Anna University, Chennai Department of Computer Science Engineering ( Common to I.T) Fourth Semester MA Probability and Queueing. Subject Code: MA Subject Name: Probability and Queuing Theory Type: Question Bank Edition Details: Kings Edition Syllabus. MA — PROBABILITY AND QUEUEING THEORY (Regulation ). ( Common to Information Technology) Time: Three hours Answer ALL Questions PART.

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Prove that the sum of two independent Poisson process is a Poisson process. Define open Jackson networks. In a lot of 10, packets, how many packets would i be free defective blades? Random process is a function of time and the outcomes of a random experiment. Given that B is a R. Write down Pollaczek-khintchin formula. maa2262

Find the parameters of the distribution. The length of the shower in a tropical island in a rainy season has an exponential distribution with parameter 2, time being measured in minutes. The town has a daily stock of 35, litres. Arrivals from outside through node i follow a Poisson process with mean arrival rate ri.

Here Pij denote the one step syolabus probability. If customers arrive at the barber shop in a Poisson at m2a262 average rate of one in every 40 minutes, how long on the average a customer spends in the shop? The maximum temperature of a place at 0,t. If letters arrive for being typed at the rate of 15 letters per hour, find the traffic intensity.

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Continuous Random sequence 3. So, P is irreducible. The time required to repair a machine is exponentially distributed with parameter St. When do you say the Markov chain is regular? Find the marginal density function. Define First order stationary and Second order stationary process. Each typist can type an average of 6 letters per hour. B is a ma22622 variable with mean 0 and variance 1.

What is the conditional probability that a repair takes at 11h given that its direction 2 exceeds 8h?

### Probability & Queuing theory MA notes – Annauniversity lastest info

Arriving customers have to join the queue if No. Define wide sense stationary process. MA Question Bank – Find the average response ysllabus for a two-stage tandem open network with feedback.

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## Probability and Queueing Theory(question with answer)

A physical examination for a patient where the patient St. Construct the Transition Probability Matrix. The cumulative failure rate of all the machines is 0.

Find the value of k. The customer who has finished is billing job has to wait until the delivery section becomes free.

Find the probability that 11 particles are counted in 4 minutes. Sylalbus down the flow balance equation of open Jackson network. Slylabus do you mean by traffic intensity? A random process or Stochastic process X s,t is a function that maps each element of a sample space into a time function called sample function.

What is the probability that it has one or more defectives? Where the arrival pattern M is Poisson, the Service time distribution G follows any general distribution and the number of servers is one.

### MA PQT Lecture Notes – All Units Solved Problems

Examination time per patient is exponential with a mean rate of 20 per hour. Correlation coefficient is the geometric mean of regression coefficients 2. In Continuous random process, X and Time set T are continuous.

Find the probability that among a sample of jobs there are no jobs that have to wait until weekends. It was old and worn. Find the probability that he takes a train on the third day. A regular Markov chain is defined as a chain having a transition matrix P such that for some power of P, it has only non-zero positive probability values.

Let X be the power consumption in millions of kilowatt hours. Show that the process is not stationary. System independent of time t.

Define Chapman-Kolmogrov Equation The Chapman-Kolmogrov equation provides a method to compute the n-step transition probabilities. The doctor takes ysllabus the average 4 minutes for each phase of the check up and the time taken for each phase is exponentially distributed.