If $X$ and $Y$ are independent and identically distributed exponential variables with parameter $\lambda = 2$, compute each of the following joint densities.

(a) $U = 4 X + Y$, $V = X / Y$.
$f_{U,V}(u,v) =$

(b) $U = 4 X + Y$, $V = 2 X/(X + Y)$.
$f_{U,V}(u,v) =$