Set 2 c and solve to nd the limiting probabilities in

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Unformatted text preview: istribution. 4.27. We now take a di↵erent approach to analyzing the Duke Basketball chain, Example 4.11. 154 CHAPTER 4. CONTINUOUS TIME MARKOV CHAINS 0 3 0 1 6 0 1 2 3 1 2 5 0 0 2 1 5 2.5 0 3 0 0 1.5 6 (a) Find g (i) = Ei (V1 ) for i = 0, 2, 3. (b) Use the solution to (a) to show that the number of Duke scores (visits to state 1) by time t has N1 (t)/t ! 0.6896 as computed previously. (c) Compute h(i) = Pi (V3 < V1 ) for i = 0, 2. (d) Use this to compute the distribution of X = the number of time UNC scores between successive Duke baskets. (e) Use the solution of (d) to conclude that the number of UNC scores (visits to state 3) by time t has N3 (t)/t ! 0.6206 as computed previously. 4.28. Brad’s relationship with his girl friend Angelina changes between Amorous, Bickering, Confusion, and Depression according to the following transition rates when t is the time in months. A B C D A 4 4 2 0 B 3 6 3 0 C 1 2 6 2 D 0 0 1 2 (a) Find the long run fraction of time he spends in these four states? (b) Does the chain satisfy the detailed balance condi...
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