If X and Y are two independent random variables, then $\displaystyle E[X]E[Y] = E[XY]$. The converse is not true in general, because there are examples of two random variables where this equality holds but they are dependent, however, in all the examples I've seen, $\displaystyle E[XY] = 0$, so I feel like this is kind of a "fluke". Can anyone give an example of two dependent random variables such that $\displaystyle E[X]E[Y] = E[XY] \neq 0$?