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KERALA UNIVERSITY MCA - I (SEM 1) MAY 2009 : Probability And Statistics

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*1589* 1589 (Pages : 2) Reg. No. : ..................................... Name : .......................................... First Semester M.C.A. Degree Examination, May 2009 PROBABILITY AND STATISTICS Time : 3 Hours Max. Marks : 100 PART A Answer all questions. All questions carry equal marks. (10 4=40 Marks) 1. The probability density function of a random variable X is f(x) = C(1 x2) if 1 < x < 1 = 0 otherwise Find : a) C ( ) b) P 1 < X < 1 . 4 2 2. X follows Binomial distribution with parameters n = 6 and P. If 9 P[X = 4] = P[X = 2] find P. 3. A point X is chosen at random on the line segment (0, 2). What is the probability that the chosen point lies between 1 2 and ? 4 3 4. Explain weak laws and strong laws of large numbers. 5. Distinguish between correlation and regression. 6. A random sample of size 36 is taken from an infinite population with = 63 and variance 2 = 81 . Find the probability of getting the sample mean greater than 66.75. 7. Explain null hypothesis, alternate hypothesis, critical region; power of the test. 8. Explain the properties of a good estimator. ( ) 9. A random sample of size 10, taken from a normal population N , 2 has standard deviation 4. Find a and b such that P[ a 2 b ] = 0.95 . 10. Explain the properties of normal curve and normal distribution. P.T.O.

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