I just need help with part B. Thanks! (a) You are given the following payoff tab
ID: 374695 • Letter: I
Question
I just need help with part B. Thanks!
(a) You are given the following payoff table (in units of thousands of dollars) for a decision analysis problem with the probabilities, (1) Which alternative should be chosen under the maximin payoff criterion? (2) Which alternative should be chosen under the maximum likelihood criterion? (3) Which alternative should be chosen under Bayes' decision rule? (4) Using Bayes' decision rule analysis graphically with respect to the prior probabilities of states S1 and S2 (without changing the prior probability of state S3) to determine the decision State of Nature Alternative 2 220 200 170 180 110 150 Prior probability 0.6 0.3 (b) If the payoffs are themselves uncertain, how can you find the solution, Explain.Explanation / Answer
The given payoff matrix is analysizes as follows:
Maximum likely is 194 corresponding to A1 (Ans.2)
Also maximum probaility is for state S1 under which alternative A1 gives the maximum expected gain,
Under Bayes' decision rule it is assumed that all states have the same probabilities and decision maker first calculate the average outcome for every option and then selects that with the maximum value.
States Sigma-pixi Alternatives S1 S2 S3 Expected A1 220 170 110 194 220*.6+170*.3+110*.1 A2 200 180 150 189 200*.6+180*.3+150*.1 Prior Probability 0.6 0.3 0.1 Minimum 200 170 110 MaxiMin is 200 corresponding to A2 (Ans.1)Maximum likely is 194 corresponding to A1 (Ans.2)