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midterm_solutions_v3

midterm_solutions_v3 - MS&E 252 Decision Analysis I Midterm...

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MS&E 252 Midterm Solutions Decision Analysis I Nov 14 th , 2006 Page 1 of 12 Midterm Midterm Examination Solutions Grade Distribution 0 5 10 15 20 25 30 35 -INF - 0 5 - 10 15 - 20 25 - 30 35 - 40 45 - 50 55 - 60 65 - 70 75 - 80 85 - 90 95 - 100 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Number of Grades within Range Cumulative The grade distribution for the midterm was better than what we usually observe in this class. Grade Distribution by Question Questions 2, 6, 9 and 14 were no challenge for most people in the class. Questions 13 and 15, which were designed by the teaching team to be the hardest on the exam, were the ones that students struggled with the most.

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MS&E 252 Midterm Solutions Decision Analysis I Nov 14 th , 2006 Page 2 of 12 Midterm Score on HW Question (./1) -8.00 -6.00 -4.00 -2.00 0.00 2.00 4.00 6.00 8.00 Question 1 10% 50% 90% Question 2 10%50%90% Question 3 10% 50% 90% Question 4 10% 50% 90% Question 5 10% 50% 90% Question 6 10% 50% 90% Question 7 10% 50% 90% Question 8 10% 50% 90% Question 9 10% 50% 90% Question 10 10% 50% 90% Question 11 10% 50% 90% Question 12 10% 50% 90% Question 13 10% 50% 90% Question 14 10% 50%90% Question 15 10% 50% 90%
MS&E 252 Midterm Solutions Decision Analysis I Nov 14 th , 2006 Page 3 of 12 Midterm 1. Answer: c) Many answers to these questions can be found in the slides for Problem Session 4. Statement I is true – The Order Rule is ordering the prospects in a preference ordering. Statement II is true – The Substitution Rule does use the logic of replacing an uncertain deal with a certain equivalent. All the information in a complex decision tree is re- structured into terms of a simple deal between the best and worst prospects. In the end, the simple deal should have the same preferences as the original decision-tree. Statement III is false – Alternatives , information , and preferences are used in the Choice Rule. The Choice Rule tells the decision-maker which alternative he or she should choose. However, the choice rule does not actually mean that the decision-maker will necessarily be committed to choosing that alternative. 2. Answer: a) As Emily has bid \$68, her PIBP for acquiring the certificate must have been greater than \$68 (as stated in class, in a closed bid setting, one should bid below their PIBP). We also know that since she has accepted Marcus’s offer, her PISP must have been less than or equal to \$80. 3. Answer: a) 0.7 No Rain 1 >>> Skydiving 0.82 0.3 Rain 0.4 0.82 0.9 No Snow 0.9 Bungee Jumping 0.81 0.1 Snow 0 We only need the preference probabilities to answer this question. We do not need to take the dollar values into consideration at all. From the decision tree above, we can see that Veronique should go Skydiving.

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MS&E 252 Midterm Solutions Decision Analysis I Nov 14 th , 2006 Page 4 of 12 Midterm 4. Answer: c)
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