Exercise 2. (Joint PDF) (25pt) . Let the joint pdf for (X, Y) be given by 2 0

Exercise 2. (Joint PDF) (25pt) . Let the joint pdf for (X, Y) be given by {0 .fxy@, y) = otherwise (a) Sketch on the (:r, y)-plane the region on which y) IS positive. (b) Find the probability of (X, Y) e A where A = : O y 1/2}. (Start by describing the set A. Justify every step) (c) Find the marginal pdf of X. (Keep in mind that the value of pdf must be specified for all (00, oc).) 1