Question: The random vector ((X, Y)) has the joint probability density [f_{X, Y}(x, y)=frac{1}{2} e^{-x}, quad 0 leq x, 0 leq y leq 2] (1) Determine

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

\[f_{X, Y}(x, y)=\frac{1}{2} e^{-x}, \quad 0 \leq x, 0 \leq y \leq 2\]

(1) Determine the marginal densities and the mean values \(E(X)\) and \(E(Y)\).

(2) Determine the conditional densities \(f_{X}(x \mid y)\) and \(f_{Y}(y \mid x)\). Are \(X\) and \(Y\) independent?

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