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Problem 6: The networks Lab opens in the morning at 9:00 am. Students arrive at random for the Lab following a Poisson process with average rate A. Each student stays in the Lab for a random duration X. Students arriving when there is already a student in the Lab, wait outside in the corridor. Find the probability P that the second arriving student will have to wait and also find W, his/her mean waiting time, for the two cases (a) X = C constant; (b) X is exponentially distributed with mean .

Problem 6: The networks Lab opens in the morning at 9:00 am. Students arrive at random for the Lab following a Poisson process with average rate A. Each student stays in the Lab for a random duration X. Students arriving when there is already a student in the Lab, wait outside in the corridor. Find the probability P that the second arriving student will have to wait and also find W, his/her mean waiting time, for the two cases (a) X = C constant; (b) X is exponentially distributed with mean .

A First Course in Probability (10th Edition)
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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Problem 6: The networks Lab opens in the morning at 9:00 am. Students arrive at random for the Lab following a Poisson process with average rate A. Each student stays in the Lab for a random duration X. Students arriving when there is already a student in the Lab, wait outside in the corridor. Find the probability P that the second arriving student will have to wait and also find W, his/her mean waiting time, for the two cases (a) X = C constant; (b) X is exponentially distributed with mean .
Transcribed Image Text:Problem 6: The networks Lab opens in the morning at 9:00 am. Students arrive at random for the Lab following a Poisson process with average rate A. Each student stays in the Lab for a random duration X. Students arriving when there is already a student in the Lab, wait outside in the corridor. Find the probability P that the second arriving student will have to wait and also find W, his/her mean waiting time, for the two cases (a) X = C constant; (b) X is exponentially distributed with mean .
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