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Suppose that a company has determined that the number of jobs per week,N, varies from week to week and has a Poisson distribution with mean?.

Suppose that a company has determined that 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 isT=?Ni=1Yi.

Find the expected value and the variance of the total time to complete all jobs.

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(b) (20 marks) Suppose that a company has determined that the number of jobs per week, N , varies from week to week and has a Poisson distribution with mean A. The number of hours to complete each job, Y}, is gamma distributed with parameters 05 and 6. The total time to complete all jobs in a week is T = 2:11 Yi. Find the expected value and the variance of the total time to complete all jobs

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