Expected Value Calculator

Your details

The possible values the random variable can take, separated by commas (e.g. payouts, dice faces, returns).
The probability of each outcome, in the same order. Enter decimals (0.25) or percentages (25). Should sum to 1.
Toggle on to also compute Var(X) and the standard deviation sigma(X).
Expected value E[X]Probabilities sum to 1
0.5
Variance Var(X)27.25
Standard deviation sigma(X)5.2202
Probability total1
Outcomes used3
Expected value E[X]0.5
Std deviation sigma(X)5.2202

E[X] = 0.5, sigma = 5.2202.

  • Across many repetitions each trial averages 0.5, that long-run average is what "expected value" means, even if no single outcome equals it.
  • The expected value is positive, so over the long run outcomes drift in that direction.
  • The standard deviation is 5.2202, meaning roughly two-thirds of outcomes (in a symmetric distribution) fall within 0 to 5.7202. Variance is 27.25.
  • Your probabilities sum to 1, so this is a complete, valid probability distribution and the results are reliable.

Next stepAdjust an outcome or its probability to see how the expected value and spread change.

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