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# rec20 - Massachusetts Institute of Technology Department of...

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Massachusetts Institute of Technology Department of Electrical Engineering & Computer Science 6.041/6.431: Probabilistic Systems Analysis (Fall 2010) Recitation 20: November 18, 2010 1. In your summer internship, you are working for the world’s largest producer of lightbulbs. Your manager asks you to estimate the quality of production, that is, to estimate the probability p that a bulb produced by the factory is defectless. You are told to assume that all lightbulbs have the same probability of having a defect, and that defects in different lightbulbs are independent. (a) Suppose that you test n randomly picked bulbs, what is a good estimate Z n for p , such that Z n converges to p in probability? (b) If you test 50 light bulbs, what is the probability that your estimate is in the range p ± 0 . 1? (c) The management asks that your estimate falls in the range p ± 0 . 1 with probability 0.95. How many light bulbs do you need to test to meet this specification?

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rec20 - Massachusetts Institute of Technology Department of...

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