Question

3. (-/6 Points] DETAILS DEVORESTAT9 5.E.081. MY NOTES PRACTICE ANOTHER We have seen that if E(X1) = E(X) = ... = E(X) = 4, then E(X, + ... + x) = nu. In some applications, the number of X's under consideration is not a fixed number n but instead is an rv N. For example, let N = the number of components that are brought into a repair shop on a particular day, and let X, denote the repair shop time for the ith component. Then the total repair time is X, + x2 + ... + Xxx the sum of a random number of random variables. When N is independent of the X;'s, it can be shown that E(X1 + ... + Xx) = E(N). H. (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, in minutes, for components submitted on any particular day? min (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 2.5. What is the expected value of the total number of defects on components submitted for repair during an 8-hour period? Be sure to indicate how your answer follows from the general result just given. For this process we would expect components to come in for repair during an 8-hour period. This number is ---Select-- v using the above notational scheme. Similarly, we would expect to see defects on each repair. This number is --Select--- in the above notational scheme. So, we would expect to see defects over an 8-hour period time period. Need Help? Read it Talk to a Tutor

Answer 1

a)

= 40 *10

= 400 minutes

b)

40 Componets , cacluated using , 2.5 defect , calculated , 100 defects over 8 hour

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