Let $X$ and $Y$ be two independent and identically distributed random variables. Let $Z=\max (X, Y)$ and $W=\min (X, Y)$. Which of the following is true?

- $Z$ and $W$ are independent
- $E(X Z)=E(Y W)$
- $E(X Y)=E(Z W)$
- $(a), (b)$, and $(c)$
- $(a)$ and $(b)$ only