All Modules

Probability & Stochastic Processes

Discover the mathematics of randomness through 21 interactive demonstrations. Watch random walks converge to Brownian motion, see the Central Limit Theorem in action, and explore Markov chains as flowing particle systems.

See also: Measure Theory for the formal foundations of probability spaces, Combinatorics for counting outcomes in finite probability, and Information Theory for entropy as a measure of uncertainty.

  1. 01

    Random Walks

    Animated 1D and 2D random walks converging to Brownian motion

    3 demos
  2. 02

    Central Limit Theorem

    Watch any distribution converge to a bell curve as you add samples

    3 demos
  3. 03

    Distribution Explorer

    Interactive PDF, CDF, and parameter exploration for common distributions

    3 demos
  4. 04

    Monte Carlo Methods

    Estimate pi, integrate curves, and simulate Buffon's needle

    3 demos
  5. 05

    Law of Large Numbers

    Coin flips, sample means, and the gambler's ruin

    3 demos
  6. 06

    Markov Chains

    State transitions, stationary distributions, and random walks on graphs

    3 demos
  7. 07

    Bayesian Inference

    Prior-to-posterior updating, medical tests, and Bayesian reasoning

    3 demos

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