Question75:-Let {x,} be a Markov chain having a state space {1, 2, 3, 4, 5} and

a

transition probability matrix is given by ० =| ‡; ६ |

Which of the following statements is/are correct ?

i. 1 and 4 are in the same communicating class.
ii. 2 and 3 are in the same communicating class.
iii. 2 and 5 are in the same communicating class.
iv. 3 and 4 are in the same communicating class.

A:-Only (i and iii)

B:-Only (ii and iii)

C:-Only (iv)

D:-All the above (i, ii, iii and iv)
Correct Answer:- Option-A

Question76:-The interval between two successive occurrence of a Poisson process
N(t), t = O having parameter A follows

A:-Exponential with mean A

B:-Exponential with mean +

C:-Poisson with parameter A

D:-Geometric distribution with parameter A
Correct Answer:- Option-B

Question77:-Suppose {x,} is a random walk on real line. A unit is moving from state
i toi + 1 with probability % and also from state i to i-1 with probability %. Then
random walk is
(i) Recurrent
(ii) Null recurrent
(iii) Aperiodic
(iv) Ergodic
A:-All of the above (i, ii, iii and iv)
B:-Only (i and ii)
C:-Only (i, ii and iii)
D:-Only (iii)
Correct Answer:- Option-B

Question78:-Consider a birth and death process with A as birth rate and yas death
rate. The probability of ultimate extinction when the death rate is greater than the
birth rate is

A:-}
B:-1
1
D:-0