Expected Value Calculator
E[X] and Var(X) for any discrete distribution you define — values plus their probabilities.
Probabilities must be ≥ 0 and add up to 1. Example: a game paying $0/$1/$5/$10.
① Answer
② Steps
③ Why it works
Expected value is the long-run average: weight each outcome by its probability and add, E[X] = Σx·P(x). It is not the “most likely” value — it’s where the distribution balances. Variance Σ(x−μ)²P(x) measures the typical squared distance from that balance point, i.e. the risk.