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Hw10 - SIEO 3600(IEOR Majors Introduction to Probability...

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SIEO 3600 (IEOR Majors) Assignment #10 Introduction to Probability and Statistics April 6, 2010 Assignment #10 – due April 13th, 2010 ( Central limit theorem, maximum likelihood estimator ) 1. Charity University announces a fund raising target of $10 millions. It sends out n letters to its alumni. From past experience, there is a probability of 0.6 that each alumni will not respond at all. Given that an alumni does respond (with probability 0.4), the amount of contribution is a random variable with mean $ μ and standard deviation $ σ . (a) What is the mean and variance of the amount of contribution from each letter sent? (b) We can reasonably assume that each letter recipient will behave independently with the above characteristic. What is the minimum number of letters to send so that Charity University will hit its target with at least 90% probability? Hint: Think about the fire-hydrant example discussed in class. 2. A roulette wheel has 38 slots, numbered 0, 00, and 1 through 36. If you bet 1 on a specified number, you either win 35 if the roulette ball lands on that number or lose 1 if it does not.
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