Project: Interactive Statistics & Probability Course

This project is a web-based Statistics & Probability Explorer, designed to help users understand key statistical concepts through visualizations, explanations, and interactive elements. The tool will be mostly static (prebuilt components) rather than dynamically processing user data, making it easier to develop and deploy within a couple of weeks. The long-term vision is for this to serve as the foundation for a college-level statistics course.

• Showcase knowledge in statistics, probability, and Bayesian statistics.
• Serve as an educational tool that could be sold or used as a curriculum component.
• Keep complexity manageable by focusing on static but informative content.

• Frontend: React (for UI development)
• Backend: Flask (Python for data processing and API)
• Data Processing & Visualization: Python (Flask API for precomputed stats), D3.js or Chart.js for graphs
• Hosting & Deployment: GitHub & GitHub Pages (for frontend), Render/Heroku (for Flask backend)

• Static visualizations for:
  • Normal Distribution
  • Binomial Distribution
  • Poisson Distribution
• Explanations of parameters (mean, standard deviation, etc.)

• Central Limit Theorem: Precomputed visualization of how sample sizes affect distributions.
• Law of Large Numbers: Static example showing averages converging to expected values.
• Hypothesis Testing: Step-by-step breakdown of t-tests and p-values.
• Regression Analysis: Example dataset showcasing linear regression.

• Introduction to Bayesian Inference.
• Bayes’ Theorem: Explanation and real-world applications.
• Prior, Likelihood, and Posterior Distributions.
• Bayesian vs. Frequentist Statistics.

• Preloaded datasets with insights (e.g., sports stats, finance, demographics).
• Guided analysis showing how statistics and Bayesian methods apply in various fields.

• PDFs of explanations and sample exercises.
• Code snippets for running statistical and Bayesian tests in Python.

1. Week 1:

   • Set up the project repo and base UI layout in React.
   • Build static pages for each statistical concept.
   • Create precomputed charts & graphs using Python & JavaScript.

2. Week 2:

   • Implement Flask API for data retrieval and calculations.
   • Finalize all case studies & dataset examples.
   • Polish UI and add interactive elements (sliders, hover effects, tooltips).
   • Test deployment on GitHub Pages (frontend) & Render/Heroku (backend).

• Add interactive quizzes.
• Enable CSV uploads for user-driven analysis.
• Expand Bayesian models with Markov Chain Monte Carlo (MCMC).