Chance 0.139292024 0.139292024 0.0% 0.259181779 0.0% 0.08 10800 0.329679954 0.0% 0.1 11000 0.39346934 0.0% 0.01 10100 0.048770575 0.0% 0.09 10900 0.362371848 0.0% 0.17 11700 0.572585068 0.0% 42522 10350 0.160542979 10.0% 42530 10750 100.0% 3% Gaurantee 10300 0.06 10600 Risk-Free -10000 0.312710721 5.0% 42538 11150 0.437295131 10.0% 42583 10450 0.201483781 25.0% 42591 10850 0.346230215 5.0% 42599 11250 0.464738571 20.0% 42644 10550 0.240427877 10.0% 42652 10950 0.378114944 5.0% 42660 11350 0.490843579 10.0% 25.0% Safe -10000 Chance 0.328002757 50.0% 25.0% 45.0% Risky -10000 Chance 0.305336563 Decision 0.32808241 15.0% 40.0% 10.0% 5.0% 10.0% 25.0% Safe & Risky -10000 Chance 0.32808241 5.0% 20.0% 10.0% 5.0% 10.0% Homework 7 (due Apr. 13th by the beginning of the class) Please type your answers in a Excel or Word le, labeled by your last name. Please submit your le to Canvas. Problem 1 An aircraft emergency locator transmitter (ELT) is a device designed to transmit a signal in the case of a crash. Company A makes 80% of the ELTs, company B makes 15% of them, and company C makes the other 5%. The ELTs made by A have a 4% rate of defects, B's ELTs have a 6% rate of defects, and C's ELTs have a 9% rate of defects. If a randomly selected ELT is tested and is found to be defective, nd the probability that it was made by company A. Problem 2 Consider an investor with $10,000 available to invest. He has the following options regarding the allocation of his available funds: (1) he can invest in a risk-free savings account with a guaranteed 3% annual rate of return; (2) he can invest in a fairly safe stock, where the possible annual rates of return are 6%, 8%, or 10%; or (3) he can invest in a more risky stock, where the possible annual rates of return are 1%, 9%, or 17%. Note that the investor can place all of his available funds in any one of these options, or he can split his $10,000 into two $5,000 investments in any two of these options. The joint probability distribution of the possible return rates for the two stocks is given in the table below. Risky stock return: R Safe stock return: S R=1% R=9% R=17% S=6% 0.1 0.05 0.1 S=8% 0.25 0.05 0.2 S=10% 0.1 0.05 0.1 a) Use PrecisionTree to identify the strategy that maximizes the investor's expected wealth in one year from the given investment opportunities. b) Let the investor's utility function be U (x) = 1 ex/2000 . Find the decision that maximizes the investor's expected utility. 1 Chance 300 300 0.0% 600 0.0% 0.08 10800 800 0.0% 0.1 11000 1000 0.0% 0.01 10100 100 45.0% 0.09 10900 900 15.0% 0.17 11700 1700 40.0% 42522 10350 350 0.0% 42530 10750 100.0% 3% Gaurantee 10300 0.06 10600 Risk-Free -10000 750 0.0% 42538 11150 1150 0.0% 42583 10450 450 0.0% 42591 10850 850 0.0% 42599 11250 1250 0.0% 42644 10550 550 0.0% 42652 10950 950 0.0% 42660 11350 1350 0.0% 25.0% Safe -10000 Chance 800 50.0% 25.0% 45.0% Risky -10000 Chance 860 Decision 860 15.0% 40.0% 10.0% 5.0% 10.0% 25.0% Safe & Risky -10000 Chance 830 5.0% 20.0% 10.0% 5.0% 10.0%