HW3_Soln

# HW3_Soln - MS&E 252 Decision Analysis I Handout#10 Homework...

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MS&E 252 Handout #10 Decision Analysis I 10/22/2007 Page 1 of 15 HW #3 Solutions Homework Assignment #3 Solutions Student Distribution: 0 5 10 15 20 25 30 35 40 -INF-0 0-0.5 0.5-1 1-1.5 1.5-2 2-2.5 2.5-3 3-3.5 3.5-4 4-4.5 4.5-5 5-5.5 5.5-6 6-6.5 6.5-7 7-7.5 7.5-8 8-8.5 8.5-9 9-9.5 9.5-10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

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MS&E 252 Handout #10 Decision Analysis I 10/22/2007 Page 2 of 15 HW #3 Solutions Distribution by Question: Score on HW Question -1.50 -1.00 -0.50 0.00 0.50 1.00 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%
MS&E 252 Handout #10 Decision Analysis I 10/22/2007 Page 3 of 15 HW #3 Solutions Distinctions s An expert: • has powerful distinctions and knows how they relate to each other, • in some cases, has required physical skills, • knows the history and borders of the field, and • has humility (and knows what he or she does not know) s We define clairvoyance as information, which resolves all uncertainty about an uncertain distinction. We call the PIBP of clairvoyance on a distinction the value of clairvoyance on that distinction. s We define a distinction as a thought, which separates one large group of things into two or more smaller groups. We call the small groups the degrees of the distinction. We require the degrees to be mutually exclusive (a thing only falls into one degree) and collectively exhaustive (a thing will always fall into one of the degrees). We can create several kinds of distinctions over the same large group; for example, we can create the two distinctions "sex" and "hair length" over the group "humans." s We call a distinction clear when it satisfies the clarity test . This means that a clairvoyant could, without exercise of judgment, tell in which degree any particular thing falls. s We call a distinction observable when we "know it when we see it." In other words, the decision maker could tell in which degree any particular thing falls. s We call a distinction useful when it • means what we want it to mean, and/or • helps us achieve clarity of action. s Decision Basis: • Alternatives are what you can do. Need more than one. • Preferences are what you want. You must care about what might happen. • Information is what you know. Information links what you want to what you can do. s The probability of an event is a number from 0 to 1 describing a person's beliefs about the likelihood of that event occurring. Since a probability describes a person's belief, we say that it is conditioned on that person's background state of information (written &), or the sum of all that person's knowledge and experience, which affects his or her belief. s

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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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HW3_Soln - MS&E 252 Decision Analysis I Handout#10 Homework...

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