2. (9.11) Consider the project network of Problem 1 again. We now recognized that the activity times are subject to uncertainty or random variation. The optimistic (a), mostly likely ( m), and pessimistic (b) estimates for the activity times are as follows. - Disregard the activity times in Problem 1. We assume beta distributions for the activity times. (a) Compute the expected values () and variances (2) of the activity times. (b) Assuming the expected values, we computed the minimum completion time, the critical path and the slack times again. The critical path was identified as 2-6-9-11-12, which is the same as the one in Problem 1. (c) Compute the expected value and the standard deviation ( ) of the project completion time. - EXCEL will be helpful for your computation. (d) Compute the probability that the project completion time exceeds 50 weeks by using PERT method. Assume a normal distribution of the project completion time. (e) Suppose that you simulate the project network many times by randomly generating the activity times from the beta distributions. Will the critical path be always the same as 2-6-9-11-12 for each project instance with newly sampled activity times? Explain the reason shortly. (f) We assumed a normal distribution in (d). Why do we assume such a normal distribution for the project completion time? Justify it