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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?

  1. $Z$ and $W$ are independent
  2. $E(X Z)=E(Y W)$
  3. $E(X Y)=E(Z W)$
  4. $(a), (b)$, and $(c)$
  5. $(a)$ and $(b)$ only
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