In probability theory, the expected value (also called expectation, expectancy,
expectation operator, 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.
Since it is obtained through arithmetic, the expected value sometimes may not even be included in
the sample data set; it is not the value you would “expect” to get in reality. 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.
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