Probability

A comprehensive survey of probability theory, covering foundational axioms, discrete and continuous distributions, and the limit theorems that underpin statistical inference.

How this guide is organized

1. Foundations

   • Core probability language: events, sample spaces, independence
   • “What does probability mean?” (frequentist vs Bayesian intuition)
   • Key metrics and reading charts (PDF vs CDF, z-scores)

2. Discrete distributions (counting outcomes)

   • Bernoulli, Binomial, Geometric, Poisson, and friends
   • When to use each distribution and how parameters change the shape

3. Continuous distributions (measuring quantities)

   • Uniform, Normal, Exponential + tools like Q–Q plots
   • How areas/intervals translate into probability

4. Advanced distributions

   • Distributions used in inference and testing (Chi-square, t, F)
   • Common transformations and shape families (Gamma, Beta)

5. Inequalities & limit theorems

   • Inequalities: Markov and Chebyshev (distribution-free guarantees)
   • Convergence: Law of Large Numbers and the Central Limit Theorem
   • Why these results matter for sampling, estimation, and “why normal shows up”