5. Customers arrive at coffee shop according to a Poisson process at a mean rate of 5 customers every 10 minutes. (a) Let X denote the waiting time (in minutes, counted from 7 am) until the first customer arrives. What is the pdf of X? Name the distribution if it has a name. (b) Find the probability that the owner of the coffee shop will have to wait longer than 5 minutes before the arrival of the first customer. (c) Find the conditional probability that the owner of the coffee shop will have to wait longer than 5 minutes before the arrival of the first customer, given that no customer came in the first three minutes.
5. Customers arrive at coffee shop according to a Poisson process at a mean rate of 5 customers every 10 minutes. (a) Let X denote the waiting time (in minutes, counted from 7 am) until the first customer arrives. What is the pdf of X? Name the distribution if it has a name. (b) Find the probability that the owner of the coffee shop will have to wait longer than 5 minutes before the arrival of the first customer. (c) Find the conditional probability that the owner of the coffee shop will have to wait longer than 5 minutes before the arrival of the first customer, given that no customer came in the first three minutes.
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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