Please help me with this question, i will be very very appreciate!!!!! Problem 3We 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].

The continuous-time Markov chain (CTMC) for this problem is a birth-death process, where each state…

Answered: Problem 3 We consider a group of 4…

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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Suppose Martin is a very talented used-car salesman. Whenever Martin talks to a new customer, there is a 90% chance that he convinces the customer to purchase one of his used cars. Brian, Martin's boss, is envious that Martin sells many more cars than he does. Because of his jealousy, Brian institutes a new rule that Martin is only allowed to talk to 35 customers per day. Thus, Martin continues to work each day until he speaks to 35 customers, at which point Brian sends him home. Let ? represent the number of used cars that Martin sells on a given day. What are the mean, ?, and variance, ?^2, of ?? Please round your answers to the nearest two decimal places. ?=_______? ?^2=_________?
From time to time, the UTM Human Resource (UTMHR) department observes various employees fortheir work productivity. Recently UTMHR wanted to check whether the four employees at theDepartment XYZ counters, serve on average the same number of customers per hour. The HR managerobserved each of the four employees for a certain number of hours. The following Table 5 gives thenumber of customers served by the four employees during each of the observed hours. employee a employee b employee c employee d 19 14 11 24 21 16 14 19 26 14 21 21 24 13 13 26 18 17 16 20 employee a employee b employee c employee d mean 21.6 14.8 15.0 22.0 s 3.4 ? 3.8 ? c) Find variance between sample,d) Find variance within sample, e) Calculate the test statistic, F.f) Determine the numerator and denominator.g) Find the critical value of F at the 5% significance level, and test the claim that the mean numberof customers served per hour by each of these four employees is…
2. Two individuals, A and B, both require kidney transplants. If she does not receive a new kidney, then A will die after an exponential time with rate iA, and B after an exponential time with rate uB. New kidneys arrive in accordance with a Poisson process having rate A. It has been decided that the first kidney will go to A (or to B if B is alive and A is not at that time) and the next one to B (if still living) (a) What is the probability that A obtains a new kidney? (b) What is the probability that B obtains a new kidney? (c) What is the probability that neither A nor B obtains a new kidney? (d) What is the probability that both A and B obtain new kidneys?
a man is investigating the populaion of bear in two areas. Area 1 and Area 2. He expect the number of bear to be X and Y in area 1 and area 2 to be Poisson- distributeted. If a bear is in one of his areas , there is an expected probability of 0.2 for the dear to be observed. If there are 5 dear in one of the areas what is the probability for 3 of them to be observed and what is expected dears observed ?
From time to time, the UTM Human Resource (UTMHR) department observes various employees fortheir work productivity. Recently UTMHR wanted to check whether the four employees at theDepartment XYZ counters, serve on average the same number of customers per hour. The HR managerobserved each of the four employees for a certain number of hours. The following Table 5 gives thenumber of customers served by the four employees during each of the observed hours. employee a employee b employee c employee d 19 14 11 24 21 16 14 19 26 14 21 21 24 13 13 26 18 17 16 20 a) Define the hypothesis null, H0 and hypothesis alternative, H1.b) Given below are means and standard deviation for some of the employees. Calculate thestandard deviation for Employee B and D.
On average, 24 customers per hour arrive in the checkout line of a clothing store (following a Poisson process). The service times of the store are exponentially distributed with an average of 2.3 minutes. When there are less than 5 customers in the checkout area (queue and attended), the store keeps only one box open. If there are from 5 to 9, then the store operates with two open boxes to pay. If there are more than 9 clients then open 3 boxes. 1. On average, how many customers are there in line? 2. What is the probability of having 2 or more open cash registers?
2. A vehicle travelling in a minor street arrives at an intersection with a main street. The driver has to decide when to cross the (one-way) main street. Suppose that: each vehicle on the main street independently has a 90% chance of being a car and a 10% chance of being a bus, and ● the time interval between any two vehicles on the main street has a 50% chance being 4 seconds and a 50% chance being 6 seconds. The driver will cross the main street when x, the time until the next vehicle on the main street to reach the intersection, is at least 3 seconds if that vehicle is a car. If the next vehicle is a bus, the driver will cross if x>= 5 seconds. a. What is the probability that the driver will arrive in a 4-second interval? b. What is the probability that the driver will cross the main street immediately? C. If the driver arrived exactly when a vehicle on the main street has just passed the intersection, what is the probability that he will allow k vehicles on the main street to pass…
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 ]
6. (The following problem is not for credit; this is the homework problem I'd assign for the material from the lecture on Monday, May 1st. You don't have to write this up, but it's there for practice if you want it.) A broken gumball vending machine spontaneously spits out gumballs of different colors. Over a short time scale, we can model this as a Poisson process which independently produces 0.1 red gumballs per second, 0.2 blue gumballs per second, and 0.3 yellow gumballs per second. Identify the distribution of the following quantities: (a) The number of blue gumballs produced in 1 minute. (b) The time until 5 yellow gumballs are produced. (c) The time interval between two consecutive gumballs produced (of any color). (d) The number of red gumballs produced after 10 total gumballs of all colors have been produced.
Question 4 Multi-Server QueueA supermarket manager is trying to decide how many cashers to employ for the peak time. The service times for check outs are exponentially distributed with a mean service time of 3 minutes. Customer arrivals to cashiers follow a Poisson arrival process with an average 110 customers per hour.a. What is the minimum number of cashers that would be needed to have the utilization less than one?b. If the waiting time is too long, customers might leave the store or even do not enter the store. It is estimated that for every minute of waiting time, the supermarket loses a potential profit of 50 HKD every hour from lost sales. The hourly wage for a casher is 80 HKD / hour. How many cashers should the supermarket employ to maximize its profit? (Keep four decimal places.
Is there a link between dark chocolate and weight loss when compared to milk chocolate? A nutritionist gathers 60 people, selected at random, then randomly assigns half of the group to eat a single dark chocolate bar after dinner each night and the other half to eat a single milk chocolate bar after dinner each night for 6 months. Everyone is to keep track of the other food they eat in an app provided. The nutritionist then compares each person’s weight after the 6 months to their weight before eating the different chocolates accounting for the other calories consumed. 12) What type of study does this describe? a) Survey b) Observational study c) Experimental study
There are X-Mart and Y-Mart convenience stores. It is assumed that each customer purchases once a week at one of the two supermarkets (but not both). In a study, a sample of 100 buyers was taken for 10 weeks. From this research it is known that if buyers go to X-mart store one week, 85 people will still buy at X-mart store the following week and if buyers go to Y-mart store one week, 70 people will still buy at Y-mart store. mart the following week. 1. Make a table and matrix of transition probabilities. 2. If John purchases at X-mart in the first week, what is the probability that Bob purchases at X-store in the third and fourth weeks?

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