🎲 Probability & Statistics

Central Limit Theorem (2D)New📱Draw repeated random samples from a Uniform, Exponential, Bimodal, Poisson or Right-Skewed… Markov Chains: State Diagram & Stationary Distribution (2D)New📱A token hops between states of a Markov chain along a 2D transition-probability diagram,… Law of Large Numbers (2D)New📱Flip a coin, roll a die, or sample a custom biased trial and watch the running sample… Gambler's Ruin (2D)New📱Watch a gambler's capital random-walk between two absorbing barriers at 0 and a target N.… Wiener Process (2D)New📱Watch the Wiener process build up in real time on a classic value-versus-time chart:… Lévy Flight vs Brownian Motion (2D)New📱Top-down 2D random-walk trajectories comparing Lévy flights (heavy-tailed power-law step… Hidden Markov Model — Canvas Trellis (2D)New📱2D Canvas trellis view of a hidden Markov model: sample observations from editable… Monte Carlo Importance Sampling (2D)New📱Watch naive Monte Carlo and importance sampling estimate a rare-tail probability side by… Percolation Theory (2D) — Site & Bond Lattice, Union-FindNew📱2D percolation lab on a real square lattice: a weighted union-find over independently random… Memory Palace in 3D — Forgetting Curve & Spaced Repetition SimulatorNew📱3D companion to the memory-techniques simulator: walk a method-of-loci corridor where the… Markov Chain — Random Walker & Stationary Convergence (2D)New📱A 2D companion to the 3D Markov Chain simulator: drag states around a live transition graph,… St. Petersburg Paradox — Probability Ladder CascadeNew📱Watch the St. Petersburg coin-flip game cascade down a 2D probability ladder thousands of… Poisson Process — Timeline, Staircase & Gap HistogramNew📱2D three-panel Poisson process simulator: events arrive with exponentially-distributed gaps… St. Petersburg Paradox — Why Expected Value Can DivergeNew📱Play the classic St. Petersburg coin-flip game thousands of times per second and watch a… Martingales & the Optional Stopping TheoremNew📱Race a bundle of independent fair-coin random walks in 3D, each stopped the instant it… Poisson Process — Live Event ArrivalsNew📱A live continuous-time Poisson process: events arrive with exponentially-distributed gaps… The Binomial Distribution and the Galton BoardNew📱A 3D Galton board where falling beads bounce left or right at each row of pegs, piling into… The Birthday ParadoxNew📱Watch people fill day-of-year buckets one by one until two share a birthday, while a live… Bayes' Theorem and the Medical Testing ParadoxNew📱Watch why a highly accurate medical test can still be wrong more often than right when the… Galton Board (Bean Machine) — Binomial Distribution & CLT SimulatorNew📱This simulation demonstrates the binomial distribution and the Central Limit Theorem through… Monte Carlo Simulator Pi, Integration & RandomnessNew📱This simulation demonstrates the Monte Carlo method for approximating numerical values,… 3D Monte Carlo PiNew📱This simulation demonstrates the Monte Carlo method for approximating pi by generating… Advanced Statistics Simulator: Statistical Analysis & ProbabilityNew📱This simulation allows users to explore complex statistical concepts such as distributions,… Bayesian Inference Explained — Priors, Likelihoods, and PosteriorsNew📱This simulation visually explains Bayesian inference, a statistical method used to update… Climate Weather Prediction SimulationNew📱This simulation demonstrates the process of weather prediction using a simplified model.… Dice Roll Probability SimulationNew📱This simulation explores the fundamental principles of probability by simulating multiple… Differential Privacy - Comprehensive GuideNew📱This simulation explains the concept of differential privacy, a technique for protecting… Future Technology Precognition SimulationNew📱This simulation demonstrates the challenges of predicting future events based on available… Hypothesis Testing Explained — p-values, Power, and ErrorsNew📱This simulation provides an interactive exploration of statistical hypothesis testing. Users… Learning Memory Techniques SimulationNew📱This simulation demonstrates the principles of memory encoding and retrieval. It explores… Percolation Phase TransitionNew📱This simulation allows you to visualize and manipulate the process of percolation – a phase… Monte Carlo Pi CalculationNew📱This simulation allows you to explore the Monte Carlo method for calculating Pi by… Planetary Orbits Simulator — Gravitational Dynamics, Kepler's Laws, and Orbital DragNew📱This simulation lets you model planetary orbits under Newtonian gravity, adjusting… Linear Regression Analysis ToolNew📱This simulation allows users to explore linear regression by manipulating data points and… Statistical Analysis SimulationNew📱This simulation demonstrates the principles of statistical analysis by allowing users to… Statistics SimulatorNew📱This simulation allows users to explore the core principles of statistics by manipulating… Time Series Analysis — Stationarity, ARIMA, and ForecastingNew📱This simulation explores time series analysis techniques used to understand and predict… Galton Board PhysicsNew📱This simulation models the probabilistic distribution of particle movement on a Galton… Monte Carlo Importance SamplingNew📱Estimate rare-event probabilities with importance sampling: shift the proposal distribution… Buffon's Needle — Monte Carlo π EstimationNew📱Estimate π by dropping needles on a lined floor: π ≈ 2L·N / (d·crossings). Watch the… Coupon Collector's Problem — Expected Draws to Collect AllNew📱Collect all N coupons from random draws: watch the grid fill, compare empirical averages to… Secretary Problem — Optimal Stopping & the 37% RuleNew📱Reject the first ~37% of candidates, then hire the first one better than all seen.… Hidden Markov Model — States & ObservationsNew📱Watch a hidden Markov model emit observations from latent states, then recover the most… Reservoir Sampling — Fair Samples from a StreamNew📱Pick k uniform samples from a stream of unknown length in one pass: item i replaces a… Dynamic Time Warping — Aligning Time SeriesNew📱Dynamic time warping aligns two time series that vary in speed by warping the time axis. A… Geometric Brownian Motion Simulation & Drift ControlNew📱Witness a simulation of geometric Brownian motion, where users can manipulate drift and… Law of Large NumbersNew📱Roll dice thousands of times and watch the running average converge to the expected value… Central Limit Theorem📱Draw repeated samples from Uniform, Exponential, Bimodal or Poisson distributions and watch… Lévy Flight📱Simulate Lévy flights: tune the stability exponent α from Brownian motion (α=2) to rare long… Gambler's Ruin📱Set stake, target and win probability, then run Monte Carlo random walks to see how often… Wiener Process Dynamics & Stochastic Drift📱Explore the behavior of a Wiener process, observing how drift, volatility, and mean… Markov Chains📱Edit a transition matrix, step a random walker between states, and watch the distribution… Markov Chain — Transition Matrix📱Edit the transition matrix and watch state probabilities converge to a stationary… Percolation Theory — Site & Bond Percolation, Phase Transition📱Interactive percolation simulation on a 2D lattice. Adjust the occupation probability p and… Monte Carlo π📱Estimate π by throwing random darts at a unit square with an inscribed circle. The ratio… Martingales & the Optional Stopping Theorem (2D)📱Watch a bundle of fair-coin random walks race on a 2D step-vs-value chart toward a stopping…