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Formula verified · Deterministic calculation

Expected Value Calculator

Enter equal-length outcome and probability lists whose probabilities sum to 1 to calculate the probability-weighted expected outcome.

Expected value7.5
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Result methodology

Deterministic calculation using the displayed formula and supplied inputs.

Solution steps
  1. Σp = 1
  2. E(X) = Σx·p(x) = 7.5

How this calculator works

E(X)=Σx·p(x).

Formula

E(X)=Σx·p(x)

Computes the probability-weighted average outcome.

Worked example

Expected value is a verified test case used by the calculation engine.

Assumptions and limitations

  • Outcomes and probabilities have equal length.
  • Probabilities are between 0 and 1 and sum to 1.
  • The model represents a discrete probability distribution.

Methodology & sources

This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint.

  • CalcuMint deterministic statistics engine

Frequently asked questions

What is expected value?

It is the probability-weighted average of the possible outcomes.

Must probabilities sum to 1?

Yes. This calculator requires a valid discrete probability distribution.

Related calculators

Probability CalculatorCombine two event probabilities under an explicit independence assumption.Bayes Theorem CalculatorCalculate a posterior probability from a prior and conditional likelihoods.Weighted Mean CalculatorCalculate a weighted mean from values and positive weights.