Question 2 You are given the following payoff table (in units of thousands of Rands) for a decision Analysis Problem. Show all formulas and calculations. Alternatives S3 A1 A2 Prior Probability State of Nature S1 S2 22000 17000 20000 18000 0,6 0,3 11000 15000 0,1 a. Which alternative should be chosen under the maximin payoff criterion? (1 Mark) b. Which alternative should be chosen under the maximum likelihood criterion? (1 mark) c. Which alternative should be chosen under Bayes decision rule? (2 Marks) d. Using Bayes decision rule, do sensitivity analysis graphically with respect to the prior probabilities of states S1 and 52 (without changing the prior probability of state S3) to determine the crossover point where the decision shifts from one alternative to the other. Then use algebra to calculate this crossover point. (6 Marks) e Repeat part (d) for the prior probabilities of states S1 and 53. (6 Marks) f. Repeat part (d) for the prior probabilities of states $2 and 53. (6 Marks) g. If you feel that the true probabilities of the states of nature are within 10 percent of the given prior probabilities, which alternative would you choose? (2 Marks)