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IE 336
Handout #9
Mar. 28, 2011
Due Apr. 4, 2011
Homework Set #8
1.
Let the following function represent a realization of a continuous time Markov process
during a time span of 31 hours. Assume that the process has only 2 states.
t (hours)
12
2
9
22
19
16
7
29
31
25
27
3
1
state
(a) Estimate the transition rates of the process.
(b) Form the system of diﬀerential equations that as a solution has the transition proba
bilities as functions of time. (Do not solve the system.)
(c) If the process is in state 2 what is the expected length of time that it will stay in state
2 before a transition to state 1 occurs.
(d) If the process has been in state 1 for 10 minutes what is the expected length of time
that it will stay in state 1 before a transition to state 2 occurs.
2.
Consider a continuous time Markov process with the following transition rate matrix.
Λ =

5
2
q
p
2
r

3
2
p
4
r
q

4
.
(The transition rates given in the above matrix are in number of transitions per one hour.)
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 Spring '08
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