Let \( (X,Y)\) have joint density \(f(x,y) = e^{-y}\), for \(0<x<y\), and \(f(x,y)=0\) elsewhere.

1. Are \(X\) and \(Y\) independent ?
2. Compute the marginal density of \(Y\).
3. Show that \(f_{X|Y}(x,y)=\frac1y \), for \(0<x<y\).
4. Compute \(E(X|Y=y)\)
5. Use the previous result to find \(E(X)\).