4 Suppose the process of entering customers to aclinic is a Poisson process with rate of onepatient in every 3 minutes. There is one doctorin the clinic and the time the doctor spent forvisiting each patient is according to discreteuniform on {2, 3,4} minutes. Suppose thesystem capacity is infinity.Simulate the clinic for 20 patients and estimatethe average time that each patient stay in clinicand in queue.

Given, Number of patients arriving every 3 minutes= 1 Number of patients arriving every 60 minutes=…

Answered: Suppose the process of entering…

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...

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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)?
Suppose that the number of customers arriving to a store follows the Poisson process with rate 1/λ per minute. Choose an option that is not correct. The expected number of customers arriving to the store between 9am and 11am is twice bigger than the expected number of customers arriving to the store between 10am and 11am. The number of customers arriving to the store between 9am and 10am is independent of the number of customers arriving to the store between 10am and 11am. The expected number of customers arriving to the store between 9am and 10am is 60λ. The number of customers arriving to the store between 9am and 10am follows the same distribution as the number of customers arriving to the store between 10am and 11am
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)? Now suppose that the arrival rate increases 20 percent.What is the corresponding change in L and W?
We consider a group of 4 students among which a rumour is spreading. At time 0, only one studentis aware of the rumour. Whenever two students meet, if one is aware of the rumour and not theother, the second one becomes aware of it. We assume that for any pair of students, the times atwhich they meet forms a Poisson process with rate 1. We also assume that, for the 6 possible pairsof students, we get 6 independent Poisson processes.a. Let A(t) be the number of students aware of the rumour at time t. We admit this is a continuous-time Markov chain. Give its parameters. No proof is required.b. Let T be the first time at which all students become aware of the rumour. Compute E[T ]
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 at a bank teller window the customers arrive in their cars at the average rate oftwentyper hour according to a Poisson distribution. Assume also that the bank teller spendsan average oftwo minutes per customer to complete a service, and the service time is exponentially distributed.Customers, who arrive from an infinite population, are served on a first-come-first-served basis,and there is no limit to possible queue length.a. What is the expected waiting time in the system per customer?b. What is the mean number of customers waiting in the system?c. What is the probability of zero customers in the system?d. What value is the traffic intensity?
What is the average length of non-empty queue that forms from time to time?
Suppose we know that the number visits to a webpage can be modeled as a Poisson Process with rate α = 4 per minute. The probability that the webpage gets exactly 10 visits during a particular 2 minute period is approximately
A group of medical professionals is considering theconstruction of a private clinic. If the medical de-mand is high (i.e., there is a favorable market for theclinic), the physicians could realize a net profit of$100,000. If the market is not favorable, they couldlose $40,000. Of course, they don’t have to proceedat all, in which case there is no cost. In the absenceof any market data, the best the physicians can guessis that there is a 50–50 chance the clinic will be suc-cessful. Construct a decision tree to help analyze thisproblem. What should the medical professionals do?
The process for cleaning up waste in a nuclear reactor core room eliminates 85% of the waste present in the area. If there is 1.7 kg of waste in the room at the beginning of the monitoring period and 2 kg of additionalwaste are generated each week, determine a recurrence relation and initial conditions describing the amount wn, of waste in the core room at the end of week n of the monitoring period.
A small bank has two tellers, one for deposis and one for withdrawals. The service time for each teller is exponentially distributed, with a mean of 1 min. Customers arriving at the bank according to a poisson process, with mean rate 40 per hour; it is assumed that depositors and withdrawers constitute separate poisson processes, each with mean rate 20 per hour , and that no customer is both a depositor and a withdrawer. The bank is thinking of changing the current arrangement to allow each teller to handle both deposits and withdrawals. The bank would expect that each teller's mean service time would increase to 1.2 min, but it hopes that the new arrangement would prevent long lines in front of one teller while the other teller is idle, a situation that occurs from time to time under the current setup. Analyze the two arrangements with respect to the average idle time of teller and the expected number of customers in the bank at any given time.
Let X1,...Xn be iid Poisson(λ1) and Y1,...,Ym be iid Poisson(λ2). Write out the GLRT for testing H0: λ1 = λ2 versus Ha: λ1 ≠ λ2.

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