Let $$ and $$ have the joint density function $(,)=\frac 1{x^2y^2}$. Let $U=4xy$, $v = \frac {2x}y$. Find $f(u,v)$. Find the marginal density of $v$. Your answer should be piecewise defined.
I found $f(u,v) = \frac 2{u^2v}$, which was correct. I'm struggling to find the marginal density of $v$. I integrated $f(u,v)$ in terms of $u$ from 4 to infinity (bounds on $u$) and found $f(v) = \frac 1{2v}$. This was not correct, and not sure how to work with the piecewise part. How to continue?