1. Alice has 2 jobs that she will process sequentially. The first job takes an exponential...

1. Alice has 2 jobs that she will process sequentially. The first job takes an exponential amount of time with a mean of 15 minutes. Once the first job is completed, then we start working on the second job. The second job also takes an exponential amount of time to complete with a mean of 15 minutes. (a) Let T be the total time to complete both jobs. Give the distribution of T, its mean and its standard deviation. (b) Compute the probability that it would take more than 45 minutes to complete both jobs. (c) Suppose that Bob takes an exponential amount of time to process both jobs (i.e. both, not each) with a mean time of 30 minutes. Compute the probability that it would take Bob more than 45 minutes to complete both jobs. (d) Suppose that Alice and Bob start to work at the same moment. Give the probability that Bob will complete both jobs before Alice.

2. Suppose that Alice that an exponential amount of time with a mean of 20 minutes for the first job, but the second job takes an exponential amount of time with a minutes of 30 minutes. Let T be the total time needed (in minutes) to complete both jobs. (a) Give the moment generating function for T. (b) Clearly E[T] = 50, however use the moment generating function in part (a) to show that this is indeed the mean of T. (c) What is the probability that the second job would take less time than the first job?

Expert Solution

orchestra answered 2 years ago

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