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Unformatted text preview: 4 (b) 1 1 .1 2 .1 30 4 .1 50 60 (c) 1 10 20 3 .1 40 5 .3 2 0 .2 .2 .6 0 3 0 0 .3 0 0 4 0 .8 .4 .4 0 5 1 0 0 0 .7 (d) 1 2 1 .8 0 2 0 .5 3 00 4 .1 0 5 0 .2 6 .7 0 2 0 .2 .1 0 0 0 34 0 .4 .2 0 .3 0 0 .9 0 .4 00 5 .5 .5 0 0 0 .5 6 0 0 .6 0 .6 .5 3 0 0 .3 0 0 0 5 0 .5 .3 0 .8 0 6 0 0 0 0 0 0 4 .2 0 .4 .9 0 .3 64 CHAPTER 1. MARKOV CHAINS 1.9. Find the stationary distributions for the Markov chains with transition matrices: (a) 1 1 .5 2 .2 3 .1 2 .4 .5 .3 (b) 1 1 .5 2 .3 3 .2 3 .1 .3 .6 2 .4 .4 .2 (c) 1 1 .6 2 .2 30 3 .1 .3 .6 2 .4 .4 .2 3 0 .2 .8 1.10. Find the stationary distributions for the Markov chains on {1, 2, 3, 4} with transition matrices: 0 1 0 1 0 1 .7 0 .3 0 .7 .3 0 0 .7 0 .3 0 B.6 0 .4 0 C B.2 .5 .3 0 C B.2 .5 .3 0 C C C C (a) B (b) B (c) B @ 0 .5 0 .5A @.0 .3 .6 .1A @.1 .2 .4 .3A 0 .4 0 .6 0 0 .2 .8 0 .4 0 .6 (c) The matrix is doubly stochastic so ⇡ (i) = 1/4, i = 1, 2, 3, 4. 1.11. Find the stationary distributions for the chains in exercises (a) 1.2, (b) 1.3, and (c) 1.7. 1.12. (a) Find the stationary distribution for the transition probability 1 2 3 4 1 2 3 4 0 2 /3 0 1/3 1...
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## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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