Tamil Nadu Open University (TNOU) 2009-1st Year M.Sc Mathematics Tamilnadu open university Maths Mathematical statistics - Question Paper

M.Sc. DEGREE EXAMINATION JUNE 2009.

(AY 2006-07 batch onwards)

First Year

Mathematics

MATHEMATICAL STATISTICS

Time : 3 hours Maximum marks : 75

PART A (5 5 = 25 marks)

Answer any FIVE questions.

Each question carries 5 marks.

1.         Define probability set function. State the axioms of probability.

2.         Find the marginal density function for X and Y if the joint p.d.f. is

3.         A continuous random variable X has p.d.f.

             0 ; otherwise

             Find the mean of the random variable.

4.         If a random variable has a binomial population with parameters n and p. Show that the sample proportion is an unbiased estimator of p.

5.         Show that the sample variance is a consistent estimator of the population variance where is a random sample from a normal population .

6.         Define conditional probability. Hence define mutually independent events.

7.         What is point estimation? How is it different from interval estimation?

8.         Write a note on Bayesian estimation.

PART B (5 10 = 50 marks)

Answer any FIVE questions.

Each question carries 10 marks.

9.         State and prove Chebychev's inequality.

10.       Find the moment generating function of the Poisson distribution. Hence find its mean and variance.

11.       Derive the density function of the -distribution.

12.       Find the critical region of the likelihood ratio test for testing the null hypothesis against the composite alternative hypothesis on the basis of a random sample of size n from a normal population with the known variance .

13.       State and prove central limit theorem.

14.       Derive the confidence interval for the difference of two proportions for a normal population.

15.       State and prove Rao-Blackwell theorem.

16.       State and prove Rao-Cramer inequality.