Expected Value of Identically distributed random variables I have a very quick question regarding the expected value of two random variables $X,Y$ that are identically distributed and not necessarly independent.
Is this equation valid?
$E[XY]=E[X^2]$
If this is not true, why is this? and what relations can I get (regarding expected value, variance and covariance) when two random variables are identically distributed? 

By definition:
$$cov(X, Y) = E(X-EX)(Y-EY) = EXY - (EX)(EY).$$
If $X, Y$ are independent, then $cov(X, Y) = 0,$
so that
$EXY = (EX)(EY).$
