Expected Value & Variance
Calculate the expected value, variance and standard deviation of a discrete random variable from its outcomes and probabilities, free online.
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E[X] = Σ x·P(x), Var(X) = Σ (x − E[X])²·P(x) and SD = √Var. List each outcome as "value: probability", with probabilities as decimals (0.25) or percentages that sum to 100. Handy for games, bets, insurance and decision analysis.