4. When John enters the bank office, there are four customers waiting in line and one...

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4. When John enters the bank office, there are four customers waiting in line and one customer is being served. There is a single clerk and the service time is exponentially distributed with λ-10 customer per hour, independent of everything else. (a) (2 points) What is the average service time per customer? (b) (4 points) What is the distribution of Johns waiting time? (c) (4 points) Calculate the expected value and variance of Johns waiting time. (d) (10 points) It has been 15 minutes and now John is the first person in queue (Y- 15). Calculate the probability that John waits more than 30 minutes in total? What is Johns expected waiting time?

math Statistics-And-Probability

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Answer 1

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a) x : Random variable Let x be the weuthng time of the next c ustamer to be served (expon enha/ wi mean ya vero e service ti xp uohhs Waihrg teHe 2 Variance of Tohns Ncuting tima PLY〉30 lo 13 lO

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