
Joint Density
(X,Y) has density 3x^2 + 1/2 on [0,1]x[0,1].
I need to compute the joint density of Y and Z where Z = XY.
I tried substituting X = Z/Y into the (X,Y) but that didn't work...My next guess is to just multiply X*Y together, to get the density of Z. I'm lacking a formula to put that into to find the joint distribution of Z and Y, so maybe that isn't right.
Some direction would be appreciated.

Re: Joint Density
Try to find the joint distribution F(y,z), after that take derivatives to find f(y,z)

Re: Joint Density
I'm not sure what you mean?

Re: Joint Density
First try to find F(y,z) = Pr(Y<=y,Z<=z) making a graph

Re: Joint Density
f(x,y) = 3x^2 + 1/2
Z = XY
Use transformation of variable technique

Re: Joint Density