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Unformatted text preview: 1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.262 Discrete Stochastic Processes Problem Set #8 Issued: April 10, 2010 Due: April 16, 2010 Reading : For this problem set, please study all of Sections 5.1 5.5. For the week of April 12  16, begin reading Chapter 6. 1) Exercise 5.1. (Assume the Markov chain is an arbitrary finite or countably infinite chain. Do the proof first for n = 1, then for n = 2, and then proceed by induction on n. Also does the limit, lim( ( )) ij n F n , necessarily always exist? Either show that it does, or else give a counterexample.) 2) a) Consider the Markov chain in Figure 5.1. Show that the solutions F ij ( ) given in Exercise 5.2 satisfy eq. (5.9) for this chain as well. For the special case p = q = 1/2, show that the chain is recurrent, (i.e., show that the solutions given in Exercise 5.2, F ij ( ) = 1, i,j , are correct) by showing that there is no smaller solution to eq. (5.9). (You may use, without proof, the symmetric behavior of that there is no smaller solution to eq....
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This note was uploaded on 10/21/2010 for the course EE 5581 taught by Professor Moon,j during the Spring '08 term at Minnesota.
 Spring '08
 Moon,J
 Computer Science, Electrical Engineering

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