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 5<br />
Arrival-Counting Processes<br />
1. (a)<br />
(b)<br />
(c)<br />
Pr{Y 2 =5} = e−2(2) (2(2)) 5<br />
5!<br />
≈ 0.16<br />
Pr{Y 4 − Y 3 =1} =Pr{Y 1 =1} = e−2 2<br />
1!<br />
Pr{Y 6 − Y 3 =4| Y 3 =2} =Pr{Y 3 =4}<br />
≈ 0.271<br />
= e−2(3) (2(3)) 4<br />
4!<br />
≈ 0.134<br />
(d)<br />
Pr{Y 5 =4| Y 4 =2} =Pr{Y 5 − Y 4 =2| Y 4 =2}<br />
=Pr{Y 1 =2} = e−2 2 2<br />
2!<br />
≈ 0.271<br />
2. No answer provided.<br />
3. λ = 2/hour. Let t be measured in hours from 6 a.m.<br />
(a)<br />
Pr{Y 4 =9| Y 2 =6} = Pr{Y 4 − Y 2 =3| Y 2 =6}<br />
= Pr{Y 2 =3}<br />
= e−2(2) (2(2)) 3<br />
3!<br />
≈ 0.195<br />
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