This is a problem from a book, I am working on this to prepare for an exam.
If $X$ and $Y$ be independent random variables with an exponential distribution with parameters $u$ and $D$. Let
$U=\min\{X,Y\},\quad V=\max\{X,Y\},\quad W=V-U.$
Prove that $U$ and $W$ are independent.
I am not even able to proceed on this one. The hint given is to remove $\max$ and $\min$ out of equation by using this formula. If $E_1 = \{X\leq Y\}\quad \text{and}\quad E_2=\{Y\leq X\}$ then $P(A) = P(A \cap E1) + P (A \cap E2).$