Question: The random vector ((X, Y)) has the joint density [f_{X, Y}(x, y)=2 e^{-(x+y)} text { for } 0 leq x leq y

The random vector \((X, Y)\) has the joint density

\[f_{X, Y}(x, y)=2 e^{-(x+y)} \text { for } 0 \leq x \leq y<\infty\]

Determine the densities of \(Z=\max (X, Y)\) and \(Z=\min (X, Y)\).

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