You are given the following payoff table (in units of thousands of dollars) for a decision analysis problem: T (a) Which alternative should be chosen under the maximin payoff criterion? T (b) Which alternative should be chosen under the maximum likelihood criterion? T (c) Which alternative should be chosen under Bayes’ decision rule? (d) Using Buyes’ decision rule, do sensitivity analysis graphically with respect to the prior probabilities of states S_1 and S_2 (without changing the prior probability of state S_3) to determine the crossover point where the decision shifts from one alternative to the other. Then use algebra to calculate this crossover point. (e) Repeat part (d) for the prior probabilities of stales S_1 and S_3. (f) Repeal part (d) for the prior probabilities of stales S_2 and S_3. (g) If you feel that the true probabilities of the suites of nature are within 10 percent of the given prior probabilities, which alternative would you choose?