=mean, scale=sd)\n", + "\n", + "def qnorm(p, mean=0, sd=1):\n", + " return norm.ppf(p, loc=mean, scale=sd)\n", + "\n", + "def rnorm(n, mean=0, sd=1):\n", + " return norm.rvs(loc=mean, scale=sd, size=n)\n", + "\n", + "\n", + "# Uniform Distribution Functions\n", + "def dunif(x, min_val=0, max_val=1):\n", + " return uniform.pdf(x, loc=min_val, scale=max_val - min_val)\n", + "\n", + "def punif(q, min_val=0, max_val=1):\n", + " return uniform.cdf(q, loc=min_val, scale=max_val - min_val)\n", + "\n", + "def qunif(p, min_val=0, max_val=1):\n", + " return uniform.ppf(p, loc=min_val, scale=max_val - min_val)\n", + "\n", + "def runif(n, min_val=0, max_val=1):\n", + " return uniform.rvs(loc=min_val, scale=max_val - min_val, size=n)\n", + "\n", + "\n", + "# Visualization Function\n", + "def plot_distributions():\n", + " # Binomial Distribution\n", + " size, prob = 10, 0.2\n", + " x_binom = np.arange(0, size + 1)\n", + " pmf_binom = dbinom(x_binom, size=size, prob=prob)\n", + " cdf_binom = pbinom(x_binom, size=size, prob=prob)\n", + "\n", + " fig, ax = plt.subplots(3, 1, figsize=(8, 12))\n", + " ax[0].stem(x_binom, pmf_binom, linefmt='r-', basefmt='k', markerfmt='ro')\n", + " ax[0].set_title(\"Binomial PMF\")\n", + " ax[0].set_xlabel(\"x (Number of Successes)\")\n", + " ax[0].set_ylabel(\"Probability\")\n", + "\n", + " ax[1].step(x_binom, cdf_binom, where=\"post\", color=\"b\")\n", + " ax[1].set_title(\"Binomial CDF\")\n", + " ax[1].set_xlabel(\"x (Number of Successes)\")\n", + " ax[1].set_ylabel(\"Cumulative Probability\")\n", + "\n", + " random_probs = np.linspace(0, 1, 11)\n", + " quantiles_binom = [qbinom(p, size=size, prob=prob) for p in random_probs]\n", + " ax[2].stem(random_probs, quantiles_binom, linefmt='g-', basefmt='k', markerfmt='go')\n", + " ax[2].set_title(\"Binomial Quantile Function\")\n", + " ax[2].set_xlabel(\"Probability\")\n", + " ax[2].set_ylabel(\"Quantile (x)\")\n", + "\n", + " plt.tight_layout()\n", + " plt.show()\n", + "\n", + " # Normal Distribution\n", + " mean, sd = 0, 1\n", + " x_norm = np.linspace(-4, 4, 100)\n", + " pdf_norm = dnorm(x_norm, mean=mean, sd=sd)\n", + " cdf_norm = pnorm(x_norm, mean=mean, sd=sd)\n", + "\n", + " fig, ax = plt.subplots(2, 1, figsize=(8, 8))\n", + " ax[0].plot(x_norm, pdf_norm, 'r-')\n", + " ax[0].set_title(\"Normal PDF\")\n", + " ax[0].set_xlabel(\"x\")\n", + " ax[0].set_ylabel(\"Density\")\n", + "\n", + " ax[1].plot(x_norm, cdf_norm, 'b-')\n", + " ax[1].set_title(\"Normal CDF\")\n", + " ax[1].set_xlabel(\"x\")\n", + " ax[1].set_ylabel(\"Cumulative Probability\")\n", + "\n", + " plt.tight_layout()\n", + " plt.show()\n", + "\n", + " # Uniform Distribution\n", + " min_val, max_val = 0, 1\n", + " x_unif = np.linspace(min_val, max_val, 100)\n", + " pdf_unif = dunif(x_unif, min_val=min_val, max_val=max_val)\n", + " cdf_unif = punif(x_unif, min_val=min_val, max_val=max_val)\n", + "\n", + " fig, ax = plt.subplots(2, 1, figsize=(8, 8))\n", + " ax[0].plot(x_unif, pdf_unif, 'r-')\n", + " ax[0].set_title(\"Uniform PDF\")\n", + " ax[0].set_xlabel(\"x\")\n", + " ax[0].set_ylabel(\"Density\")\n", + "\n", + " ax[1].plot(x_unif, cdf_unif, 'b-')\n", + " ax[1].set_title(\"Uniform CDF\")\n", + " ax[1].set_xlabel(\"x\")\n", + " ax[1].set_ylabel(\"Cumulative Probability\")\n", + "\n", + " plt.tight_layout()\n", + " plt.show()\n", + "\n", + "\n", + "# Example Usage\n", + "if __name__ == \"__main__\":\n", + " np.random.seed(42)\n", + " plot_distributions()\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "base", + "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": "3.12.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}