If X and Y are random variables, what is the meaning of E(XY) ?
Theorem 2 (Expectation and Independence) Let X and Y be independent random variables.
Then, the two random variables are mean independent, which is defined as,
E(XY ) = E(X)E(Y ).
More generally, E[g(X)h(Y )] = E[g(X)]E[h(Y )] holds for any function g and h.
That is, the independence of two random variables implies that both the covariance and correlation
are zero. But, the converse is not true. Interestingly, it turns out that this result helps us prove
a more general result, which is that the functions of two independent random variables are also