I ran into this problem:

Suppose , obtain the pdf for .

Because of the nasty square root, I can't seem to find the appropriate transformation functions for a change of variables. I tried letting and looking for the joint pdf of and , but the function is not 1-1. Since is a standard cauchy, I've also tried breaking into: for for for , but that doesn't help much.

What am I supposed to do when I see this type of questions? I need some hints.