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solution_hw3

# solution_hw3 - 23 74 ï£ ï£ ï£ ï£ ï£ ï£ ï£¸ All the states...

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Solution to Assignment 3 By Li Xu * April 20th, 2008 1. The transition matrix is 0 0 . 5 0 0 . 5 0 0 0 . 7 0 0 . 3 0 0 0 0 0 1 0 0 0 0 0 0 0 . 1 0 . 4 0 . 5 0 0 0 1 0 0 0 0 0 0 0 1 ; And the two step transition matrix is 0 . 35 0 0 . 15 0 . 05 0 . 2 0 . 25 0 0 . 35 0 . 3 0 . 35 0 0 0 0 1 0 0 0 0 0 0 0 . 41 0 . 04 0 . 55 0 0 0 0 . 1 0 . 4 0 . 5 0 0 0 0 0 1 . There are 3 classes: { 0 , 1 } , { 3 , 4 } , { 2 } and { 5 } . Transient states: 0, 1, 3; Recurrent states: 2, 4, 5; Absorbing states: 2, 5. * 1

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State 0 1 2 3 4 5 Period 2 2 1 1 1 1 This chain is not irreducible, so there is no steady state probability. f (1) 35 = 0 . 5, f (2) 35 = 0 . 05, f (3) 35 = 0 . 205, f (4) 35 = 0 . 0405. μ 35 = 2 . 8 2. The transition matrix is 0 0 . 1 0 . 9 0 0 0 . 4 0 . 6 0 0 0 0 1 0 . 1 0 0 . 7 0 . 2 ; And the two step transition matrix is 0 0 . 04 0 . 06 0 . 9 0 0 . 16 0 . 24 0 . 6 0 . 1 0 0 . 7 1 . 2 0 . 02 0 . 01
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Unformatted text preview: . 23 . 74 ï£¶ ï£· ï£· ï£· ï£· ï£· ï£¸ ; All the states form one class of this chain. Transient states & Absorbing states: none; Recurrent states: all. State 1 2 3 Period 1 1 1 1 Steady-state probabilities: Ï€ = 0 . 0522, Ï€ 1 = 0 . 0087, Ï€ 2 = 0 . 418, Ï€ 3 = 0 . 522. Î¼ 01 = 172, Î¼ 02 = 1 . 167, Î¼ 03 = 2 . 167. Î¼ 00 = 19 . 167. 2...
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solution_hw3 - 23 74 ï£ ï£ ï£ ï£ ï£ ï£ ï£¸ All the states...

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