# expected value

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## expected value

[ek′spek·təd ′val·yü] (mathematics)

For a random variable

*x*with probability density function ƒ(*x*), this is the integral from -∞ to ∞ of*xƒ*(*x*)*dx*. Also known as expectation.For a random variable

*x*on a probability space (Ω,*P*), the integral of*x*with respect to the probability measure*P*. (systems engineering)

In decision theory, a measure of the value or utility expected to result from a given strategy, equal to the sum over states of nature of the product of the probability of the state times the consequence or outcome of the strategy in terms of some value or utility parameter. Abbreviated EV. Also known as expected utility (EU).

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