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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 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 to 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

Expected value is the model average over a very large number of repetitions, not a promise for one trial. Weights need not sum to 1 because the calculator divides each by their total.

A negative expected value means an average long-run loss; a positive value does not remove single-outcome risk.

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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