The expected value of the product of two random variables is equal to the product of the expected value, assuming that the variables are independent.

** Statement**: If the two variables X and Y are independent we have that the expectation of XY is equal to the product of the expectation of X and the expectation of Y.

**E(XY) = E(X) E(Y) assuming that X and Y are independent.**

** Proof**: We have the formula for covariance given as,

Cov(X,Y) = E(XY) – E(X) E(Y).

Since X and Y are independent we have that Cov(X, Y) = 0.

Substituting Cov(X, Y) = 0 in the above formula we get that,

E(XY) = E(X) E(Y).