we have the joint PDF of two RVs $X$ and $Y.$ we also have two RVs $U = f(X,Y)$ and $V = g(X,Y),$ where $f$ and $g$ are two variable functions. How can I calculate the joint PDF of $U$ and $V$? for example: $U = X^2-Y^2$ and $V = XY.$

  • $\begingroup$ This is the kind of question where reading your textbook to see what it says about solving such problems is more useful than asking on this forum. Heck. the book might even use $X^2+Y^2$ and $XY$ in its illustration of the method. $\endgroup$ – Dilip Sarwate Nov 8 at 20:07
  • $\begingroup$ @DilipSarwate No, it's related to something else that requires this as one of its steps. and also the book does not mention anything about it and the functions are just my example nothing else. I just want to understand the process, so if I get anything like it, I am able to solve it. $\endgroup$ – Hossein Shahbodaghkhan Nov 9 at 8:04

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