Mathematical Expectation
If X denotes a discrete random variable which can assume the values x1, x2, ..., xn with respective probabilities p1, p2, ..., pn then the mathematical expectation of X, denoted by E(X) is defined by
The mathematical Expectation E(X) of a random variable is simply the arithmetic mean.
Result
If ϕ(X) is a function of the random variable X,
then E[ϕ(X)] = ∑ P(X = x) ϕ(x)