I am having trouble finding the joint distribution of the following.
Joint distribution of $Y_1=X_1/X_2, \quad Y_2=X_2$ when $h(x_1,x_2) = 8x_1x_2$ when $0 < X_1 < X_2 < 1$.
I think I am having trouble with the support for the Ys.
I am thinking that the joint pdf itself is $$f(y_1,y_2)=8y_1y_2^3$$
and I am confident that $0 < Y_1 < 1$.
However, I am having trouble with the region where $Y_2$ should be.
So far I know that $$0 < Y_1Y_2 < Y_2 < 1$$
but I am not sure how to manipulate this to isolate $Y_2$.
My ultimate goal is to find the marginal distributio of $Y_2$, but I am stuck.
I would really appreciate your input.