🎲 概率与统计

The Binomial Distribution and the Galton BoardNewA 3D Galton board where falling beads bounce left or right at each row of pegs, piling into… The Birthday ParadoxNewWatch people fill day-of-year buckets one by one until two share a birthday, while a live… Bayes' Theorem and the Medical Testing ParadoxNewWatch why a highly accurate medical test can still be wrong more often than right when the… Galton Board (Bean Machine) — Binomial Distribution & CLT SimulatorNewThis simulation demonstrates the binomial distribution and the Central Limit Theorem through… Monte Carlo Simulator Pi, Integration & RandomnessNewThis simulation demonstrates the Monte Carlo method for approximating numerical values,… 3D Monte Carlo PiNewThis simulation demonstrates the Monte Carlo method for approximating pi by generating… Advanced Statistics Simulator: Statistical Analysis & ProbabilityNewThis simulation allows users to explore complex statistical concepts such as distributions,… Bayesian Inference Explained — Priors, Likelihoods, and PosteriorsNewThis simulation visually explains Bayesian inference, a statistical method used to update… Climate Weather Prediction SimulationNewThis simulation demonstrates the process of weather prediction using a simplified model.… Dice Roll Probability SimulationNewThis simulation explores the fundamental principles of probability by simulating multiple… Differential Privacy - Comprehensive GuideNewThis simulation explains the concept of differential privacy, a technique for protecting… Future Technology Precognition SimulationNewThis simulation demonstrates the challenges of predicting future events based on available… Hypothesis Testing Explained — p-values, Power, and ErrorsNewThis simulation provides an interactive exploration of statistical hypothesis testing. Users… Learning Memory Techniques SimulationNewThis simulation demonstrates the principles of memory encoding and retrieval. It explores… Percolation Phase TransitionNewThis simulation allows you to visualize and manipulate the process of percolation – a phase… Monte Carlo Pi CalculationNewThis simulation allows you to explore the Monte Carlo method for calculating Pi by… Planetary Orbits Simulator — Gravitational Dynamics, Kepler's Laws, and Orbital DragNewThis simulation lets you model planetary orbits under Newtonian gravity, adjusting… Linear Regression Analysis ToolNewThis simulation allows users to explore linear regression by manipulating data points and… Statistical Analysis SimulationNewThis simulation demonstrates the principles of statistical analysis by allowing users to… Statistics SimulatorNewThis simulation allows users to explore the core principles of statistics by manipulating… Time Series Analysis — Stationarity, ARIMA, and ForecastingNewThis simulation explores time series analysis techniques used to understand and predict… Galton Board PhysicsNewThis simulation models the probabilistic distribution of particle movement on a Galton… Monte Carlo Importance SamplingNewEstimate rare-event probabilities with importance sampling: shift the proposal distribution… Buffon's Needle — Monte Carlo π EstimationNewEstimate π by dropping needles on a lined floor: π ≈ 2L·N / (d·crossings). Watch the… Coupon Collector's Problem — Expected Draws to Collect AllNewCollect all N coupons from random draws: watch the grid fill, compare empirical averages to… Secretary Problem — Optimal Stopping & the 37% RuleNewReject the first ~37% of candidates, then hire the first one better than all seen.… Hidden Markov Model — States & ObservationsNewWatch a hidden Markov model emit observations from latent states, then recover the most… Reservoir Sampling — Fair Samples from a StreamNewPick k uniform samples from a stream of unknown length in one pass: item i replaces a… Dynamic Time Warping — Aligning Time SeriesNewDynamic time warping aligns two time series that vary in speed by warping the time axis. A… Geometric Brownian Motion Simulation & Drift ControlNewWitness a simulation of geometric Brownian motion, where users can manipulate drift and… Law of Large NumbersNewRoll dice thousands of times and watch the running average converge to the expected value… Central Limit TheoremDraw repeated samples from Uniform, Exponential, Bimodal or Poisson distributions and watch… Lévy FlightSimulate Lévy flights: tune the stability exponent α from Brownian motion (α=2) to rare long… Gambler's RuinSet stake, target and win probability, then run Monte Carlo random walks to see how often… Wiener Process Dynamics & Stochastic DriftExplore the behavior of a Wiener process, observing how drift, volatility, and mean… Markov ChainsEdit a transition matrix, step a random walker between states, and watch the distribution… Markov Chain — Transition Matrix SimulatorEdit the transition matrix and watch state probabilities converge to a stationary… Percolation Theory — Site & Bond Percolation, Phase TransitionInteractive percolation simulation on a 2D lattice. Adjust the occupation probability p and… Monte Carlo πEstimate π by throwing random darts at a unit square with an inscribed circle. The ratio…