We know X and Y are iid distributed e^-x.

I am having trouble finding the joint pdf of Min(X,Y)/Max(X,Y).

I have already found the pdf of the min(x,y) and Max(x,y), I know that I cannot use convolutions or assume that the min(x,y) and Max(x,y) are independent. Would I need to find the Jacobian of Min(x,y) , Max(x,y) vs. X and y or is there some other method I am missing.