Q2 Cars arrive at a parking lot at a rate of 20 per hour. Assume that a Poisson process model isappropriate. Answer the following questions. No derivations are needed but a justification of youranswers is necessary.Q2(i.) What assumptions are necessary to model the arrival of cars as a Poisson process?Q2 (ii.) What is the expected number of cars that arrive between 10:30 a.m. and 12:45 p.m.?Q2 (iii.) Suppose you walk into the parking lot at 11:05 a.m.; how long do you have to wait onaverage to see a car entering the lot?Q2 (iv.) Assume that the lot opens at 8 a.m. what is the expected time at which the tenth cararrives at the parking lot.

Given: Cars arrive at a parking lot at a rate of 20 per hour. That is, λ=20

Answered: Q2 Cars arrive at a parking lot at a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

If we are watching buses pass by in a Poisson process with buses arriving at the average rate of 10 per hour, then what is the probability (to three decimal place accuracy) that between 3:06pm and 3:24pm we see less than 5 buses?
If we are watching buses pass by in a Poisson process with buses arriving at the average rate of 10 per hour, then what is the probability (to three decimal place accuracy) that between 3:06pm and 3:24pm we see at most 5 buses?
Huang’s television-repair service receives an average offour TV sets per 8-hour day to be repaired. The servicemanager would like to be able to tell customers that theycan expect their TV back in 3 days. What average repairtime per set will the repair shop have to achieve to provide 3-day service on the average? (Assume that thearrival rate is Poisson distributed and repair times areexponentially distributed.)
A pump operates 1000 hours/year. Under a minimal repair concept, the pump failures generated a non-homogenous Poisson process having the following intensity function with t measured in operating hours. Row(t)=0.00003t^2. a) From the information given, is the rate of occurance of failure (ROCOF) increasing, decreasing or remaining constant? b) Calculate the number of expected failures of the pump over 1000 hours of operation. c) Calculate the MTBF for the 1000-hour operation. d) The repair time of the pump is best described by the following probability density function h(t)=t^2/3 for 0<_t<_3 hours. WHat is the mean time of repair, in hours? e)What is the inherent availability of the pump over the 1000 hours?
At 15:00 it is the end of the school day, and it is assumed that the departure of the students from school can be modelled by a Poisson distribution. On average, 24 students leave the school every minute. (e) There are 200 days in a school year. Given that Y denotes the number of days in the year that at least 700 students leave before 15:30, find (ii) P(Y > 150).
Suppose small aircraft arrive at a certain airport accordingto a Poisson process with rate a 5 8 per hour, so thatthe number of arrivals during a time period of t hours isa Poisson rv with parameter m 5 8t.a. What is the probability that exactly 6 small aircraftarrive during a 1-hour period? At least 6? At least 10?b. What are the expected value and standard deviationof the number of small aircraft that arrive during a90-min period?c. What is the probability that at least 20 small aircraftarrive during a 2.5-hour period? That at most10 arrive during this period?
Consider the previous question above, A further study determined that cars arrive to this shopping center according to a non-stationary Poisson process. The mean arrival rate increases linearly from 0.17 to 0.49 cars per minute between 10 am and 2 pm. Then the rate remains constant at 0.49 cars per minute between 2 pm and 4 pm. Finally, the rate changes to a constant 0.33 cars per minute between 4 pm and 5 pm. What is the probability that 60 cars will arrive between 1:45 pm and 4:15 pm?
Starting at time 0, amusement park attendees enter the park and arrive according to a Poisson process with rate equal to 48 per hour. If 10 attendees arrive in the first minute, what is the expected number of attendees that arrive in the first two minutes?
If it is known that the random process X (t) is a stationary process in a broad sense, could the following autocorrelation function belong to this process? Explain the reason for your answer.
Suppose taxicab arrivals from 3 to 5 p.m. are a Poisson process. If the cabs arrive at an average rate of 18 per hour, what is the probability that a person will have to wait up to 5 minutes for a cab?
2a) The number of flowers per square meter in Sarah’s garden has a Poisson distribution with mean 0.35. Her garden is covered with 150 square meters of grass. Find lambda λ? 2b) The number of flowers per square meter in Sarah’s garden has a Poisson distribution with mean 0.35. Her garden is covered with 150 square meters of grass. Using Normal approximation, we will need to find the probability that the Sarah’s garden will contain less than 45 flowers. First graph and answer what is the continuity correction? 2c) Using the previous results for lambda and continuity correction, find z, then graph and use your table to find φ table value of z Write down your final answer for the probability that Sarah’s garden will contain less than 45 flowers as a decimal number with 4 decimal places.
Huang’s television-repair service receives an average offour TV sets per 8-hour day to be repaired. The servicemanager would like to be able to tell customers that theycan expect their TV back in 3 days. What average repair time per set will the repair shop have to achieve to pro-vide 3-day service on the average? (Assume that the arrival rate is Poisson distributed and repair times areexponentially distributed.)

SEE MORE QUESTIONS

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS