Suppose that a company has determined that the the number of jobs per week, N, varies

Chapter 5, Problem 5.139

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Suppose that a company has determined that the the number of jobs per week, N, varies from week to week and has a Poisson distribution with mean . The number of hours to complete each job, Yi , is gamma distributed with parameters and . The total time to complete all jobs in a week is T = N i=1 Yi . Note that T is the sum of a random number of random variables. What is a E(T | N = n)? b E(T ), the expected total time to complete all jobs?

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