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Expected value

The expected value is the weighted average of the values, where the weights are the probabilities. For a fair die every outcome is equally likely, so the expectation is the ordinary average of the faces. It need not be an outcome you can get. Over many rolls the average approaches the expectation. That is the law of large numbers, not a promise about the next roll.

Symbols

Example

One fair die: $E(X) = \dfrac{1 + 2 + 3 + 4 + 5 + 6}{6} = 3.5$.

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Part of Mathematics S2: Probability distributions.