Model discrete probability distributions for fixed trials with $P(X=k) = inom{n}{k}p^k(1-p)^{n-k}$. Visualize how the number of trials and success probability affect the shape, mean $mu = np$, and standard deviation $sigma = sqrt{np(1-p)}$ of binomial distributions.
Struggle with the Central Limit Theorem? Draw 10,000 samples from highly skewed or bimodal parent populations and watch the perfect normal bell curve emerge.
Visualize how Statistical Power responds dynamically to Effect Size (mu_a), Sample Size, and Alpha. Plot the complete functional power curve.
Deconstruct Analysis of Variance geometrically. Shift group means (MSB) and internal scatter (MSW) to see the massive impact on the F-statistic and P-value.
Visualize how sampling distributions of means approach normality as sample size increases, regardless of population shape. Explore the CLT formula $sigma_{ar{x}} = rac{sigma}{sqrt{n}}$ and see how larger samples produce tighter distributions around the population mean.