Probability Distribution Lab

Understand probability distributions from the first equation. Probability Distribution Lab helps you study derivations, transformations, and proofs of the mean and variance one line at a time, inside the app. No equation entry is required: tap to reveal the next step and its explanation, then record your understanding. FOLLOW THE REASONING Start with the initial equation and reveal each transformation in sequence. Mark difficult steps for review. Set familiar transformations to be skipped next time, and reveal skipped sections again when needed. DERIVE THE MEAN AND VARIANCE Study the reasoning behind the formulas, not only the final result. After a lesson, assess whether you can derive it without an explanation or understand it with a hint. CONNECT FORMULAS TO SHAPES AND USES Explore each distribution's graph, parameters, and concrete examples. Use the relationship map to study sums, limits, and transformations together with their conditions. REVISIT THE MATHEMATICS YOU NEED Refer to prerequisite concepts while studying a derivation. Save difficult steps and self-assessed understanding to organize your next review. Progress indicators reflect your own assessment; they do not guarantee exam results. FREE EDITION AND FULL ACCESS The free edition includes four distributions: Bernoulli, Binomial, Poisson, and Normal. Banner ads are shown in the free edition. Full Access is a one-time in-app purchase that unlocks all 15 distributions and their related derivations and proofs, and removes banner ads. There is no subscription. Restore purchases is available. Available in Japanese and English. No app account or login is required.