Suppose that visitors to a state carnival which is open from 5 pm to 10 pm daily arrive according toa non-homogeneous Poisson process. The rate at which visitors arrive decreases linearly from 30 perhour at 5 pm to 5 per hour at 10 pm. What is the probability that 3 customers will arrive between9:30 pm and 10 pm?

Solution: From the given information, arrival of visitors follows a non-homogeneous Poisson process.…

Answered: Suppose that visitors to a state…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Suppose that customers arrive at a diner at a Poisson rate of A = 3 per hour. What is the probability that exactly 6 customers arrive between 1PM and 3PM and that exactly 4 customers arrive between 4PM and 5PM? Hint: You're dealing with two discrete rv's, in this case. (Answer as a decimal number, and round to 3 decimal places).
6. The Hayward campus has become a dangerous place for people on motorized scooters. There are six intersections on the campus loop, independent of one another, for which accidents occur following a Poisson process with different rates, say A₁,..., A6, per week. The Board of Campus Safety is interested in the total number of accidents that occur next semester (sixteen weeks). (a) Using the moment generating function, derive the distribution of the total number of accidents that occur next semester at these intersections combined. Make sure you define all variables used. (b) Suppose, from past experience, it is known that the values of A₁,..., A6 are 0.8, 1.2, 2.9, 0.2, 1.1, and 2.8 respectively. What is the probability that there are between 142 and 146 (inclusively) accidents on the campus loop next semester? (c) What is the expected value and standard deviation for the number of accidents on the campus loop next quarter?
The time between successive calls to a corporate office is exponentially distributed with a mean of 10 minutes. Assume that the times between successive calls are independent of each other. Thus, the calls arrive according to a Poisson process. Determine x such that the probability that there are no calls within x minutes is 0.005.
The arrival of buses from the campus to student housing in the late afternoon is modeled by a Poisson process with an interarrival time of 30 minutes. Consider the situation where a bus has just arrived at 4.29 PM. (a) A student arrives at 4.30 PM and misses the bus. Find the expected value of time that the student will have to wait for the next bus to student housing? (b) At 4.52 PM the next bus has not yet arrived, and another student comes to the bus stop. Find the expected value of time that these two students will have to wait for the next bus?
It is known from past experience that in a certain plant there are on the average 4 incidents per month. Find the proba- bility that in a given year there will be less than 4 accidents. Assume Poisson distribution.
2. Suppose the defective rate at a particular factory is 1%. Suppose 50 parts were selected from the daily output of parts. Let X denote the number of defective parts in the sample. a) Find the probability that the sample contains exactly 2 defective parts. b) Use Poisson approximation to find the probability that the sample contains exactly 2 defective parts. c) Find the probability that the sample contains at most 1 defective part. d) Use Poisson approximation to find the probability that the sample contains at most 1defective part.
please show steps neatly with answer.
4. The owner of a tree farm specializes in growing pine trees. They are grown in rows of 50 trees and the owner has found on the average, about 4 trees per row will not be suitable to sell. Assuming that the Poisson distribution is applicable here, find the probability that a row of tree selected for shipment will contain 2 unsaleable trees.
Consider two types of call arrivals to a cell in a mobile telephone network: new calls that originate in a cell and calls that are handed over from neighboring cells. It is desirable to give preference to handover calls over new calls. For this reason, some of the channels in the cell are reserved for handover calls, while the rest of the channels are available to both types of calls. = = Suppose that all calls arrive in a cell according to a Poisson process with rate Anc 125 calls per hour for new calls, and λho 50 calls per hour for handover calls. The cell has a capacity of 10 channels. Each call occupies 1 channel and the call time has an exponential distribution with mean two minutes. Suppose that no channels are reserved for handover calls. (a) Calculate the blocking probability in the cell and find the average number of channels used. (b) When a call has to wait, find its average waiting time.
ee
A manufacturing company claims that the number of machine breakdowns follows a Poisson distribution with a mean of two breakdowns every 500 hours. Let x denote the time (in hours0 between successive breakdowns. assuming that the manufacturing company's claim is true, find the probability that the time between successive breakdowns is at most five hours.
A service company receives on average 4 service requests per day. The requests are received randomly according to Poisson process. The company has 2 service engineers and sends one engineer to attend each request. 1 An engineer needs an exponentially distributed service time with the mean of day(s). 2 The company's policy is to have maximum of 2 requests waiting in the queue If this number is reached, all incoming requests are rejected (sent to a competitor). Answer the following questions based on the information provide above: (a) Using the Kendall's notation, indicate what type of queueing system it is: (b) Compute the system state probabilities (provide at least 3 decimals): Po = P1= P2 = P3 = Pa = (c) Compute the expected total number of customer requests (waiting and served) in the system. ELL] = (d) Compute the expected number of accepted requests. Aaccepted = (e) Compute the expected total processing time (waiting + being served) for the accepted requests. E[Time] =

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS