Part CCSIR NET December 2024no-state-of-a-finite-irreducible-chain-is-transient

No state of a finite irreducible chain is transient

Consider the Markov chain with state space {0, 1, 2} and the transition probability matrix P = [[0, 1/2, 1/2], [3/4, 0, 1/4], [3/4, 1/4, 0]]. Let P⁽ $^{n}$ ⁾ = ((P⁽ $^{n}$ ⁾ $_{ij}))$ denote the n-step transition probability matrix. Then, which of the following statements are true?

A.P⁽ $^{2}$ ⁾ $_{00} = 3/4$ ✓
B.P⁽ $^{3}$ ⁾ $_{10} = 39/64$ ✓
C.The stationary probability that the chain is in state 2 is 2/7.✓
D.State 1 is transient.

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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No state of a finite irreducible chain is transient

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