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