- Example 5: Project managers often use a method labeled PERT - for program evaluation and review technique to coordinate the various activities making up a large project (One successful application was in the construction of the Apollo spacecraft). A standard assumption in PERT analysis is that the time necessary to complete any particular activity one it has been started has a beta distribution with A = the optimistic time (everything goes well) and B = the pessimistic time (if everything goes badly). Suppose that in constructing a single-family house, the time X (in days) necessary for laying the foundation has a beta distribution with A = 2, B = 5, = 2, and = 3. B a) Find the probability that it takes at most 3 days to lay the foundation. b) Find the expected number of days it takes to lay the foundation.