Distribution Playground

Every distribution in one sandbox. Pick one, drag its parameters, and watch the shape respond — the dashed line is the mean, the dotted lines sit one standard deviation to each side. Formulas can't show you this; sliders can.

What to try

• t vs. normal: pick Student's t, turn on the normal overlay, and drag df from 1 upward — the fat tails melt away. That's why t-tables stop mattering around df ≈ 100. (lesson)
• The normal approximation: pick Binomial with the overlay on. At n = 5 the bell is a bad costume; by n = 50 it fits beautifully — the Central Limit Theorem in action. (lesson)
• Skew that won't quit: chi-square with small df is heavily right-skewed; drag df up and watch it slowly normalize. (lesson)
• Beta as belief: Beta(2, 5) says "probably a low proportion"; Beta(20, 50) says the same thing with confidence. This is exactly how Bayesian updating sharpens a prior. (lesson)
• Counts: Poisson's variance equals its mean — watch the spread grow with λ. When real data spread more than that, you've met overdispersion. (lesson)