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 randomvariable, Xk, in this situation can be estimated by E(Xk) = (1/6)(H+4M+L) and V(Xk) = [(HL)/6]2. The randomvariables, Xk , are assumed to be statisticallyindependent, and the applicable MARR=18% per year.

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, X, in this situation can be estimated by E(X,) = (1/6)(H + 4M + L) and V(X,) = [(H-L)/6]". The random variables, X, , are assumed to be statistically independent, and the applicable MARR = 18% per year. Click the icon to view the estimated net cash-flow data for one alternative associated with a project. Click the icon to view the interest and annuity table for discrete compounding when the MARR is 18% per year. Click the icon to view the normal probability table for z 2 0. Click the icon to view the normal probability table for z = 0. a. What are the mean and variance of the PW? E(PW) =$ (Round to the nearest dollar.) V(PW) = ($)2 million (Round to three decimal places.) b. What is the probability that PW 2 0? Assume that the PW of the net cash flow is a normally distributed random variable with u = E(PW) and of = V(PW). The probability that PW 2 0 is . (Round to four decimal places.) c. Is this the same as the probability that the IRR is acceptable? This the same as the probability that the IRR is acceptable.\fDiscrete Compounding; i =18% Single Payment Uniform Series Compound Compound Sinking Capital Amount Present Amount Present Fund Recovery Factor Worth Factor Factor Worth Factor Factor Factor To Find F To Find P To Find F To Find P To Find A To Find A Given P Given F Given A Given A Given F Given P FIP PIF FIA PIA AIF AIP 1.1800 0.8475 1.0000 0.8475 1.0000 1.1800 1.3924 0.7182 2.1800 1.5656 0.4587 0.6387 G A U N - 2 1.6430 0.6086 3.5724 2.1743 0.2799 0.4599 1.9388 0.5158 5.2154 2.6901 0. 1917 0.3717 2.2878 0.4371 7.1542 3.1272 0.1398 0.3198