We have seen that if the sum of a random number of random variables. When N is indepen...

We have seen that if the sum of a random number of random variables. When N is independent of the Xi’s, it can be shown that

a. If the expected number of components brought in on a particularly day is 10 and expected repair time for a randomly submitted component is 40 min, what is the expected total repair time for components submitted on any particular day?

b. Suppose components of a certain type come in for repair according to a Poisson process with a rate of 5 per hour. The expected number of defects per component is 3.5.What is the expected value of the total number of defects on components submitted for repair during a 4-hourperiod? Be sure to indicate how your answer follows from the general result just given.