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Cars arrive at a toll booth according to a Poisson process at a mean rate of 15 cars every 30 minutes. Find the probability that the toll collector will have to wait longer than 28.41 minutes before collecting the 10th toll. Use two approaches to answer the question, namely (i) the relationship between gamma and Chi-square distributions, and (ii) the relationship between Poisson and gamma distributions. You can use R to obtain the final numerical answers.

Cars arrive at a toll booth according to a Poisson process at a mean rate of 15 cars every 30 minutes. Find the probability that the toll collector will have to wait longer than 28.41 minutes before collecting the 10th toll. Use two approaches to answer the question, namely (i) the relationship between gamma and Chi-square distributions, and (ii) the relationship between Poisson and gamma distributions. You can use R to obtain the final numerical answers.

MATLAB: An Introduction with Applications
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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Cars arrive at a toll booth according to a Poisson process at a mean rate of 15 cars every 30 minutes. Find the probability that the toll collector will have to wait longer than 28.41 minutes before collecting the 10th toll. Use two approaches to answer the question, namely (i) the relationship between gamma and Chi-square distributions, and (ii) the relationship between Poisson and gamma distributions. You can use R to obtain the final numerical answers.
Transcribed Image Text:Cars arrive at a toll booth according to a Poisson process at a mean rate of 15 cars every 30 minutes. Find the probability that the toll collector will have to wait longer than 28.41 minutes before collecting the 10th toll. Use two approaches to answer the question, namely (i) the relationship between gamma and Chi-square distributions, and (ii) the relationship between Poisson and gamma distributions. You can use R to obtain the final numerical answers.
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