410Hw05 - STAT 410 Summer 2009 Homework #5 (due Friday,...

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STAT 410 Summer 2009 Homework #5 (due Friday, July 10, by 4:00 p.m.) 1. Let X and Y be independent random variables, each geometrically distributed with the probability of “success” p , 0 < p < 1. That is, p X ( k ) = p Y ( k ) = ( 29 1 1 - - k p p , k = 1, 2, 3, … , a) Find P ( X > Y ). [ Hint: You may find it helpful to find P ( X = Y ) first. ] b) Find P ( X + Y = n ), n = 2, 3, 4, … , and P ( X = k | X + Y = n ), k = 1, 2, 3, … , n – 1. 2. Suppose the size of largemouth bass in a particular lake is uniformly distributed over the interval 0 to 8 pounds. A fisherman catches (a random sample of) 5 fish. a) What is the probability that the smallest fish weighs less than 2 pounds? b) What is the probability that the largest fish weighs over 7 pounds? c) What is the probability that the largest fish weighs between 6 and 7 pounds? d) What is the probability that the second largest (fourth smallest) fish weighs between 4 and 6 pounds? 3. Three actuaries are independently hired to appraise the value of a company. The true value of the company is θ million dollars, and each actuary’s estimate is uniformly
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410Hw05 - STAT 410 Summer 2009 Homework #5 (due Friday,...

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