Customers arrive at coffee shop according to a Poisson process at a mean rate of 5 customers every 10 minutes. (a) Let X
Posted: Tue Apr 26, 2022 5:50 pm
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. (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 between
the gamma, Poisson, and chi-square distributions. You are allowed
to use R to obtain the numerical answers.
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. (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 between
the gamma, Poisson, and chi-square distributions. You are allowed
to use R to obtain the numerical answers.