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hw9_2 - AMS 311(Fall 2010 Joe Mitchell PROBABILITY THEORY...

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Unformatted text preview: AMS 311 (Fall, 2010) Joe Mitchell PROBABILITY THEORY Homework Set # 9 Due at the beginning of class on Thursday, December 9, 2010. Reminder: Show your reasoning! Chapter 8, Sections 8.1-8.3, and first part of Section 8.5 (on one-sided Chebyshev); handout on Chebyshev inequality. Examples to read carefully: Chapter 8: 2a, 2b, 3a, 3b, 3c, 3d, 5a. (1). (20 points) The AMS department receives, on average, three requests per day for students to sign into the major. We do not know the probability distribution for the number, X i , of students who sign into the AMS major on day i . (a). Let p be the probability that five or more students sign into the AMS major on Monday. Give the best guaranteed estimate you can for the probability p . (What inequality are you using?) (b). For the next three parts ((b), (c), (d)) assume that we also know that the variance, var ( X i ), is 9. Try now to use an appropriate Chebyshev inequality to give an improved pair of bounds (upper and lower) on the probability...
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