Probability Distribution Lab

A comprehensive Streamlit application to visualize and understand fundamental probability distributions. Explore Bernoulli, Binomial, Normal, Poisson, Exponential distributions, analyze the Central Limit Theorem, and run Monte Carlo simulations.

Features

• Interactive Visualizations: Adjust parameters and see real-time updates to distribution plots.
• Bernoulli Distribution: Explore single-trial success/failure with probability slider.
• Binomial Distribution: Simulate coin flips/trials with varying n and p.
• Normal Distribution: Adjust mean (μ) and standard deviation (σ) to see the bell curve transform.
• Poisson Distribution: Analyze rare events with the lambda (λ) parameter.
• Exponential Distribution: Understand waiting times between events.
• Central Limit Theorem: Prove the CLT by observing the convergence of sample means to a normal distribution.
• Monte Carlo Simulation: Simulate random processes like coin flips to verify theoretical probabilities.

Getting Started

Prerequisites

• Python 3.7+
• pip (Python package installer)

Installation

1. Clone the repository (or download the source code):

   git clone https://github.com/shuvam776/Distribution.git
   cd Distribution

2. Install dependencies: This project uses streamlit, numpy, and matplotlib.

   pip install -r requirements.txt

3. Run the application:

   streamlit run app.py

Usage

1. Open your web browser and navigate to the local URL provided by Streamlit (usually http://localhost:8501).
2. Use the sidebar on the left to select the distribution you want to explore.
3. Adjust the sliders to change the parameters of the distribution.
4. Observe the probability plot and the statistics below it.

Troubleshooting

If you encounter issues running the app, especially on Windows, ensure you are using the correct command:

streamlit run app.py --server.port=8501