Program Evaluation

In the Program Evaluation and Review Technique (PERT), we are interested in the total time to complete a project that is comprised of a large number of subprojects. For illustration, let  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  If these are in parallel (can be worked on simultaneously), then we are interested in Z = max(). In the case each of these random variables has the uniform distribution with pdf , zero elsewhere, find (a) the pdf of Y and (b) the pdf of Z.