In the Program Evaluation and Review Technique (PERT). we are interested in the total time t of a large number of subprojects. For illustration, let X., X2 , X 3 be three independent random times for three subprojects. If these subprojects are in series (the first one must be completed before the second starts, etc.), then we are interested in the sum Y = X , + X 2 + X 3 • If these are in parallel (can be worked on simultaneously), then we are interested in Z = max (X , , X 2 , X3). In the case each of these random variables has the uniform distribution with p.d.f. J{ x) = 1, 0 x 1, zero elsewhere, find (a) the p.d.f. of Y and (b) the p.d.f. of Z.