In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a large number of independently selected outcomes of a random variable.

The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration.

The expected value of a random variable X is often denoted by E(X), E[X], or EX, with E also often stylized as E or ${\displaystyle \mathbb {E} .}$[1][2][3]