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5 9 8 0M.Sc. DEGREE EXAMINATION, 2010

( MATHEMATICS )

( SECOND YEAR )

( PAPER - VIII )

240. MATHEMATICAL STATISTICS

( Including Lateral Entry )

December ] [ Time : 3 Hours

Maximum : 100 Marks

SECTION A ( 8 5 = 40 )

Answer any EIGHT questions.All questions carries equal marks.

1. An absent minded secretary places 5 letters in5 envelopes at random. What is the probabilitythat she will misplace every letter?

2. Explain the measures of skewness and Kurtosis.

Turn Over

3. If X and Y are independent rvs with pmfsP(

1) and P(

2) , respect ively, f ind the

conditional distribution of given X + Y isbinomial.

4. What is the signif icance of correlat ionco-efficient?

5. If Xn X, prove that as X

n X.

6. State and prove Borel-Cantelli Lemma.

7. Prove that : Fn

*(x) F(x) as n .8. Prove that : (n 1) s2/2 is 2(n 1).9. What is the problem of point estimation?

10. Explain Bayes estimation method.

SECTION B ( 3 20 = 60 )

Answer any THREE questions.All questions carries equal marks.

11. (a) State and prove Bonferronis inequality forprobability

(b) State and prove Lyapunov inequality.

12. (a) The number of female insects in a givenregion follows a Poisson distribution withmean . The number of eggs laid by eachinsect is a P(u) rv. Find the probabilitydistribution of the number of eggs in theregion. Also, find the mgf. (10)

(b) State and prove the two dimensional versionof the Livideberg-Levy Central LimitTheorem.

13. (a) Prove that 1 ,

where all the co-efficients of zero order areequal to P (10)

(b) State and prove Kronecker Lemma.

(2 + 8)

14. Explain two way analysis of variance with oneobservation per cell.

15. State and prove NeymanPearson fundamentallemma. (5+15)

2 3