Demos

Interactive teaching demos for foundational probability concepts and random variables.

Random events

• The Monty Hall Problem — switching beats staying; play it, simulate it, see why.

Event probabilities

• Rapid Test Bayesian Updating Lab — change prevalence, sensitivity, and specificity, then watch positive or negative results update the posterior.
• Simpson’s Paradox Mixing Lab — change the group mix and observe when within-group comparisons reverse after aggregation.

Random variables

• From pmf to cdf — build a discrete distribution by editing $(x, p)$ points, then sweep a current $x$ to watch the cdf accumulate.
• From pdf to cdf — pick a continuous distribution, tune its parameters, sweep $x$, and watch the running integral build the cdf.
• Mixed distributions — combine a continuous family with user-defined point masses; watch the cdf jump by exactly $w_i$ at each $x_i$.
• Probability Integral Transform and Inverse Transform Sampling — follow one value through the standard Cauchy pdf, cdf, and quantile function, then generate inverse-transformed samples and compare their histograms.