At the end of a production shift, it is anticipated that there will be N jobs left to be processed, where N has a Poisson distribution with mean μ. Suppose the jobs are processed in parallel and the...

At the end of a production shift, it is anticipated that there will be N jobs left to be processed, where N has a Poisson distribution with mean μ. Suppose the jobs are processed in parallel and the times to complete them are independent with a distribution G. Let Q(t) denote the number of jobs in the system at time t, and let D(t) denote the number of jobs completed in (0, t]. Find the distributions of Q(t) and D(t). Is D a Poisson process? Answer this question when the jobs are processed serially (one at a time) and G is an exponential distribution with rate λ.