HW7 - MS&E 252 Decision Analysis I Handout #22...

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MS&E 252 Handout #22 Decision Analysis I 11/30/2007 Page 1 of 12 HW #7 Homework Assignment #7 Due on Thursday, December 6 th 11:59 pm In this assignment you are required to turn in the probabilistic section only. Again the "Food for thought" section is optional but will help you think in depth about the concepts covered and will help with your grade on participation. As mentioned in the course guide, we will expect full knowledge of all sections on this assignment. Assigned Reading 1) Finish chapter 6 in the Manuscript . 2) Microrisks for Medical Decision Analysis Distinctions From the class lectures, explain the following concepts: Decision Diagram Informational arrow Influence arrow Relevance arrow Functional arrow Probabilistic Questions 1) Consider the following statements about tests and test results: I. A test must be observable to be useful II. A test may be material but not relevant III. A test may be relevant but not economic How many of the above statements are true? a) 0 b) 1 c) 2 d) 3
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MS&E 252 Handout #22 Decision Analysis I 11/30/2007 Page 2 of 12 HW #7 2) Recall Kim’s party decision and consider the following symmetric weather detectors: I. Rain detector A: cost of $15 and accuracy of 85% II. Rain detector B: free and accuracy of 55% III. Rain detector C: cost of $2 and accuracy of 30% How many of the above weather detectors are economic? a) 0 b) 1 c) 2 d) 3 3) Aishwarya, who follows the Five Rules of Actional Thought and prefers more money to less, faces the following decision situation: In other words, she needs to choose between three alternatives A, B and C, and her prospects only depend on her initial choice and on a distinction of interest I. Distinction I has two degrees – i 0 and i 1 . Aishwarya, who is quite familiar with Decision Analysis, plots her u-value for each of the three alternatives as a function of her probability that i 1 will occur: Value I Decision
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Handout #22 Decision Analysis I 11/30/2007 Page 3 of 12 HW #7 Sensitivity to {i1 | &} 0 2 4 6 8 10 12 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 U-Value Alternative A Alternative B Alternative C How many of the following statements must be true? I. If Aishwarya believes that i 1 will occur with probability 0.7, she should choose alternative B; II. Suppose that Aishwarya is offered a new alternative D, with corresponding prospects [D, i 0 ] and [D, i 1 ] such that u([D, i 0 ]) = 2 and u([D, i 1 ]) = 9. Then, if {i 1 | &} = 2/3, she should be indifferent between alternatives A, B and D, and for any other value of her belief she should not choose D; III. If Aishwarya is risk-neutral, then the value of {i 1 | &} for which her value of clairvoyance on I will be highest is {i 1 | &} = 2/3. a)
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HW7 - MS&E 252 Decision Analysis I Handout #22...

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