Could anyone help me with this question please?
Given X and Y are continuous random variables with the following joint probability density function:
i) Obtain the joint probability density function of X and Y − X.
ii) Show that X and Y − X are independent random variables and write down their (marginal)
probability density functions. Identify these distributions
For part (i)
I let U = X and Y = V - X,
My Jacobian value was 1,
and then I got Is this the correct joint p.d.f for X and Y-X?
Also for the marginal of X, I got but I'm not quite sure.