# Compute E(X^3) when X~(μ, σ^2)

Got stuck on an intermediate step in a larger problem. We are given X~(μ, σ^2), i.e. X is a random variable with standard normal distribution, and that Y=X^2. The question then asks to compute Cov(X,Y):

Cov(X,Y) = Cov(X,X^2) = E(X^3) - E(X)E(X^2) = E(X^3) - (μ)(μ^2 + σ^2)

I can't go any further however, because I don't know what E(X^3) is! I computed the last term using the variance equation and re-arranging, but I can't use that same trick.

Last edited:

Stephen Tashi