1 answer

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

Question:

4. When John enters the bank office, there are four customers waiting in line and one g served. There is a single distributed with A10 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 (Y4- 15). Calculate the probability that John waits more than 30 minutes in total? What is Johns expected waiting time?
4. When John enters the bank office, there are four customers waiting in line and one g served. There is a single distributed with A10 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 John's waiting time? (c) (4 points) Calculate the expected value and variance of John's waiting time (d) (10 points) It has been 15 minutes and now John is the first person in queue (Y4- 15). Calculate the probability that John waits more than 30 minutes in total? What is John's expected waiting time?

Answers

Qes-j When John Enters the bank oPPice, there are iting line and one customer is being served Gliven Thci. lhc a) x : Randm variable John enters the bank opPice When there are A customers ) Expected value op Johns hlaiting time Solv x: Random variable -> Let x be the waitingime op the next Castomer o be Served E exponential wth mean] Average Service time Per Customenr b) John enters the bunk opfice , hhen there gre. 4 Customers Let Y denotes Johns waiting time γ= x1X74 Shifted ExponentialExpected value of Johns waiting time 14 vatiance op Tohns waiting time UWcufin ラ PLY〉30) L e- (15-4) LO 30 Ll 13 10 lo

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