MidtermSolutions - ESI 6321 APPLIED PROBABILITY METHODS IN...

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1 ESI 6321 APPLIED PROBABILITY METHODS IN ENGINEERING OEM 2009 February 16, 2008 MIDTERM+SOLUTIONS 8:00-10:00AM Open book, open lecture notes This test consists of 3 problems Name:
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2 Problem 1: (35 points) A nuclear power company is deciding whether to build a nuclear power plant at Diablo Canyon or at Roy Rogers City. The cost of building the power plant is $10 million at Diablo Canyon and $20 million at Roy Rogers City. If the company builds at Diablo Canyon, however, and an earthquake occurs at Diablo Canyon during the next five years, construction will be terminated and the company will lose $10 million (and will still have to build a power plant at Roy Rogers City). A priori, the company believes there is a 20% chance that an earthquake will occur at Diablo Canyon during the next five years. For $1 million, a geologist can be hired to analyze the fault structure at Diablo Canyon. He will either predict that an earthquake will occur or that an earthquake will not occur. The geologist’s past record indicates that he will predict an earthquake on 95% of the occasions for which an earthquake will indeed occur, and no earthquake on 90% of the occasions for which an earthquake will not occur. Assume that the company’s goal is to minimize its total expected cost. (a) Should the power company hire the geologist? Solution: Let E denote the event that an earthquake will occur in the next five years. Let G denote the event that the geologist predicts that an earthquake will occur in the next five years. We are given the following probabilities: P(E) = 0.20 P(G|E) = 0.95 P(G’|E’) = 0.90 For the decision tree, we require the following probabilities: P(G) = P(G|E) P(E) + P(G|E’) P(E’) = 0.95 × 0.20 + (1-0.90) (1-0.20) = 0.27 P(E|G) = P(G|E) P(E) / P(G) = 0.95 0.20 / 0.27 = 0.704 P(E|G’) = P(G’|E) P(E) / P(G’) = (1-0.95) 0.20 / (1-0.27) = 0.0137 The company should hire a geologist, for a total expected cost of $13.9 million. (b)
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MidtermSolutions - ESI 6321 APPLIED PROBABILITY METHODS IN...

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