Question 4 You are given the following payoff table (in units of thousands of Rands) fora decision Analysis Problem. Show all formulas and calculations. Alternatives State of Nature 6-\"- A1 moo Prior Probability \"- . Which alternative should be chosen under the maximin payoff criterion? (1 Mark) . Which alternative should be chosen under the maximum likelihood criterion? (1 mark) . Which alternative should be chosen under Bayes decision rule? (2 Marks) . Using Bayes decision rule, do sensitivity analysis graphically with respect to the prior probabilities of states S1 and 82 (without changing the prior probability of state 83) 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) . Repeat part (d) for the prior probabilities of states 31 and 83. (6 Marks) Repeat part (d) for the prior probabilities of states 82 and $3. (6 Marks) . 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)