Question
In: Statistics and Probability
Customers arrive in a certain shop according to an approximate Poissonprocess on the average of two...
Customers arrive in a certain shop according to an approximate Poissonprocess on the average of two every 6 minutes.
(a) Using the Poisson distribution calculate the probability of two or more customersarrive in a 2-minute period.
(b) Consider X denote number of customers and X follows binomial distribution withparametersn= 100. Using the binomial distribution calculate the probability oftwo or more customers arrive in a 2-minute period.
(c) Let Y denote the waiting time in minutes until the first customer arrives. (i) Whatis the pdf ofY? (ii) Findq1=π0.75
(d) Let Y denote the waiting time in minutes until the first customer arrives. What isthe probability that the shopkeeper will have to wait more than 3 minutes for thearrival of the first customer ?
(e) What is the probability that shopkeeper will wait more than 3 minutes before bothof the first two customers arrive?
Solutions
orchestra answered 1 year agoRelated Solutions
Customers arrive in a certain shop according to an approximate Poisson process on the average of...
Customers arrive in a certain shop according to an approximate
Poisson process on the average of two every 6 minutes.
(a) Using the Poisson distribution calculate the probability of
two or more customers arrive in a 2-minute period.
(b) Consider X denote number of customers and X follows binomial
distribution with parameters n= 100. Using the binomial
distribution calculate the probability oftwo or more customers
arrive in a 2-minute period.
(c) Let Y denote the waiting time in minutes until...
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a. What is the probability that 3 customers arrive between
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b. What is the probability that 3 customers arrive between
12:00pm and 12:15pm and 6 customers arrive between 12:30pm and
1:00pm?
c. What is the probability that 3 customers arrive between
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1:00pm?
d. What is the probability that a...
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Suppose we have a single server in a shop and customers arrive in the shop with...
Suppose we have a single server in a shop and customers arrive
in the shop with a Poisson arrival distribution at a mean rate of
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Poisson process at a mean rate of 3 per hour. The
system has two servers, both of which serve both types of customer.
All service times have exponential distribution with a mean of 10
minutes. Service is provided on a first-come-first-served
basis.
a. What is the probability distribution...
A queueing system serves two types of customers. Type 1 customers arrive according to a Poisson...
A queueing system serves two types of customers. Type 1
customers arrive according to a Poisson process with a mean rate of
5 per hour. Type 2 customers arrive according to a
Poisson process at a mean rate of 3 per hour. The
system has two servers, both of which serve both types of customer.
All service times have exponential distribution with a mean of 10
minutes. Service is provided on a first-come-first-served
basis.
a. What is the probability distribution...
A queueing system serves two types of customers. Type 1 customers arrive according to a Poisson...
A queueing system serves two types of customers. Type 1
customers arrive according to a Poisson process with a mean rate of
5 per hour. Type 2 customers arrive according to a
Poisson process at a mean rate of 3 per hour. The
system has two servers, both of which serve both types of customer.
All service times have exponential distribution with a mean of 10
minutes. Service is provided on a first-come-first-served
basis.
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A barber shop has an average of 12 customers between 8.00am and 9.00am every Saturday. Customers arrive according to Poisson distribution. Let X represent the time between arrivals.
A barber shop has an average of 12 customers between 8.00am and 9.00am every Saturday. Customers arrive according to Poisson distribution. Let X represent the time between arrivals.
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Customers arrive at a two-server system according to a Poisson process having rate λ = 5....
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and server 2 free will enter service with server 2. An arrival
finding both servers busy goes away. Once a customer is served by
either server, he departs the system. The service times at server i
are exponential with rates μi, where μ1 = 4, μ2...
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