Before I begin, here is the question: If the PDF of two independent random variables X and Y are: f(x) = exp(-x)u(x) f(y) = exp(-y)u(y) Determine the join probability density function (JPDF) of Z&W defined by: Z = X+Y W = X/(X+Y). So, I know how to solve this except for one thing. How do I get the expression for Z and W. For Z do I literally just add f(x) + f(y) meaning z = exp(-x) + exp(-y) for (x,y) >0? Same with W? Once I get the expressions I just find fxy(x,y) and divide by the determinant of the Jacobian. The problem is that the Jacobian depends on the derivative of Z and W which I do not know how to get an expression for. Please help.