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Expected value calculator

Enter possible outcomes and matching probabilities or weights. The calculator normalizes them automatically.

Expected value E(X): —

Fill in the fields above — the result is computed on this page.

Outcomes
—
Weight total
—
Variance
—
Standard deviation
—
Smallest outcome
—
Largest outcome
—

Expected value components

Row Outcome x Weight p x · p
Fill in the fields above — the result is computed on this page.
What do these numbers mean?
  • E(X) is the sum of each outcome times its probability.
  • Variance describes spread around E(X).

The result requires a complete, accurate list of outcomes and weights. Unknown probabilities should not be guessed.

How do I use this page?
  1. Enter outcomes in the first field.
  2. Enter matching weights in the same order.
  3. Review the x·p table and total.

What this page does not do: The result requires a complete, accurate list of outcomes and weights. Unknown probabilities should not be guessed.

Further reading

Theory — what does expected value mean?

Expected value is the average outcome of a random model over very many repetitions, not a promise about any single trial. The calculator lets you enter possible outcomes with matching probabilities or weights, which do not need to sum to one — it divides each weight by their total. Weights must be non-negative and their sum positive, otherwise normalization makes no sense. A negative expected value indicates an average loss over the long run, not a certain loss in one trial.

Frequently asked questions

Must the weights sum to 1?
No. They are normalized automatically, but they cannot be negative and their total must be positive.
Is expected value the most likely result?
No. It may not even be one of the possible outcomes.

See also

← All calculators

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