Probability [ISS (Statistical Services) Statistics Paper I]: Questions 203 - 206 of 212
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Question 203
Appeared in Year: 2022
Question MCQ▾
Consider a Markov chain with state space and transition probabilities given as follows:
Which of the following are true?
Choices
Choice (4) | Response | |
---|---|---|
a. | There are infinitely many recurrent classes | |
b. | Zero is a transient state | |
c. | The chain has period 2 | |
d. | The chain is irreducible |
Question 204
Appeared in Year: 2022
Question MCQ▾
Let consider a Markov chain on the state space S with transition probability matrix
Then which of the following is always true?
Choices
Choice (4) | Response | |
---|---|---|
a. | State 1 has period 2 | |
b. | State 2 is recurrent | |
c. | State 3 is transient | |
d. | The chain admits at least two stationary distributions |
Question 205
Appeared in Year: 2020
Question MCQ▾
Consider a Markov chain on a finite state space S. Suppose that the transition probability matrix P is such that the transpose of P is also a stochastic matrix. Then which of the following is necessarily true? (30 November)
Choices
Choice (4) | Response | |
---|---|---|
a. | All states have the same period | |
b. | The chain admits at most one stationary distribution | |
c. | All states are recurrent | |
d. | At least one state has period 1 |
Question 206
Appeared in Year: 2020
Question MCQ▾
Consider a Markov chain transition probability matrix
Let
Then which of the following statements are correct? (26 November)
Choices
Choice (4) | Response | |
---|---|---|
a. | is a stationary distribution | |
b. | If is a stationary distribution, then | |
c. | The markov chain is periodic | |
d. | he markov chain is irreducible |