SOLUTIONS MANUAL for Stochastic Modeling: Analysis and ...
SOLUTIONS MANUAL for Stochastic Modeling: Analysis and ...
SOLUTIONS MANUAL for Stochastic Modeling: Analysis and ...
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Chapter 6<br />
Discrete-Time Processes<br />
1. ✷ session 1 2 3 2 3 3 3 3 3 2 3 2 2 3 2 4<br />
Pr{✷} = p 1 p 12 p 23 p 32 p 23 p 33 p 33 p 33 p 33 p 32 p 23 p 32 p 22 p 23 p 32 p 24<br />
∗ session 1 2 2 3 3 2 3 3 3 4<br />
= p 1 p 12 (p 23 ) 4 (p 32 ) 4 (p 33 ) 4 p 22 p 24<br />
= 1 (0.95)(0.63) 4 (0.36) 4 (0.4) 4 (0.27)(0.1)<br />
≈ 1.7 × 10 −6<br />
2. (a) 2, 2, 3, 2, 4,...<br />
(b) 3, 3, 2, 3, 2, 3, 4,...<br />
3. (a) 1, 1, 1, 1, 1,...<br />
(b) 2, 2, 1, 1, 1, 1, 2,...<br />
4. (a) p 12 =0.4<br />
(b) p (2)<br />
11 =0.68<br />
(c)p 21 p 11 =0.48<br />
5. recurrent: {2, 3, 4}<br />
transient: {1}<br />
Pr{∗} = p 1 p 12 p 22 p 23 p 33 p 32 p 23 p 33 p 33 p 34<br />
= p 1 p 12 p 22 (p 23 ) 2 (p 33 ) 3 p 32 p 34<br />
= 1 (0.95)(0.27)(0.63) 2 (0.4) 3 (0.36)(0.24)<br />
≈ 5.6 × 10 −4<br />
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