What does expected value mean in simple terms?

Expected value is the long-run average outcome you'd expect if you repeated an experiment many times. For example, if you flip a fair coin betting $1, the expected value is $0 because you'd win and lose equally over time.

Why do my probabilities need to sum to 1?

Probabilities summing to 1 means you've accounted for all possible outcomes. If they don't sum to 1, your model is incomplete — either some outcomes are missing or probabilities are incorrect. The calculator will warn you if this happens.

What is the relationship between variance and standard deviation?

Standard deviation is the square root of variance. Both measure the spread of outcomes around the expected value, but standard deviation is in the same units as the original values, making it easier to interpret practically.

Expected Value Calculator

Calculate expected value E[X], variance, and standard deviation from outcomes and probabilities. Perfect for probability theory, gambling analysis, investment decisions, and risk assessment with detailed outcome breakdown tables.

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Sample Scenarios

Try these sample scenarios to test the calculator

Outcomes & Probabilities

Enter value-probability pairs. Probabilities should sum to 1.

Value (x)Probability P(x)

How it works: Enter each possible outcome value and its probability. The expected value E[X] = Σ x·P(x) represents the long-run average. Variance and standard deviation measure the spread of outcomes around the expected value.

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