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(vii.) As an outsider, you watch the cars entering the parking lot for half an hour in themorning (between 9 a.m. and 10:30 a.m.) and then for half an hour during lunchtime (between 12p.m. and 1:30 p.m.). What can you say about the number of cars arriving at the parking lot duringthe two half-hour periods?

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).
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?
Give the resulting rate when two independent Poisson processes with rates λ1=2.546 and λ2=3.326 are merged. What is the exact rate?
The manager of a market can hire either Mary or Alice. Mary, who gives you service at an exponential rate 20 customers per hour, can be hired at a rate of $3 per hour. Alice, who gives service at an exponential rate of 30 customers per hour, can hired at a rate of $C per hour. The manager estimates that, on the average, each customer’s time is worth $1 per hour and should be accounted for in the model. Assume customers arrive at a Poisson rate of 10 per hour. a) What is the average cost per hour if Mary is hired? If Alice is hired? b) Find C if the average cost per hour is the same for Mary and Alice.
Suppose the customers arrive at a Poisson rate of on eper every 12 minutes, and that the service time is exponential at a rate of one service per 8 minutes. What are the average number of customers in the system(L) and the average time a customer spends in the system(W)?
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?
Suppose 1.5% percent of the ball bearings made by a machine are defective and the ball bearings are packed 200 to a box. Compute the pf of the number of defective ball bearings in the box and compare it to the Poisson approximation.
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.
For a non-homogeneous Poisson process, the intensity function is given by λ(t) = 5 if t is in (1, 2] or (3, 4]; λ(t) = 3 if t is in (0, 1] or (2, 3]. Find the probability that the number number of observed occurrences in the time period (1.5; 4] is more than 2. Round answer to 4 decimals.
Assume that N(t) is a Poisson process with rate λ=2024. ComputeP(N(s) =1000,N(t) =2023),for any s≤t

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