(d) What is the probability that the owner of the coffee shop will have to wait longer than 28.41 minutes before the arrival of the 10th customer? Use two different approaches to solve this question by using the relationship be- tween the gamma, Poisson, and chi-square distributions. You are allowed to use R to obtain the numerical answers.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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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.
Transcribed Image Text: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.
(d) What is the probability that the owner of the coffee shop will have to wait longer
than 28.41 minutes before the arrival of the 10th customer?
Use two different approaches to solve this question by using the relationship be-
tween the gamma, Poisson, and chi-square distributions. You are allowed to use
R to obtain the numerical answers.
Transcribed Image Text:(d) What is the probability that the owner of the coffee shop will have to wait longer than 28.41 minutes before the arrival of the 10th customer? Use two different approaches to solve this question by using the relationship be- tween the gamma, Poisson, and chi-square distributions. You are allowed to use R to obtain the numerical answers.
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