# Expected value

From AMS Glossary

## expected value

(

*Also called*expectation, mathematical expectation.) The arithmetic mean of a random variable, conceptually similar to the simple average but broader in scope.If or, if This reduces to the mean of

*g*(*x*) is a continuous function of*x*, then the expected value of*g*(*x*), denoted by*E*[*g*(*x*)], is the integral (or sum, if*x*is discrete) of*g*(*x*) times the probability element of*x*. Thus, if*x*is continuous with probability density function*f*(*x*) defined in the range*a*<*x*<*b*, then*x*is discrete with possible values*x*_{1},*x*_{2}, . . .,*x*_{n}and probability function*f*(*x*_{i}), then*x*itself in the case*g*(*x*) =*x*.