# HW6 - MS&E 252 Decision Analysis I Handout #17 11/9/2007...

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MS&E 252 Handout #17 Decision Analysis I 11/9/2007 Page 1 of 10 HW #6 Homework Assignment #6 Due on Thursday November 15th, 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) Decision analysis manuscript , read Chapter 5 and start Chapter 6. 2) Probability Encoding in Decision Analysis . Collection of readings. The material in this article will be relevant to future lectures by Professor Howard on probability encoding. 3) Speaking of Decisions: Precise Decision Language. By Ron Howard. Forthcoming in Decision Analysis Distinctions From the class lectures, explain the following concepts: Prior Likelihood Posterior Preposterior Sensitivity Specificity Symmetric test Relevant test Material test Economic test Probabilistic questions 1) For Mary, Kim’s friend, plot the sensitivity of the Value of Clairvoyance to the probability p of sunshine. How many of the following statements are true? I. For any value of p, Mary should be willing to pay at least as much as Kim for clairvoyance. II. The difference between the Value of the deal with Free Clairvoyance and the Value of the deal with No Clairvoyance is greatest when p is around 0.87.

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MS&E 252 Handout #17 Decision Analysis I 11/9/2007 Page 2 of 10 HW #6 III. Mary’s Value of Clairvoyance sensitivity curve has the same switch points as Jane’s (by “switch points” we mean the values of p at which the decision changes). a) 0 b) 1 c) 2 d) 3 2) You are trying to assess a u-curve for Patrick. Patrick reveals that he wishes to follow the delta property on prospects up to \$10,000, and that he is just indifferent between a sure \$500 and an uncertain deal with 75% chance of \$1,000 and 25% chance of \$0. Based on this information, which of the following is closest to Patrick’s risk-odds for prospects expressed in units of one dollar? a) 1.001 b) 1.002 c) 1.010 d) 3.000 3) Brett follows the Five Rules and prefers more money to less. His u-curve is given by: u(x) = 2 2 -x , with x measured in dollars How many of the following u-curves express the exact same preferences as the u- curve shown above? I. 4 4 -x , with x measured in dollars II. 2 -x , with x measured in dollars III. 2 + 2 -2x , with x measured in units of two dollars IV. 2 – 0.5 x , with x measured in dollars V. 2 1024 -x , with x measured in tens of dollars a) 0 or 1
MS&E 252 Handout #17 Decision Analysis I 11/9/2007 Page 3 of 10 HW #6 b) 2 c) 3 d) 4 or 5 4) Janice is a movie producer who must decide whether to produce a new children’s movie. She currently has \$600,000 in her bank account, and her u-curve as a function of her total wealth is described by the equation u(x) = 1 + ln(x). She draws the

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## This note was uploaded on 06/16/2010 for the course MS&E 252 taught by Professor Howard during the Fall '08 term at Stanford.

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HW6 - MS&E 252 Decision Analysis I Handout #17 11/9/2007...

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