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Summer 2006 final exam

# Summer 2006 final exam - OR 22 FINAL EXAM SUMMER 2006(23 1...

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OR 22 SUMMER 2006 FINAL EXAM June 20, 2006 (23) 1. Bounty hunter Allen Freebee and his band of cronies are planning a search-and-destroy mission for illegal stills in the mountains of Alleghany County. They are especially interested in closing down the operations of Hugh MacNeal, known far and wide as the producer of the sweetest "sippin' licker" east of the Smokies. Allen is pretty certain that Hugh’s still is located in one of two spots in the triangle formed by Laurel Springs, Sparta, and Roaring Gap. He thinks there is a 30% chance the still is in Air Bellows Gap and a 70% chance that Hugh is doing his brewing at The Devil's Garden. If Allen's raid is successful, and he finds and destroys Hugh’s still, he will receive a \$20,000 reward from the Treasury Department. He estimates that it will cost him \$4,000 to stage a raid at Air Bellows Gap, but that a raid at The Devil's Garden will cost \$6,000, because of the special equipment needed to cope with the area's known severe infestation of rattlesnakes and copperheads. Allen gets to run only one raid, because Hugh will get wind of an unsuccessful raid and shut his operation down for a while. He wishes to maximize his expected net gain (reward less cost of staging the raid). ( 6) A. Allen sketched the partial decision tree below to determine which site to raid. Fill in the missing probabilities and payoffs. Where should the raid be? How much can he expect to net from making the right decision? +------- Still at Air Bellows Gap --- 20 – 4 = 16 +---- Raid Air Bellows Gap --- ( ) | +------- Still at Devil’s Garden --- [ ] | +------- Still at Air Bellows Gap --- +---- Raid Devil’s Garden --- ( ) +------- Still at Devil’s Garden --- 20 – 6 = 14 ( 5) B. At what probability (to four (4) decimal places) of the still’s being at Air Bellows Gap will Allen be indifferent between the two spots? (Let p represent the probability that the still is at Air Bellows Gap.) NOTE: If you couldn’t do this part, you may assume in subsequent parts where you’d like to use it that the indifference probability is 0.4. In the past, Allen has often been able to get tips about the locations of stills from Joe Buylowski, a sometime CPA, known to supplement his accounting income by cooking the books of some of the more successful moonshiners in Alleghany County. His past dealings with Buylowski have made Allen somewhat leery of using him as a source of information, because his tips have been far from reliable. In cases where only two locations (A and B) were possible, Joe's tips had been accurate 25% of the time; that is, if the still was in location A, then 25% of the time Joe's tip sent Allen to location A, and similarly, when the still was at B, Joe's information sent Allen to B 25% of the time. Allen realizes he’ll need Bayes’s Law to figure out how to use Joe’s information, but he’s long since forgotten it. Fortunately, his more quantitatively oriented colleague Miguel LaBelle, does those computations and tells him that There’s a 60% chance that Joe would say the still is at Air Bellows Gap (and, accordingly, a 40% chance that it’s at The Devil’s Garden).

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• Summer '06
• RUBIN,David
• Academic degree, Doctor of Philosophy, Air Bellows Gap

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