ExpectedValue

ExpectedValue[f, list]
gives the expected value of the pure function f with respect to the values in list.

ExpectedValue[f, list, x]
gives the expected value of the function f of x with respect to the values of list.

ExpectedValue[f, dist]
gives the expected value of the pure function f with respect to the symbolic distribution dist.

ExpectedValue[f, dist, x]
gives the expected value of the function f of x with respect to the symbolic distribution dist.

For a continuous distribution dist, the expected value of f is given by where is the probability density function of dist and the integral is taken over the domain of dist.

For a discrete distribution dist, the expected value of f is given by where is the probability mass function of dist and summation is over the domain of dist.