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**Anna University Question Paper Code :.51574**

**B.E./B.Tech. DEGREE EXAMINATION, MAY/JUNE 2014.**

**Fourth Semester**

**Computer Science and Engineering.**

**MA 2262/MA.44/MA 1252/080250008/10177 PQ 401 – PROBABILITY AND QUEUEING THEORY**

**(Common to Information Technology)**

**(Regulation 200812010)**

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**PART A — (10 x 2 = 20 'marks)**

1. A continuous random variable X has the probability density function given by

f(x) = a*l+-x2), 2 5 0 otherwise

Find a and P(X < 4).

2. For a binomial distribution with mean 6. and standard deviation find the first two terms of the distribution.

3. Find the- value of k, i the joint density function of (X, Y) is. given by t.(x, y) = 0 {k0 x)(1. • y), 0 x < 4,1 < Y.< 5 otherwjse

4. Given . that. joint probability density function of (X, Y as

f(x, y) = 1 , 0 < x < 2, 0 < y 3, determine the marginal density.' 6

5. Define strict sense and wide sense stationary process.

6. A gambler has RS. 2. He bets ike. 1 at a time and wins •Re. 1 with proba'bility 112. He stops playing if he loseS Rs. 2 or wins Rs. 4. What is the transition probability Matrix of the related Matkoir chain?

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