Statistics & Probability
Intermediate

Expected Value

The long-run average value of a random variable.

Formula

E[X]=∑ixi piE[X] = \sum_i x_i\,p_i

Variables

x_iOutcomes
p_iProbabilities

Example

A fair die: E[X] = (1+2+3+4+5+6)/6 = 3.5.

Did You Know?

Expected value is the long-run average — and it's why the house always wins in the long run.

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