Probability & Statistics

Random Walk

Visualize a 1D random walk over time.

Monte Carlo Simulation

Estimating Pi using random points in a circle.

Central Limit Theorem

Sample means converge to a normal distribution regardless of the population shape.

Probability Distributions

Exploring continuous probability density functions and their parameters.

Bayes' Theorem

A fundamental theorem for updating probabilities based on new evidence.

Birthday Paradox

Hypothesis Testing

Visualize the relationship between significance level, effect size, and statistical power in a two-tailed Z-test.

Law of Large Numbers

The sample average converges to the expected value as the number of trials increases.

Poisson Process

Poisson Process.

Confidence Intervals

Visualize how confidence intervals capture the true population mean.

Correlation & Covariance

Learn how covariance and correlation measure relationships between random variables and how they differ.

Maximum Likelihood Estimation

Find the parameters of a probability distribution that best explain the observed data.

Regression to the Mean

Gambler's Ruin Problem

Visualizes the classic gambler's ruin random walk and explores ruin probabilities over time.

Markov Chain Monte Carlo

Visualize the Metropolis-Hastings algorithm sampling from complex distributions.

A/B Testing

Compare conversion rate distributions to evaluate statistical significance and power.

Benford's Law

Visualize how the leading digits of many real-life numerical datasets follow a logarithmic distribution.

Beta Distribution

Explore the Beta distribution and the effect of its shape parameters.

Bootstrapping

Visualize statistical bootstrapping through resampling with replacement to estimate distributions.

Chi-Squared Test

Visualize the Chi-Squared goodness-of-fit test by comparing observed and expected frequencies.

Conditional Probability Tree

Visualize a two-stage process and calculate joint probabilities using a tree structure.

Copulas & Joint Distributions

Explore how copulas link marginal distributions to form a joint probability distribution.

Coupon Collector Problem

Visualize the expected number of random draws required to collect all unique coupons in a set.

Kernel Density Estimation

Visualize non-parametric density estimation using different kernel functions and bandwidths.

Order Statistics

Visualize the distribution of the k-th smallest value in a sample of size n.

Prime Number Patterns

Visualize the distribution and underlying order of prime numbers using the Ulam spiral.

Survival Analysis

Estimate time-to-event outcomes using the Kaplan-Meier estimator.

Entropy & Information Theory

Visualize Shannon entropy, probability distributions, and information content for binary and ternary systems.

Exponential Distribution

Visualize the exponential distribution PDF and CDF with an adjustable rate parameter.

Kaplan-Meier Estimator

Estimate time-to-event outcomes and survival probabilities using the Kaplan-Meier estimator.

Moment Generating Functions

Visualize moment generating functions for different probability distributions and see how they derive moments.

Multivariate Normal Distribution

Visualize 2D normal distributions with varying correlation and standard deviations.

Power Analysis

Visualize statistical power, Type II error (β), and their relationship with effect size, sample size, and significance level.

Queueing Theory (M/M/1)

Visualize an M/M/1 queue with adjustable arrival and service rates.

Rejection Sampling

Generate samples from a complex target distribution by using a scaled, simpler proposal distribution.

ROC Curve & AUC

Visualize True Positives, False Positives, and trade-offs in binary classification.

Extreme Value Distribution

Visualize the Generalized Extreme Value distribution including Gumbel, Fréchet, and Weibull families.

Fisher Information

Visualize Fisher Information and the Cramér-Rao bound for normal distribution parameter estimation.