IEOR 166 Professor S. Oren April 10, 2006 MIDTERM II (50 Minutes) Closed Book Calculators allowed Two double sided note sheet 8.5” x 11” allowed Bill, an expected value decision maker, needs your help. His little dog, Puppy is showing symptoms of a very potent and lethal virus. Bill currently believes that there is a .2 probability that Puppy is infected. Fortunately, there is a treatment against the virus that works 100% of the time with no side effects. However, the treatment costs $500. On the other hand if Puppy has the virus and is not treated he will die for sure and Bill estimates his emotional cost and the cost of replacing Puppy at a total of $2000 (assume that if Puppy goes untreated and turns out not to have the virus then the cost is $0). Bill’s objective is to minimize his expected total cost. Two blood tests are available to determine if Puppy is infected. The two tests are conditionally independent given the infection state (i.e. if the virus is present or not): • TEST A which costs $X and can only tell if the virus is present. i.e., if Puppy is infected then the test
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