A practice trainer for expectation and variance: each round shows a small random distribution or two named random quantities, then asks for the average, the variance via the shortcut in two steps, or the average and variance of a sum — where some rounds hide how the pieces depend on each other, so the variance genuinely cannot be determined. Type a fraction (any equivalent form counts) or use the can't-tell button, get a worked contribution table either way, and generate fresh numbers to try again.

Every value × its chance; then the shortcut; then sums — and the fine print. Fresh numbers each round.