Hw8 - SIEO 3600(IEOR Majors Introduction to Probability and...

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SIEO 3600 (IEOR Majors) Assignment #8 Introduction to Probability and Statistics March 23, 2010 Assignment #8 – due March 30th, 2010 ( Binomial, Geometric and Uniform random variables ) 1. Polling: During a Presidential election (only two candidates for simplicity). (a) It has been determined (by extensive sample) that p = 55% of all voters will vote for candidate A and q = 1 - p = 45% for candidate B . If you randomly select 5 voters, what is the probability that exactly 3 will vote for candidate A ? (b) Suppose that apriori we do not know the proportion p of voters who will vote for can- didate A , but that when we randomly selected 5 voters, exactly 3 said they would vote for A . Find the value of p that maximizes the probability of this event (e.g., of getting exactly 3 out the 5 saying they would vote for A .) 2. Let X be a binomial random variable with E [ X ] = 7 and var( X ) = 2 . 1 Find (a) P ( X = 4); (b) P ( X > 12). 3. Suppose that a particular trait (such as eye color or left-handedness) of a person is classified on the basis of one pair of genes, and suppose that d
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