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Expected Value Calculator

Expected value, variance and standard deviation of a discrete random variable from outcomes and probabilities.

Enter values

Separate values with commas, spaces or new lines.

Separate values with commas, spaces or new lines.

Results update as you type.

Result

Expected value

10

Variance
1,080
Standard deviation
32.86335345
Step-by-stepShow
  1. E[X] = 100×0.1 + 20×0.3 + -10×0.6 = 10

About the Expected Value Calculator

Expected value, variance and standard deviation of a discrete random variable from outcomes and probabilities.

Also known as: ev calculator, mean of random variable, expected return, expectation calculator.

How to use this calculator

  1. Enter outcomes (payoffs), probabilities.
  2. The result updates instantly as you type — press Calculate (or Enter) at any time.
  3. Open “Step-by-step” to see how the answer was worked out.
  4. Use Copy result or Share to save the answer or send a link with your inputs.

Formula

E[X] = Σ xᵢ·pᵢ

Worked example

Using the values pre-filled in the calculator above:

  • Outcomes (payoffs): 100, 20, -10
  • Probabilities: 0.1, 0.3, 0.6

the calculator returns:

  • Expected value: 10
  • Variance: 1,080
  • Standard deviation: 32.86335345

Working

  1. E[X] = 100×0.1 + 20×0.3 + -10×0.6 = 10