QUESTION 1 PRDEAPS/2024 You are given the following payoff table (in units of thousands of Rands) for a decision Analysis Problem. Show all formulas and calculations. Alternatives State of Nature S1 S2 S3 A1 25000 | 20000 | 14000 A2 23000 | 21000 | 19000 Prior Probability 0.6 0.3 0.1 (a) Which alternative should be chosen under the maximin payoff criterion? (1) (b) Which alternative should be chosen under the maximum likelihood criterion? (1) (c) Which alternative should be chosen under Bayes decision rule? (2) (d) Using Bayes decision rule, do sensitivity analysis graphically with respect to the prior probabilities of states S1 and S2 (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. (e) Repeat part (d) for the prior probabilities of states S1 and S3. (f) Repeat part (d) for the prior probabilities of states S2 and S3. (6) (6) (6) (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? QUESTION 2 (2) [24] You have to make certain decisions according to Bayes' decision rule. For your current problem, you have constructed the following payoff table (in units of Rands): Show all formulas and calculations. Alternatives State of Nature 51 S2 S3 A1 8000 | 13000 |-13000 A2 0 4000 -4000 A3 5000 | 7000 -7000 Prior Probability 0.5 0.3 0.2 (a) Which alternative should you choose? (4) (b) Find EVPI. (2) PRDEAPS/2024 (c) What is the most that you should consider paying to obtain more information about which state of nature will occur? (1) [7]