Part CCSIR NET June 2025a-2-cycle-and-a-3-cycle-in-the-same-class-force-the-period-to-1

A 2 cycle and a 3 cycle in the same class force the period to 1

Consider a Markov chain { $X_{n} : n \geq 1$ } on state space {1, 2, 3, 4, 5} with the transition probability matrix whose rows are (0, 1/2, 1/2, 0, 0), (0, 0, 1, 0, 0), (0, 1/3, 0, 1/3, 1/3), (1, 0, 0, 0, 0) and (0, 0, 0, 0, 1). Then, which of the following statements are true?

A.Stationary distribution is (0, 0, 0, 0, 1).✓
B.State 5 is absorbing and recurrent.✓
C.All states are aperiodic.✓
D. $l i m_{n} \to \infty p_{55}$ ⁽ $^{n}$ ⁾ = 1.✓

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, and why this one tests execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

A 2 cycle and a 3 cycle in the same class force the period to 1

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