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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74 CHAPTER 6. DISCRETE-TIME PROCESSES<br />
32.<br />
p (n)<br />
ij = Pr{S n = j | S 0 = i}<br />
=<br />
=<br />
=<br />
=<br />
m∑<br />
Pr{S n = j, S k = h | S 0 = i}<br />
h=1<br />
m∑<br />
Pr{S n = j | S k = h, S 0 = i} Pr{S k = h | S 0 = i}<br />
h=1<br />
m∑<br />
h=1<br />
m∑<br />
h=1<br />
Pr{S n = j | S k = h}p (k)<br />
ih<br />
Pr{S n−k = j | S 0 = h}p (k)<br />
ih<br />
=<br />
m∑<br />
h=1<br />
p (n−k)<br />
hj<br />
p (k)<br />
ih<br />
=<br />
m∑<br />
h=1<br />
p (k)<br />
ih p(n−k) hj<br />
33. No answer provided.