Question 3: Decision analysis (25 marks) Consider a decision analysis problem whose payoffs (in units of thousands of dollars) are given by the following payoff table: State of nature State 2 Alternative 1 30 Alternative 2 I Alternative 3 Prior probabilities State 1 26 23 30 0.2 29 22 0.5 State 3 24 28 23 0.3 a. Which alternative should be chosen under the maximin criterion? (5 marks) b. Which alternative should be chosen under the maximum likelihood criterion? (S marks) c Which alternative should be chosen under Bayes decision rule? (S marks) d. Construct a decision tree for this problem. You should show all necessary numbers and the final decision on the tree. (10 marks) Instruction: You can draw the decision tree on a paper and include a photo of it into your file. You can do it in any drawing software like Visio, Paint, etc. as well. Question 4: Project management (25 marks) R Question 3: Decision analysis (25 marks) Consider a decision analysis problem whose payoffs (in units of thousands of dollars) are given by the following payoff table: State of nature State 2 Alternative 1 30 Alternative 2 I Alternative 3 Prior probabilities State 1 26 23 30 0.2 29 22 0.5 State 3 24 28 23 0.3 a. Which alternative should be chosen under the maximin criterion? (5 marks) b. Which alternative should be chosen under the maximum likelihood criterion? (S marks) c Which alternative should be chosen under Bayes decision rule? (S marks) d. Construct a decision tree for this problem. You should show all necessary numbers and the final decision on the tree. (10 marks) Instruction: You can draw the decision tree on a paper and include a photo of it into your file. You can do it in any drawing software like Visio, Paint, etc. as well. Question 4: Project management (25 marks) R