Question 5 The following payoff table gives several strategic alternatives, seve

Question

Question 5 The following payoff table gives several strategic alternatives, several states of nature, the probablites of the states, and the comesponding payofs. Not yet answered State State 2 State 3 Alternative 112 22 36 Points out ot Alternative 2-5 -6 -8 10.00 P Flag question Alternative 320 23 14 Probabilities 0.42 0.31 0.27 Find the best alternative using Bayes' Decision Criteria. Enter the payoff value that made the decision. Please round to two decimalplaces if Answer: Next pag Previous page

Explanation / Answer

Using Bayes Decision criteria we need to find the expected payoffs from each alternative using the given probabilities for each of the 3 states:

E( alternative 1) = 0.42*12 + 0.31*22 + 0.27*36 = 5.04 + 6.82 + 9.72 = 21.58

E( alternative 2) = 0.42*(-5) + 0.31*(-6) + 0.27*(-8) = -2.1 - 1.86 - 2.16 = -6.12

E( alternative 3) = 0.42*20 + 0.31*23 + 0.27*14 = 8.4 + 7.13 + 3.78 = 19.31

As the expected payoff from alternative 1 is highest for the given probabilities of the 3 states, therefore alternate 1 should be taken according to the Bayes' decision criteria.

Therefore the required payoff here is 21.58

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