stat2303_tutorial08

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This note was uploaded on 03/15/2014 for the course STAT 2303 taught by Professor Steven during the Fall '11 term at HKU.

Ask a homework question - tutors are online