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 1 26 23 30 Alternative 1 Alternative 2 Alternative 3 Prior probabilities State of nature State 2 30 29 22 State 3 24 28 23 0.2 0.5 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? (5 marks) C. Which alternative should be chosen under Bayes' decision rule? (5 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