Wikipedia 10K Redux

Reconstructed by Reagle from Starling archive; see blog post for context.

Expectation_Operator

back to Statistics/Theory

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.


Dick Beldin