Expected value of uniformly distributed random variables

Question

I have to compute $\text{Var}(\min(X,Y) \max(X,Y))$, where $X$ and $Y$ have uniform distribution on $[0,1]$. I calculated $E(\min(X, Y))$ and $E(\max(X, Y))$, but I do not know how to calculate $E(\min(X, Y) \cdot \max(X, Y))$.

Thanks in advance.

Answer 1

Hint: $(\min (x,y))(\max (x,y))=xy$ for all real numbers $x$ and $y$. So you only have to find $E(XY)$