Expected value

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In probability theory, the expected value (also called expectation, mean, or first moment) is a generalization of the weighted average. Provided that it is finite, the expected value can be interpreted as the long-run average of results from independent repetitions of the same random experiment, as formalized by the law of large numbers. For a random variable that takes finitely many values, the expected value is the weighted average of those values, with their probabilities as weights. More generally, it is the Lebesgue integral of the random variable with respect to the underlying probability measure. The expected value of a random variable X is often denoted by E ( X ) {\displaystyle {\text{E}}(X)} , E [ X ] {\displaystyle {\text{E}}[X]} , or E X...

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