Expectation_Operator

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Averaging across a probability distribution is so common in [[Statistics]] that a special notation has been developed to denote it. This is the '''Expectation Operator'''. The formal definition of the expectation of a function g applied to a random variable X is given by (for a [[Continuous Random Variable]])

*EX[g(x)] = INTEGRAL g(x) dF(x) where dF indicates the probability element at x and the region of integration includes all values of the variable with non-zero probability density.

In the case of discrete random variables, we have

*EX[g(x)] = SUM g(x) p(x) where p(x) is the probability distribution of the random variable X.
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[[Dick Beldin]]