hw8 - ECE320 Homework 8 Cornell University Spring 2006...

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ECE320 Homework 8 Spring 2006 Cornell University T.L.Fine Please hand in this assignment at the end of lecture on Tuesday, 4 April. Use only your assigned three-digit code and not your name. Throughout, give reasons for your answers. 1. In a Markov chain, let X = { ξ 1 , ξ 2 , ξ 3 } and π (1) = [ . 2 , . 3 , . 5] , P = . 5 . 5 0 . 3 . 3 . 4 0 . 6 . 4 . (a) Evaluate P ( X 2 = ξ 2 ). (b) Draw a state transition diagram. (c) Classify the three states as to whether they are absorbing, persistent, or transient. (d) What are the periodicities d i for ξ i ? (e) Identify the communicating classes. (f) Identify the closed communicating classes. (g) If there is a stationary or limiting initial distribution π , then determine π . If there is no such limiting initial distribution, then provide reasons. (h) If there is a stationary limiting distribution, what is the expected time between returns to state ξ 2 ? 2. Repeat Problem 1 for P = . 5 . 5 0 0 . 6 . 4 0 . 2 . 8 . 3. Repeat parts 1(c)—1(h) for the Markov chain with state transition diagram given in Figure 1.
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