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Stat 230 Assignment 5 Winter 2011 The following questions are to be answered neatly and completely on standard size (A4 or 8.5 by 11 inch) paper and...
1. An alternate approach to finding the stationary distribution of a Markov chain (rather than finding P^n), is to use the fact that if [X1 X2 X3] = the vector X transpose is a stationary distribution for a Markov chain with three states, then the vector X transpose P= the vector X transposewhere P is the 3x3 probability transition matrix for the Markov chain. This gives three equations in X1, X2, X3, and we have the fourth condition that X1+X2+X3=1. A system of 4 equations is 3 unknowns which, if has a solution, will provide the probabilities of the stationary distribution.Use this approach to find the stationary distribution for the Markov chain with probability transition matrix 01/6 1/2 1/32/3 1/3
