Drawing pictures is very helpful here; since f (x, y) =1, integrals involving the joint pdf can be interpreted as areas.

19. Suppose X and Y have the joint density function f (x, y) = 1 over the square region 0 5x 5 1, 0 5y 5 1. Determine the p.d.f. of: X (a)Z=X+Y (b) Z=|XY| (c) Z=XY (d) 2:? [Hintz In parts (a) and (b), you need not integrate to find P(Z 5 2) because the desired probability is the area of a region that can be found by simple geometric formulas. In part (c), it is easier to rst nd P(Z > z), but you will need to integrate. For part (d), you'll have to split it into two cases; the answer is very strange]