stat2303_tutorial08

8 0 and 05 0 the period for sates 1 and 3 are also 1

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Unformatted text preview: sates 1 and 3 are also 1 because the Markov chain is irreducible, i.e. all states communicate (period is also a class property). Since the Markov chain has finite states and all states are recurrent, i.e. positive recurrent, the Markov chain is ergodic and hence limiting probabilities exist. Denote , 0.8 0.5 0 0 0 0 0.2 0 0 0.5 0.5 0.5 0 0.5 0.5 0 1 0.8 0.5 0.5 0.2 0.5 0.5 0.5 0.5 0.8 0.5 0 0 0 0 0.2 0 0 0.5 0.5 0.5 0 0.5 0.5 0 1 Solving the above equations yield , , Therefore, the proportion of trials being success is lim 0 or 1 lim 0 and 1| 7 11 Page 3 of 5 STAT2303/2803 Probability Modelling/Stochastic Models 3. (Cont’d Tutorial 7 Question 4) Consider matri...
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