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: 111 244 21 0 33 32 0 55 P    . Compute 1. The steady state distribution       ,, abc , 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 | kk 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: 12 0 13 0 44 23 0 P . The initial distribution for X is given by:       0 0 0 0 2 1 2 , , , , 555 . Compute 1. The steady state distribution       . 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 n to be the number of successes in n Bernoulli trials. Let p denote the probability of success in a trail. 1. Show that N={N n : N 0 =0, n=0,1,…} is a discrete time Markov chain.
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This note was uploaded on 01/12/2011 for the course EE 132B taught by Professor Izhakrubin during the Fall '09 term at UCLA.

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20105ee132B_1_hw6 - UCLA Electrical Engineering Department...

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