Mathematics · Stochastic Processes
Consider a Markov chain {Xn: n ≥ 1} on state space {1, 2, 3, 4, 5} with the transition probability matrix: P = [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] [0, 0, 0, 0, 1] Then, which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The limit as n approaches infinity of p55(n) is 0.
- 2All states are aperiodic.
- 3State 5 is absorbing and recurrent.✓
- 4The stationary distribution is (0, 0, 0, 0, 1).
Correct answer
State 5 is absorbing and recurrent.
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