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hw9 - AMS 311(Fall 2009 Joe Mitchell PROBABILITY THEORY...

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Unformatted text preview: AMS 311 (Fall, 2009) Joe Mitchell PROBABILITY THEORY Homework Set # 9 Due at the beginning of class on Thursday, December 10, 2009. 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 average number of bank failures in the USA is two per week. (a). Estimate the probability, p , that at least five bank failures occur in the USA next week. (What inequality are you using?) (b). Assume now (for parts (b), (c), and (d)) that you are told that the variance of the number of bank failures in the USA in any one week is 4. Now give an improved estimate of p (using an inequality). (c). Give a Central Limit Theorem estimate for the probability q that during the academic year (considered to be 31 weeks total, fall and spring) there are more than 75 bank failures in the USA. (d). Use an inequality to get the best bounds you can on the probability q estimated in part (c). (2). (15 points) The cash register is broken at the bagel shop, so transactions are done by hand and recorded. Your lazy employee, Joe, charges customers exactly (e.g., if they owe $3.61, he makes sure they pay exactly $3.61); however,lazy employee, Joe, charges customers exactly (e....
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