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HW6_Soln

# HW6_Soln - MS&E 252 Decision Analysis I Handout#21 Homework...

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MS&E 252 Decision Analysis I Homew Question Distribution: Page 1 of 20 work Assignment #6 Solutions Handout #21 11/20/2007 HW#6 Solutions

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MS&E 252 Handout #21 Decision Analysis I 11/20/2007 Page 2 of 20 HW#6 Solutions Student Distribution: Distinctions These distinctions were prepared by the teaching team and reflect our best belief of the meanings of these terms. s Prior : The probability distribution of the distinction of interest conditioned on your information. s Likelihood : Conditional distribution of the observed distinction given the distinction of interest. s Posterior : Conditional distribution of the distinction of interest given the observed distinction. s Preposterior : The probability distribution of the observed distinction (e.g., test results) s Sensitivity is the probability that the test says positive given that the distinction of interest is really positive. s Specificity is the probability that the test says negative given that the distinction of interest is negative. s Symmetric test: A test is symmetric if sensitivity = specificity. Otherwise it is asymmetric. s Relevant test : A test is relevant if the probabilities assigned to the test outcome are different depending on the state of the distinction of interest (or, equivalently, vice versa) s Material test : A test is material if its results possibly change the preferred alternative. If the decision is the same regardless of test outcome, the test is immaterial. Note that the assumption here is that it is a free test. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 5 10 15 20 25 30 35 40 45
MS&E 252 Handout #21 Decision Analysis I 11/20/2007 Page 3 of 20 HW#6 Solutions Probabilistic questions 1) Solution: a Statement I is false: In fact, in the party problem, Mary’s Values of Clairvoyance are lower than Kim’s. Kim and Mary have the same beliefs but different risk-attitudes, but we cannot draw conclusions about Value of Clairvoyance from risk attitude only. Statement II is false because, for a risk-neutral decision maker, we have: VOC = VFC – VNC Mary’s Value of Clairvoyance is greatest when p=0.47. Statement III is false because Mary’s sensitivity curve has the same switch points as Kim, not Jane. This is due to the fact that they have the same preference probabilities and would choose the same alternative given the same probability p of sunshine. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 5 10 15 20 25 p Value of Clairvoyance Sensitivity to p for Kim and Mary (0.47, 20.9) (0.87, 8.9) Mary Kim (0.47, 24.4) (0.87, 15.2) \$ 2) Solution: b From the question, we know that:

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MS&E 252 Handout #21 Decision Analysis I 11/20/2007 Page 4 of 20 HW#6 Solutions This is not a deal from which we can directly compute Patrick’s risk-odds – we would like to have \$0 on the left, and a deal between some amount +m and some amount -m on the right. However, by virtue of the Delta Property, we know that if we simply subtract \$500 from each
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HW6_Soln - MS&E 252 Decision Analysis I Handout#21 Homework...

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