\(X\) and \(Y\) are jointly absolutely continuous with joint density

\[ f_{XY}(x,\, y) = \frac{1}{8} (y^2-x^2) e^{-y} ,\quad y>0 ;\, -y<x<y. \]

1. Sketch \(\textrm{Range}(X,\, Y)\).
2. Compute the marginal density of \(X\).
3. Compute the marginal density of \(Y\).
4. Compute the conditional density of \(X\) given \(Y = y\).
5. Compute the conditional density of \(Y\) given \(X = x\).