Multiple Choice Questions: Please circle the letter of the correct answer clearly:

(5 Points): Making a good decision Requires probabilities for all states of nature requires a clear understanding of decision alternatives, states of nature, and payoffs. implies that a desirable outcome will occur All of the alternatives are true.

(5 Points): Which of the methods for decision making without probabilities best protects the decision maker from undesirable results? a. the optimistic approach b. the conservative approach c. minimum regret d. minimax regret

(5 Points): Sensitivity analysis considers how sensitive the decision maker is to risk changes in the number of states of nature changes in the values of the payoffs changes in the available alternatives

(5 Points): To find the EVSI, use the EVPI to calculate sample information probabilities use indicator probabilities to calculate prior probabilities use prior and sample information probabilities to calculate revised probabilities use sample information to revise the sample information probabilities.

Quantitative Problems: Please complete the below questions on a separate paper showing all of your work. If you use EXCEL software, please attach your EXCEL worksheet to your submission.

(20 Points): The number of properties newly listed with a real estate agency in each quarter over the last four years is given. Calculate the seasonal index values. Year Quarter 1 2 3 4 1 73 81 76 77 2 89 87 85 92 3 123 115 108 131 4 92 93 87 101 (25 Points): A payoff table is given as State of Nature Decision s1 s2 s3 d1 10 8 6 d2 14 15 2 d3 7 8 9

a. What decision should be made by the optimistic decision maker? b. What decision should be made by the conservative decision maker? c. What decision should be made under minimax regret? d. If the probabilities of s1, s2, and s3 are .2, .4, and .4, respectively, then what decision should be made under expected value? e. What is the EVPI?