The use of three estimates (defined here as H = high, L = low, and M = most likely) for random variables is a practical technique for modeling uncertainty in some engineering economy studies. Assume that the mean and variance of the random variable, Xk, in this situation can be estimated by E(Xk) = (1/6)(H + 4M + L) and V(Xk) = [(H - L)/6]2. The estimated net cash-flow data for one alternative associated with a project are shown in Table PI 2-17.

The random variables, Xk, are assumed to be statistically independent, and the applicable MARR = 15% per year. Based on this information,
a. What are the mean and variance of the PW?
b. What is the probability that PW > 0 (state any assumptions that you make)?
c. Is this the same as the probability that the IRR is acceptable? Explain.

TABLE P12-17 Estimates for Problem 12-17 Three-Point Estimates for Xk End of Year, k Net Cash Flow 538,000 $41,000 -2,200 10,600 6,100 4,800 17,300 -1,900 9,800 5,600 4,600 16,500 $45,000 -2,550 11,400 6,400 5,100 18,300 F3 4X3