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Unformatted text preview: ISyE 2027 Probability with Applications Fall 2011 R. D. Foley Homework 9 November 28, 2011 due Monday 1. Let X and Y be independent, exponentially distributed random variables with parameters λ and μ , respectively. (a) Compute the c.d.f. of Z where Z = X ∧ Y . (b) Compute the p.d.f. of Z . (c) What is the name of the distribution of Z including any parameters? (d) If λ = 3 per hour and μ = 7 per hour, what is the expected value of Z in minutes? 2. Turtles A and B are racing. The length of time until A finishes the race is exponentially distributed with mean 30 minutes, and for B, exponen tially distributed with mean 20 minutes, and for C, exponentially dis tributed with mean 15 minutes. Assume that the three times are inde pendent. (a) What is the probability that A takes longer than 1 hour? (b) What is the probability that A wins? (c) What is the expected time of the winning turtle in hours? (d) What is the probability that the winning time is under 10 minutes? 3. Suppose the joint p.m.f. of X and Y is P { X = i , Y = j } = c ( i + j ) for i = 0, 1, 2 , j = 0, 1 , and 0 otherwise. Determine c and then compute...
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This note was uploaded on 01/22/2012 for the course ISYE 2027 taught by Professor Zahrn during the Fall '08 term at Georgia Tech.
 Fall '08
 Zahrn

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