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 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