Two random variables X and Y have the joint probability density function fXY (x,y) = 12(x,y) + 38(x 1,y 0) + 18(x 0,y 1) (Notation: (x,y) is a delta function at x=0,y=0. Ingeneral,(xa,yb)isadeltafunctionatx=a,y=b.

(a) (5 points) Sketch and accurately label the joint pdf fXY (x,y).

(b) (10 points) Find, sketch and accurately and completely label the probability density function of Z, where Z = X + Y .

(c) (5 points) Find, sketch and accurately and completely label the probability density function of Z, where Z = X Y .