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20105ee132B_1_hw6

# 20105ee132B_1_hw6 - UCLA Electrical Engineering Department...

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UCLA Electrical Engineering Department EE132B HW Set #6 Professor Izhak Rubin Problem 1 Consider a Markov chain X = {X k , k = 0,1,…} with state space S = {a, b, c} and the transition matrix as follows: 1 1 1 2 4 4 2 1 0 3 3 3 2 0 5 5 P . Compute 1. The steady state distribution       , , a b c   , 2. 1 2 3 4 5 6 7 0 , , , , , , | P X b X c X a X c X a X c X b X c . 3. 2 | k k P X c X b . Problem 2 Consider a discrete time Markov chain X with state space S = {a, b, c} and a transition matrix given as follows: 1 2 0 3 3 1 3 0 4 4 2 3 0 5 5 P . The initial distribution for X is given by:     0 0 0 0 2 1 2 , , , , 5 5 5 a b c . Compute 1. The steady state distribution       , , a b c   . 2. 1 3 4 6 0 , , , | P X b X a X c X b X a 3. 1 2 3 , , P X b X b X a .

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Problem 3 Define N
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