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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Documents Flashcards Grammar checker. Find the rth moment of X about the 2 origin. Find the parameters of the distribution. Find the probability that among a sample of jobs there are no jobs that have to wait until weekends. The number of monthly breakdown of a computer is a r. Find the probability that this computer will function for a month with only one breakdown. Let one copy of a magazine syllavus of 10 copies bears a special prize following Geometric distribution, Determine its mean and variance.

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The time required to repair a machine is exponentially distributed with parameter St. Probability and Queueing Theory Subject Code: What is the conditional probability that a repair takes at 11h given that its direction 2 exceeds 8h? Suppose the length of life of an appliance has an exponential distribution with mean 10 years.

What is the probability that the average life time of a random sample of the appliances is atleast Write down the moment generating function of Gamma distribution. Write the Physical conditions of Binomial distribution. What are the applications of Weibull distribution? What is the probability that out of 5 workers, at the most two contract that disease.

A random sample of 8 lamps is taken for inspection. What is the probability that it has one or more defectives? Let n and p be the parameters. MA Question Bank – Variance npq 1. Find the probability that on a randomly selected day. Find the probability that i no one joins the queue in a particular minute ii 2 or more syllabks join the queue in the minute.

Probability and Queueing Theory 7. MA Question Bank – Solutions: Blades are supplied syllxbus packets of 5 each. In a lot of 10, packets, how many packets would i be free defective blades? Probability and Queueing Theory 3 1 Subject Code: The town has a daily stock of 35, litres.

What is the probability that of 2 days selected at random the stock is insufficient for both days? 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.

What is the probability that it will last for atleast one more minute? If the power supplied to the factory is 12 million kilowatt hours, what is the probability that this power supply will be inadequate on any given day? Let X be the power consumption in millions of kilowatt hours. In a certain locality the daily consumption of water in millions of litres, can be treated as a random variable having a gamma distribution with an average of 3 million litres.

If the pumping station of the locality has a daily supply capacity of a millions litres. What is the probability that this water supply will be inadequate on any given day? It is given that X be the daily water consumption of the locality in million litres and X follows gamma distribution with average of 3 million litres.

Find a the mean life time of the component b the probability that such a component will be more than hours. What is the probability that at least 5 components are to be examined in order to get 3 defectives? Find the marginal density function. Find the value of k. Write any two properties of regression coefficients. Correlation coefficient is the geometric mean of regression coefficients 2. If one of the regression coefficients is greater than unity then the other should be less than unity.

Find the Marginal probability densty of X. Identify the regression equation on y on x: Find the correlation coefficient between X and Y x on y: Probability and Queueing Theory Find all the marginal distributions and conditional probability distributions. Are X and Y independent? When the regression equations are known the arithmetic means are computed by solving the equation.

A random sample of size is taken from a population whose mean is 60 and variance is Check whether or not the process is wide sense stationary.

## Probability and Queueing Theory(question with answer)

Show that X t is not wide sense stationary. Define a Random Process. 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.

Define First order stationary ayllabus Second order stationary process. A random process is said to be stationary to order one if the first order density functions defined for all the random variables of the process are same. In other words, the future behavior of the process depends only on the present value and not on the past value.

Define Chapman-Kolmogrov Equation The Chapman-Kolmogrov equation provides a method to compute the n-step transition probabilities.

### MA syllabus || probability and queueing theory syllabus || PQT syllabus

The Markov chain is irreducible if all states communicate with each other at some time. When do you say the Markov chain is regular? 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. Poisson process is a counting point process representing the number of occurrences of certain event in a finite collection of non overlapping statistically independent time arrivals.

What are the properties of Poisson process? It syllavus vivid from the expressions of moments of poisson process that they are time dependent.

Determine whether the given matrix is irreducible or not. So, P is irreducible. When do you say the Markov chain is homogeneous? If the one-step transition probability does not depend on the step i. What are the different types of Random process. Define Birth and Death process. A housewife buys 3 kinds of cereals A, B and C. Maa2262 never buy the same cereal in successive weeks. If she buys cereal A, the next week she buys B. However if she buys B or C the next week she is 3 times as likely to buy A as the other cereal.

Construct the Transition Probability Matrix. Check whether it is regular. The source emits particles at the rate of 6 per minute. Each emitted particle has a probability of 0. Find the probability that 11 particles are counted in 4 minutes. Prove that the sum of two independent Poisson process is a Poisson process. Show that the process is not stationary. A syllqbus either drives a car or catches a train to go to office each day. He never goes two days in a row by train but if he drives one day, then the next day he is just as likely to drive again as he is to travel syllqbus train.

Find the probability that he takes a train on the third day. Also find the probability that he drives to work in the long run. MA Question Bank – 2 3 2. The message arrivals are modelled as two independent Poisson syllaabus, with rates 20 per hour for the short messages and 15 per syplabus for the long messages. Find the probabilities that: It has found that most types of major news stories occur as Poisson processes.

Find a The mean number of stories of any of these types in each day. The actual number of ssyllabus breaking in any given day is thus distributed Poisson 15and so the expected number is Syllaubs is a random variable with mean 0 and variance 1.

Find mean and auto correlation of the process. Given that B is a R. V with mean 0 and 1 i.

The basic characteristics of queueing system are Arrival time pattern, Service time pattern, Number of services channels, Capacity of the system, Service discipline. What do you mean by transient state and steady state queueing system?