Expected Value Calculator
Compute the expected value E(X), variance, and standard deviation of a discrete distribution.
How it works
- 1Enter outcome values (e.g. 10, 20, 30) and their associated probabilities or weights in the two fields.
- 2Probabilities are normalized to sum to 1, so you can supply raw weights (e.g. 2, 3, 5) instead of fractions.
- 3The calculator returns E(X) = Σ xᵢpᵢ, Var(X) = Σ pᵢ(xᵢ − μ)², and σ = √Var(X).
Use cases
- Decision analysis: weigh financial payoffs by their likelihoods to find the most rational choice.
- Game theory: determine the fair price of a lottery or gamble from its outcomes and odds.
- Statistics coursework: verify hand-calculated E(X) and σ for discrete distributions.
Frequently asked questions
Do my probabilities have to sum to 1?
No. The calculator normalizes whatever weights you enter, so values like 2, 3, 5 are treated the same as 0.2, 0.3, 0.5.
What if the two lists have different lengths?
The result displays — because both lists must be the same length for the calculation to be defined.
Variance vs standard deviation?
Both measure spread around E(X). Variance is in squared units; standard deviation σ = √Var(X) is in the same units as the values, making it easier to interpret.
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