Probability Lab v2

Monte Carlo Simulation Engine · Statistical Toolkit

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What's New in v2.0

• Landing page with animated moving-gradient navbar
• Discrete Lab — Binomial, Geometric, Poisson (with animate button)
• Continuous Lab — Normal, Exponential, Gamma, Beta, Uniform, Chi-Squared, Student-t
• Hypothesis Testing — One-sample Z/T, Two-sample T, Chi-Square (GoF + Independence)
• Confidence Intervals — Z-interval, T-interval, Wilson Proportion CI, Variance CI, Coverage Simulation
• Bayes Theorem — Classic, Sequential updating, Beta-Binomial conjugate
• Combinatorics — nPr, nCr, Multinomial, Birthday Problem, List Generator

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Project Structure

probability_lab/
├── app_sr.py        ← main app (run this)
├── requirements.txt
├── core/
│   ├── __init__.py
│   └── distributions.py    ← all simulators + theory curves
└── tools/
    ├── __init__.py
    └── stats_tools.py       ← hypothesis tests, CIs, Bayes, combinatorics

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Quick Start

git clone <your-repo>
cd probability_lab

python3 -m venv venv
source venv/bin/activate       # macOS/Linux
venv\Scripts\activate          # Windows

pip install -r requirements.txt
streamlit run app_sr.py

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Features

⚀ Discrete Distributions

Distribution	Parameters	Formula
Binomial	n, p	P(X=k) = C(n,k)pᵏ(1-p)ⁿ⁻ᵏ
Geometric	p	P(X=k) = (1-p)ᵏ⁻¹p
Poisson	λ	P(X=k) = e⁻λλᵏ/k!

〰️ Continuous Distributions

Distribution	Parameters
Normal	μ, σ
Exponential	λ
Gamma	k, θ
Beta	α, β
Uniform	a, b
Chi-Squared	df
Student-t	df

🔬 Hypothesis Testing

• Z-test — one-sample with known σ
• T-test — one-sample and two-sample
• Chi-Square — goodness of fit + independence
• Rejection region visualizations, p-values, critical values

📏 Confidence Intervals

• Z-interval (known σ)
• T-interval (unknown σ)
• Wilson CI for proportions
• Chi-square CI for variance
• Coverage probability simulation

🎲 Bayes Theorem

• Classic P(H|E) calculator
• Sequential Bayesian updating animation
• Beta-Binomial conjugate prior/posterior

🧮 Combinatorics

• nPr, nCr with/without repetition
• Pascal's Triangle visualization
• Multinomial coefficients
• Birthday problem curve
• Full combination/permutation list generator

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Built with Python · Streamlit · NumPy · SciPy · Matplotlib · plotly