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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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 Spring '10
 DURRETT
 The Land

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