I've got two random variables, $x$ and $y$, where $x=u(y)$ and $y=v(x)$. How do I find the joint density of the two variables?
The eventual purpose is to find the integral
$\int^a\int^b f(x,y) dydx$,
where $f(.)$ is said joint density function.
This question is related (the joint distribution of dependent random variables) but I'm still a bit confused by the answer. I am indeed effectively looking for $Prob(x \leq a, y \leq b)$ but don't understand how I can get there without knowing the PDF first.
Any advice is much appreciated. Thanks a lot in advance!