In a printing shop, print requests arrive randomly and independently at an average rate of 20 per hour and are placed in a queue according to arrival times. Suppose that the time it takes to process each request is exponentially distributed and that the print times for different jobs are independent. (a) Calculate the probability that this printer will be idle for the next 5 minutes if the queue is currently empty. (b) A particular printer in this shop is capable of printing five pages per minute. The average request results in ten printed pages of poster. (1) Calculate the probability that the next request will take more than 2 minutes to process. (ii) There is currently one job in the queue and it has been active for the last 5 minutes. Calculate the probability that this job will still be active 1 minute from now. (iii) State the property of the distribution that you can see from the result in (ii).

In a printing shop, print requests arrive randomly and independently at an average rate of 20 per hour and are placed in a queue according to arrival times. Suppose that the time it takes to process each request is exponentially distributed and that the print times for different jobs are independent. (a) Calculate the probability that this printer will be idle for the next 5 minutes if the queue is currently empty. (b) A particular printer in this shop is capable of printing five pages per minute. The average request results in ten printed pages of poster. (1) Calculate the probability that the next request will take more than 2 minutes to process. (ii) There is currently one job in the queue and it has been active for the last 5 minutes. Calculate the probability that this job will still be active 1 minute from now. (iii) State the property of the distribution that you can see from the result in (ii).

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

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In a printing shop, print requests arrive randomly and independently at an
average rate of 20 per hour and are placed in a queue according to arrival times.
Suppose that the time it takes to process each request is exponentially
distributed and that the print times for different jobs are independent.
(a) Calculate the probability that this printer will be idle for the next 5 minutes
if the queue is currently empty.
(b) A particular printer in this shop is capable of printing five pages per
minute. The average request results in ten printed pages of poster.
(i)
Calculate the probability that the next request will take
more than 2 minutes to process.
(ii)
There is currently one job in the queue and it has been active for the
last 5 minutes. Calculate the probability that this job will still be
active 1 minute from now.
(iii) State the property of the distribution that you can see from the
result in (ii).
(iv) There are currently five jobs in the queue - one active and four
waiting to be processed. A new customer submit a job to this printer
and it becomes the sixth job in the queue. Calculate the probability
that he will have to wait more than 5 minutes for the printer to
begin processing his job. Assume that the time between consecutive
jobs in the queue is negligible.
(v)
Name the alternative distribution of the random variable that you
are considering in (iv).

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