GATE 2024 ST – Question 53
A chain on {0,1,2} has $P=\begin{pmatrix}1/2&1/2&0\\1/2&1/2&0\\1/3&1/3&1/3\end{pmatrix}$. Which hold?
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Show answer and explanation
Correct answer: (A) 0,1 recurrent; (B) 2 transient; (C) Unique stationary distribution
Explanation
States 0,1 form a closed finite communicating class and are recurrent. State 2 can leave for that class and never return, so it is transient. All stationary mass must lie in {0,1}, and its equal-row transition gives unique stationary vector (1/2,1/2,0). The chain is not irreducible. **A,B,C**.