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?