52,

53.

55.

൭6.

Let R be the sample correlation coefficient of a sample of size n from a bivaraite

normal population with correlation coefficient p. If p=0 then the statistic g ‏جع‎ = ன follows
L=

a:
(4) t distribution with (n—1) d.f. (8) t distribution with (n—2) d.f.
{C) F distribution with (1, n) d.f. (D) ¥ distribution with (1, n—1) d.f,
The distribution of Hotelling’s 13 51211911: 1011೧೪5 :

(A) Chi - square distribution (8) tdistribution

(9) Wishart distribution (D) F distribution

Let X3, ಸ್ತು... X, (n =P} be iid random vectors fram Np (0, ¥). Then the distribution of
8 ‏ے‎ = മട 20) 0-0 Where X = ‏ا‎ 15:
n

(க WE n-1) ற ۷۳۳ 00 © W ‏م۷۷۰ م لحم‎ n)

n

15172
If (X, X)' follows a bivaraite normal distribution with dispersion matrix 72-1 ] then

the dispersion matrix of (X;+X,, X; - ^ 15 :
3 0 3 2 3 9 3.2
(ಗಿ) [ം ‏٦‎ (ಗ) (1 1 | (೧ (1 . (7) ॥ A

If [N, t e T} is a Poisson process with rate A then which of the र्ण is/are correct :
(a) N, has independent increment

(ण) (1 ++ - पि, = 1) =) 1000)

(८) N, is a stationary increment process

(A) abandc (8) aandb (€) aandce (D) गावल
57. I (X, n=0, ‏مما‎ | 15 @ Galton - Watson branching process with E(X;)=m, then the

probability of ultimate extinction is 1 if :

(A) m>1 (B} m>2 (ಲ ms2 D) m=1
58. LetY), Y,and Y, be the three principal components of the random vector >= (21, 22, 33).

Which of the following is/are true :

(@) VOV + VIV + V(Y3)= V(X)) + V(X)) யற்று

ஐ று

€ 8 Y5 are uncorrelated

(^) (ध) शात्‌ (€) (8) (b)and (c) (^) (a)and (b) 12) (a), (b) and (c)
59. ‏عط ٤ہ ۰ ٢۷۸۷۳‎ following statement(s) is/are true 7

(a) സ state space of a finite Markov chain contain atleast one recurrent state

(0) In a finite irreducible Markov chain all states are non-null recurrent

[9] A null recurrent aperodic state of a Markov chain is called ergodic

@ @and®) ൫ ഭൂജജി്ര (©) ജ്ജ്‌ (7) (ग), (9 जद (©
122/2014 10 A