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Unformatted text preview: IEOR 172: Probability and Risk Analysis for Engineers, Fall 2007 Review Questions for Midterm2 1. The lifetime of each light bulbs is exponetially distributed with mean 5 hours. We test 12 light bulbs (one at a time) whether its quality exceeds our standard. If it lasts longer than 4 hours, we say it passes the test; otherwise, it fails. Let X be the number of light bulbs that pass the test. (a) What is the distribution of X ? Let L i denote the lifetime of light bulb i . We have L i exp(1 / 5). The probability that each light bulb passes the test is P( L i > 4) = e- 4 / 5 . The distribution of X is Binomial(12, e- 4 / 5 ). (b) Let Y denote the number of light bulbs that fail the test. What are E[ Y ] and Var( X )? We have Y = 12- X . So E[ Y ] = E[12- X ] = 12- E[ X ] = 12- 12 e- 4 / 5 . Similarly, Var( Y ) = Var(12- X ) = (- 1) 2 Var( X ) = 12 e- 4 / 5 (1- e- 4 / 5 ) . (c) What is the probability that X > Y ?...
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This note was uploaded on 04/02/2008 for the course IEOR 172 taught by Professor Righter during the Fall '07 term at University of California, Berkeley.
- Fall '07