12-17. The use of three estimates (defined here as H =

high, L = low, andM = 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 P12-17.

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. (12.5)