Question A2 Consider the following payoff table which shows the profit for a four-state and two-decision problem with probability assessment. Decision Alternative | State of Nature s1 | s2 | s3 | s4 d1 | 600 | 400 | -100 | 120 d2 | 700 | -200 | 0 | 400 P(si) | 0.3 | 0.4 | 0.2 | 0.1 For a lottery having a payoff 700 with probability p and -200 with probability (1 - p), the decision maker expressed the following indifference probabilities. Suppose U(700) = 100 and U(-200) = -10. Payoff | Indifference Probability 600 | 0.95 400 | 0.8 120 | 0.5 0 | 0.35 -100 | 0.2 (a) Complete the utility table by using the above payoff and indifference probabilities. (4 marks) (b) Find the optimal decision for the decision maker by using expected utility approach. (4 marks)
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We are given a decision-making problem with two decisions (d1 and d2) and four states of nature (S1, S2, S3, S4). The payoffs for each decision in each state of nature are provided. Additionally, we have a lottery with payoffs of 700 and -200, with corresponding Show more…
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The following profit payoff table was presented in Problem 1: State of Nature S2 100 100 Decision Alternative S1 250 100 S3 25 75 d d2 The probabilities for the states of nature are F(S1) = 0.65, F(S2) = 0.15, and F(S3) = 0.20. What is the optimal decision strategy if perfect information were available? b. What is the expected value for the decision strategy developed in part (a)? Using the expected value approach, what is the recommended decision without perfect information? What is its expected value? d. What is the expected value of perfect information?
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The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature. Decision Alternative | States of Nature ---------------------------------------------- s1 | 230 s2 | 80 s3 | 5 d1 | 80 d2 | 80 d3 | 55 The probabilities for the states of nature are: P(s1) = 0.65, P(s2) = 0.15, and P(s3) = 0.20. (b) What is the expected value for the decision strategy developed in part (a)? _______ (THE ANSWER IS NOT 162.6) (c) Using the expected value approach, what is the recommended decision without perfect information? What is its expected value? The recommended decision without perfect information is d1. EV = _______(THE ANSWER IS NOT 75) (d) What is the expected value of perfect information? EVPI = __________ (THE ANSWER IS NOT 162.5)
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