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HO6-PS2

# HO6-PS2 - MS&E 352 Handout#6 Decision Analysis II January...

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MS&E 352 Handout #6 Decision Analysis II January 29 th , 2009 ________________________________________________________________________ ________________________________________________________________________ 01/29/09 1 of 3 Problem Set #2 Problem Set #2 Due Thursday February 5 th Part I – Advanced Information Gathering Problem 1 – Alpha / Beta Detectors [35 points] Kim faces the Party Problem in Professor Howard's manuscript. Two salesmen approach her, one selling an Alpha Rain Detector, the other selling a Beta Rain Detector. After conferring with one another, they offer Kim the following opportunities. Kim can buy the Alpha Detector (at any time) for \$10. Kim can buy the Beta Detector (at any time) for \$13. Kim can buy both detectors (at the same time) for \$16. Kim believes that the Alpha Detector is symmetric, and it has an accuracy of 0.8. In other words, {"S" | S, &} = {"R" | R, &} = 0.8 where "S" is the event that the test indicates sunny, S is the event that the weather is actually sunny (similarly for rain). Kim also believes that the Beta Detector is symmetric, with accuracy of 0.9, and that the two detector indications are irrelevant given the weather and her background state of information. She will buy a maximum of one indication from each detector (in other words, she will not buy two alpha detectors).

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