https://github.com/justin-pyne/probability-projects

A collection of Python scripts that demonstrate various probability concepts for review/fun. Each script is a separate project that focuses on a specific topic, such as different probability distributions, random variables, expected values, etc.
https://github.com/justin-pyne/probability-projects

Last synced: 3 months ago
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A collection of Python scripts that demonstrate various probability concepts for review/fun. Each script is a separate project that focuses on a specific topic, such as different probability distributions, random variables, expected values, etc.

• Host: GitHub
• URL: https://github.com/justin-pyne/probability-projects
• Owner: justin-pyne
• Created: 2023-10-31T18:45:42.000Z (over 1 year ago)
• Default Branch: main
• Last Pushed: 2023-10-31T22:17:24.000Z (over 1 year ago)
• Last Synced: 2025-01-02T18:41:37.158Z (5 months ago)
• Language: Python
• Homepage:
• Size: 15.6 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# probability-projects

This repository contains a collection of Python scripts that demonstrate various probability concepts. Each script is a separate project that focuses on specific topic in probability.

## Projects

1. **Probability Distributions (`probability_distributions.py`)**

   - Simulate and visualize different probability distributions, including normal, binomial, and Poisson distributions.

   - Input parameters for the selected distribution, generate a sample, and plot the sample data along with the theoretical probability density function (PDF) or probability mass function (PMF).

   - Calculate and display relevant statistics, such as mean, variance, skewness, and kurtosis.

2. **Random Variables and Expected Values (`random_variables.py`)**

   - Understand random variables and expected values by creating a probability distribution with user-defined outcomes and probabilities.

   - Visualize the distribution and calculate/display the expected value and variance.

   - Perform operations on random variables (addition, subtraction, multiplication, division) and visualize the resulting distribution.

3. **Custom Probability Distribution (`custom_probability_distribution.py`)**

   - Create and visualize custom discrete or continuous probability distributions.

   - Calculate and display expected values and variance for the created distribution.

   - Perform and visualize operations on random variables, including addition, subtraction, multiplication, and division.

4. **Law of Large Numbers (`law_of_large_numbers.py`)**

   - Demonstrate the Law of Large Numbers through simulations and visualizations.

   - Show how the average of results obtained from a large number of trials converges to the expected value.

   - Compare results for different sample sizes to illustrate the concept.

5. **Central Limit Theorem (`central_limit_theorem.py`)**

   - Demonstrate the Central Limit Theorem through simulations and visualizations.

   - Show how the distribution of sample means approximates a normal distribution, regardless of the shape of the original data distribution.

   - Include a normal distribution fit to highlight the convergence towards normality.

## Installation

You need Python installed on your machine, and the following Python packages:

```bash

pip install numpy matplotlib scipy

```

## Usage

Each script can be run independently from the command line. For example, to run the probability distributions script, use:

```bash

python probability_distributions.py

```