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Class Problems: DTMC analysis
1. A company uses two forecasting tools to predict the demand of its product. Tool
i
is eﬀective w.p.
p
i
(for
i
= 1
,
2). If the
n
th
prediction uses tool
i
and it is observed to be eﬀective, then the (
n
+ 1)
st
prediction is also done using the same tool; if it is observed to be ineﬀective, then the (
n
+ 1)
st
prediction is made using the other tool. Let
X
n
be the tool used for the
n
th
prediction. In steady
state what is the probability that tool 1 is used for prediction? What is the long run fraction of
predictions made by tool 2?
2. Students switch between 3 phone companies
A
,
V
, and
S
according to the following transition
probability matrix
0
.
4 0
.
2 0
.
4
0
.
6 0
.
4
0
0
.
3 0
.
5 0
.
2
.
What is the steady state market share for the 3 phone companies if all the students behaved according
to the above matrix.
3. Consider a machine tool that is used on an NCmachine. The time to produce a part and inspect it
is 1 hour. If the tool has produced
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This note was uploaded on 09/18/2011 for the course ISEN 609 taught by Professor Klutke during the Spring '08 term at Texas A&M.
 Spring '08
 Klutke

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