Problem 5. (20 points) You are given the following table of payments (in units of thousands of dollars) for a decision analysis problem. STATE OF NATURE ACTION A1 Prior Probability 0.2 0.5 0.3 a) (2 points) If you use the maximin (pessimistic) criterion, what action should you take and what is the associated payment? b) (2 points) If you use the maximax (optimistic) criterion, what action should you take and what is the associated payment? c) (2 points) If you use the maximum likelihood criterion, what action should you take and what is the associated payment? d) (4 points) If you use the minimax regret criterion, what action should you take and what is the associated opportunity loss? e) (3 points) If you want to maximize the expected value of payments, what action should you take and what is the associated expected payment? f) (4 points) What is the Expected Value of Perfect Information? g) (3 points) You are given the opportunity to pay $1,500 to obtain more information about which state of nature is likely to occur. Is it worthwhile to pay for this information? Why