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Let $X$ and $Y$ be two zero mean independent continuous random variables. Let $Z_{1}=\max (X, Y)$, and $Z_{2}=\min (X, Y)$. Then which of the following is TRUE.

  1. $Z_{1}$ and $Z_{2}$ are uncorrelated.
  2. $Z_{1}$ and $Z_{2}$ are independent.
  3. $P\left(Z_{1}=Z_{2}\right)=\frac{1}{2}$.
  4. Both $(a)$ and $(c)$
  5. Both $(a)$ and $(b)$

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