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Unformatted text preview: 10.11 Problems 383 If the amount of money paid on each policy is uniformly distributed be- tween $2000 and $10,000, what is the mean of the total amount of money that the company pays out in a four-week period? 10.22 Customers arrive at the neighborhood bookstore according to a Poisson process with an average rate of 10 customers per hour. Independent of other customers, each arriving customer buys a book with probability 1 / 8. a. What is the probability that the bookstore sells no book during a par- ticular hour? b. What is the PDF of the time until the first book is sold? 10.23 Joe is a student who is conducting experiments with a series of lightbulbs. He started with 10 identical lightbulbs, each of which has an exponentially distributed lifetime with a mean of 200 hours. Joe wants to know how long it will take until the last bulb burns out (or fails). At noontime Joe stepped out to get some lunch with 6 bulbs still on. Assume that Joe came back and found that none of the 6 bulbs has failed. a. After Joe came back, what is the expected time until the first bulb fail- ure? b. What is the expected length of time between the fourth bulb failure and the fifth bulb failure? 10.24 Three customers A , B , and C , simultaneously arrive at a bank with two tellers on duty. The two tellers were idle when the three customers arrived, and A goes directly to one teller, B goes to the other teller, and C waits until either A or B leaves before she can begin receiving service. If the service times provided by the tellers are exponentially distributed with a mean of 4 minutes, what is the probability that customer A is still in the bank after the other two customers leave? 10.25 The times between component failures in a certain system are exponen- tially distributed with a mean of 4 hours. What is the probability that at least one component failure occurs within a 30-minute period? 10.26 Students arrive at the professors office for extra help according to a Pois- son process with an average rate of 4 students per hour. The professor does not start the tutorial until at least 3 students are available. Students who arrive while the tutorial is going on will have to wait for the next session. a. Given that a tutorial has just ended and there are no students currently waiting for the professor, what is the mean time until another tutorial can start? b. Given that one student was waiting when the tutorial ended, what is the probability that the next tutorial does not start within the first 2 hours? 384 Chapter 10 Some Models of Random Processes 10.27 Customers arrive at a bank according to a Poisson process with an average rate of 6 customers per hour. Each arriving customer is either a man with probability p or a woman with probability 1- p . It was found that in the first 2 hours the average number of men who arrived at the bank was 8....
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This note was uploaded on 01/05/2010 for the course STAT 350 taught by Professor Carlton during the Fall '07 term at Cal Poly.
- Fall '07