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 (iv.) Assume that the lot opens at 8 a.m. what is the expected time at which the tenth cararrives at the parking lot.Q2(v.) What is the expected waiting time between the arrival of the 10th and 11th car?Q2(vi.) How is the waiting time between the arrival times of 10th and 12th car distributed? Writethe density function of the waiting time.

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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

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A producer of pocket calculators purchases the main processor chips in lots of1,000. The producer would like to have a 1 percent rate of defectives but willnormally not refuse a lot unless it has 4 percent or more defectives. Samples of50 are drawn from each lot, and the lot is rejected if more than two defectives arefound.b. Compute A and B Use the Poisson approximation for your calculations
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).
A Packages arrive at a warehouse that has a single reception point with a Poissondistribution mean of once every 12 minutes. It takes on the exponentially distributedaverage of 9-minutes to process each package.(a) What is the average wait time of a package in the queue?(b) On the average, how many packages are in the queue at any given time?(c) On the average, how many packages are in the system at any given time?(d) On the average, what is the wait time of packages in the system?(e) What percent of the time is the server idle?(f) What is the probability that there are exactly 7 packages in the system at any givenpoint in time>
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?
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.)
Taking expectation of a Wiener process wich is normally distrubuted with n(0,1) what is the value of that expectation?
In a video game with a time slot of fixed length T, signals are generated according to a Poisson process with rate λ, where T > 1/λ. During the time slot you can push a button only once. You win if at least one signal occurs in the time slot and you push the button at the occurrence of the last signal. Your strategy is to let pass a fixed time s with 0 < s < T and push the button upon the first occurrence of a signal (if any) after time s. What is your probability of winning the game? What value of s maximizes this probability?
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.
A computer system queues up batch jobs and processes them on an FCFS basis. Between 2 and 5 P.M., jobs arrive at an average rate of 30 per hour and require an average of 1.2 minutes of computer time. Assume the arrival process is Poisson and the processing times are exponentially distributed.a. What is the expected number of jobs in the system and in the queue in the steady state?b. What are the expected flow time and the time in the queue in the steady state?c. What is the probability that the system is empty?d. What is the probability that the queue is empty?e. What is the probability that the flow time of a job exceeds 10 minutes?
Assume that interest rate is 0.02, growth rate of the Geometric Brownian Motion of the stock price is 0.03, and its volatility is 0.1. The current stock price is $100. If one independent sample from a standard normal distribution is 0.6, simulate the stock prices at t = 0.05 using the Euler-Maruyama scheme under the risk-neutral probability measure.
Assume that the variables Y1, Y2,... in a compound Poisson process have Bernoulli distribution with parameter p . Show that the process reduces to the Poisson process of parameter λp.
(a) Auto vehicles arrive at a petrol pump, having one petrol unit, in Poisson fashion with anaverage of 10 units per hour. The service time is distributed exponentially with a mean of3 minutes. Find the following:i. Average number of units in the system ii. Average waiting time iii. Average length of queue

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