Suppose a high-tech shop opens at 9 am. During the release of a long-waited new generation smart phone people start arriving at the shop at 8 am and queue in front of the shop. The arrivals follow a non-homogeneous Poisson process with rate function λ(t) = 25t2 (t = 0 refers to 8 am and t = 1 to 9 am).(a) Find the distribution of the number of people waiting in front of the shop when the shop opens.(b) If we know that exactly 30 people are waiting in front of the shop at 9 am, what is the probability that exactly 20 of them arrived between 8.30am and 9 am?(c) Calculate the average waiting time of a person who is present at 9 am.

Given:- Suppose a high-tech shop opens at 9 am. During the release of a long-waited new generation…

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6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose a high-tech shop opens at 9 am. During the release of a long-waited new generation smart phone people start arriving at the shop at 8 am and queue in front of the shop. The arrivals follow a non-homogeneous Poisson process with rate function λ(t) = 25t2 (t = 0 refers to 8 am and t = 1 to 9 am).
1. (a) Find the distribution of the number of people waiting in front of the shop when the shop opens.
2. (b) If we know that exactly 30 people are waiting in front of the shop at 9 am, what is the probability that exactly 20 of them arrived between 8.30am and 9 am?
3. (c) Calculate the average waiting time of a person who is present at 9 am.