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

Edit

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

Edit

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

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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

Edit