This is online homework, and I'm not always clear on which chapter questions are from, so I might be completely off base.
I have two random variables, $X_1$~UNI(5,10) and $X_2$~UNI(4,10), and then two variables that are functions of those, Y=$\frac{X_1}{X_2}$ and Z=${X_1}{X_2}$. I need to find the joint density of Y and Z on their support.
Solving for $X_1$ and $X_2$ in term of Y and Z gives me $X_1$=$\sqrt{YZ}$ and $X_2$=$\sqrt{Z/Y}$. Solving for the Jacobian, I get $\frac{\sqrt{Z/Y}}{2\sqrt{YZ}}$ (simplified from $\frac{Y \sqrt{\frac{Z}{Y}}}{4 Y \sqrt{Y Z}}+\frac{Z \sqrt{\frac{Z}{Y}}}{4 Z \sqrt{Y Z}}$). I know f($X_1,Y_1$)=1 over their support, and it would be nice if f(Y,Z) were just 1 times the Jacobian, but I think I need to address the support of Y and Z?
Thanks.
Actually, I don't need the support of Y and Z at all. "f($X_1,X_2$)=1 over their support" means that f($X_1,X_2$)=$\frac{1}{(10-4)(1-5)}$=$\frac{1}{30}$, so f(Y,Z)=$\frac{\sqrt{Z/Y}}{2\sqrt{YZ}}$*$\frac{1}{30}$=$\frac{\sqrt{Z/Y}}{60\sqrt{YZ}}$
Thank you, @Tunk-Fey for the help.