160a09_hw6

160a09_hw6 - Pstat160 Homework #6 Due Friday, March 5...

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Pstat160 Winter 2009 Homework #6 Due Friday, March 5 Problem 1. Problem 14, p. 254. Find the also the period for each classes. For the matrix P 1 , now change P 31 = 0 , P 32 = 1. Answer the same questions as before. Problem 2. We are given a MC with state space { 1 , 2 , 3 } and transition matrix P given below. The following matrices are also given. P = . 5 . 5 0 0 . 4 . 6 . 3 0 . 7 P 5 = . 2814 . 2176 . 5010 . 3006 . 2379 . 4615 . 2808 . 2505 . 4687 Q = 1 0 0 0 . 4 . 6 . 3 0 . 7 Q 5 = 1 0 0 0 . 6741 0 . 0102 0 . 3157 0 . 8319 0 0 . 1681 Q a = 0 0 0 1 0 . 4 . 6 0 . 3 0 . 7 0 0 0 0 1 Q 5 a = 0 0 0 1 0 . 1287 0 . 0102 0 . 3157 0 . 5454 0 . 0720 0 0 . 1681 0 . 7599 0 0 0 1 P T1 = . 4 . 6 0 . 7 ! ( I - P T1 ) - 1 = 1 . 667 3 . 333 0 3 . 333 ! ( P T1 ) 5 = . 0102 . 3157 0 . 1681 ! P T2 = . 5 . 5 0 . 4 ! ( I
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