Multiplication Rule For Expected Value

Independence for Random Variables:

Two random variables X and Y are independent if and only if P(X, Y) = P(X)P(Y).

Independence is a stronger property than uncorrelatedness because correlation addresses only linear relationships.

Multiplication Rule for expected value of the product of uncorrelated random variables.

If X and Y are uncorrelated: E(XY) = E(X)E(Y)