(rho)/(1+rho)*

D:-* (rho)/(1-rho)*

Correct Answer:- Option-C
Question46:-Let X be a trivariate normal random vector with dispersion matrix ‘sum=[[1,1,1],[1,3,2],[1,2,2]]. Then the
variance of *3X_(1)-2X_(2)+X_(3)° is

A:-23

8-6

வே

0-25

Correct Answer:- Option-C

Question47:-Let X and Y are two independent *N_(p)° (0, 2) random vectors with rank (2) `
then the distribution of X’AX + Y'AY is

A:-Non-central chi-square with p df

B:-Non-central chi-square with ‘p*(2)* df

C:-Chi-square with *p*(2)> df

D:-Chi-square with 2p df

Correct Answer:- Option-D
Question48:-Which distribution is the multivariate generalization of Wishart distribution ?

A:-t-distribution

B:-chi-square distribution

C:-F distribution

D:-Normal distribution

Correct Answer:-Question Cancelled
Question49:-Let X be a 4 xx’ 1 random vector with covariance matrix 2. Suppose the eigen values of = are 6, 3, 2 300 1
and let *Y_(1)°, “Y_(2)’, *Y_(3)° and *Y_(4)° be the four principle components. Then ‘sum_(i=1)*4Var(Y_(1))° is

A:-12

B:-15

6-36

D:-6

Correct Answer:- Option-A
Question50:-Consider a Markov chain with two states and transition probability ೧78% `[[(3)/(4),(1)/(4)1,[(1)/(2),(1)/(2)1]',
Stationary distribution of this Markov chain is

A:-Do not exists
` [[(1)/(2),(1)/(2)]]

6: [[(2)/(3),(1)/(3)]]`

0:- [[(1)/(3),(2)/(3)1]

Correct Answer:- Option-C
Question51:-Suppose that customers arriving at a service counter in accordance with a Poisson process with a mean rate of
3 per minute. Then the probability that the interval between two consecutive arrivals is more than one minute is

* p. If Ais the g-inverse of 5,

റ്റ)

0:- 1-6” (-(1)/3))

Correct Answer:- Option-B
Question52:-Consider a branching process whose population size at stage n is denoted by ‘{X_(n)}* . Assume that the
offspring distribution has the probability generating function ‘as*(2)+bs+c’, where a, b, c are positive and c < a. Then the
probability of ultimate extinction is

(9/9)

B:-1

C (cate)

D:-*(c)/(a-c)’

Correct Answer:- Option-A
Question53:-Which of the following is not a process with stationary independent increments ?

A:-Poisson process

B:-Compound Poisson process

C:-Brownian motion process

D:-None of the above

Correct Answer:- Option-D