Let $X, Y$ be independent uniform in $[−1, 1]$. Find the covariance between $U = \min(X, Y )$ and $V = \max(X, Y )$
I know that $\operatorname{Cov}(U,V)= E\left(UV\right) - EUEV$ and I know how to calculate $EU$ and $EV$. However, I'm not sure how to calculate $E\left(UV\right)$. Since we have only two variables in this case, is it correct to reason that $UV = XY$, since if one of $X,Y$ is the max then the other is the min?