A colleague of your proposes that a certain pair of random variables be modeled with a joint CDF of the form
Fx, y (x,y) = [1 – ae–x – be–y +ce–(x+y)] u (x) u (y).
(a) Find any restrictions on the constants a, b, and c needed for this to be a valid joint CDF.
(b) Find the marginal CDFs, and under the restrictions found in part (a).