Let $X$ and $Y$ have the joint density function $$f(x,y) = \frac1{x^2 y^2},$$ $x\ge 1$, $y\ge 1$. Let $U = 4 X Y$ and $V = 2 X / Y$.

(a) What is the joint density function of $U$,$V$?
$f_{U,V}(u,v) =$

(b) On what domain is this defined?
$u \ge$ and
$\le v \le$