12. A laser printer on a local area computer network is capable of printing eight pages per minute. Print requests arrive randomly and independently at an average rate of 20 per hour and are placed in a queue according to their arrival times. The average request results in ten printed pages. Suppose that the time it takes to process each request is exponentially distributed and that the print times for different jobs are independent. a. What is the probability that this printer will be idle for the next 5 minutes if the queue is currently empty? b. What is the probability that the next request will take more than 2 minutes to process? c. There is currently one job in the queue and it has been active for the last 5 minutes. What is the probability that this job will still be active I minute from now? d. There are currently five jobs in the queue-one active and four waiting to be processed. You submit a job to this printer and it becomes the sixth job in the queue. What is the probability that you will have to wait more than 5 minutes for the printer to begin processing your job? More than 10 minutes? Assume that the time between consecutive jobs in the queue is negligible.

12. A laser printer on a local area computer network is capable of printing eight pages per minute. Print requests arrive randomly and independently at an average rate of 20 per hour and are placed in a queue according to their arrival times. The average request results in ten printed pages. Suppose that the time it takes to process each request is exponentially distributed and that the print times for different jobs are independent. a. What is the probability that this printer will be idle for the next 5 minutes if the queue is currently empty? b. What is the probability that the next request will take more than 2 minutes to process? c. There is currently one job in the queue and it has been active for the last 5 minutes. What is the probability that this job will still be active I minute from now? d. There are currently five jobs in the queue-one active and four waiting to be processed. You submit a job to this printer and it becomes the sixth job in the queue. What is the probability that you will have to wait more than 5 minutes for the printer to begin processing your job? More than 10 minutes? Assume that the time between consecutive jobs in the queue is negligible.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

12. A laser printer on a local area computer network is capable of printing eight pages
per minute. Print requests arrive randomly and independently at an average rate of
20 per hour and are placed in a queue according to their arrival times. The average
request results in ten printed pages. Suppose that the time it takes to process each
request is exponentially distributed and that the print times for different jobs are
independent.
a. What is the probability that this printer will be idle for the next 5 minutes if the
queue is currently empty?
b. What is the probability that the next request will take more than 2 minutes to
process?
c. There is currently one job in the queue and it has been active for the last 5 minutes.
What is the probability that this job will still be active I minute from now?
d. There are currently five jobs in the queue-one active and four waiting to be
processed. You submit a job to this printer and it becomes the sixth job in the
queue. What is the probability that you will have to wait more than 5 minutes for
the printer to begin processing your job? More than 10 minutes? Assume that the
time between consecutive jobs in the queue is negligible.

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