University of the Philippines – Diliman
Department of Industrial Engineering and Operations Research
IE 143 Short Quiz
Short Quiz 3 – Class 2
10 out of 10
All answers and relevant solutions should be written at the back of this questionnaire.
1.
Which of the following are transition matrices? (1 point)
A.
g
0.5
0.3
0.2
0.1
0.75
0.15
1
0
0
G
B.
g
0.15
0.2
0.6
0.1
0.8
0.1
0.5
0.45
0.05
G
C.
g
0
1
0
0
0
1
1
0
0
G
D.
g
0.05
0.35
0.6
0.65
0.55
−0.2
0.1
0.01
0.89
G
2.
True or False: A periodic class is also a recurrent class. (1 point)
3.
Assume the following is a onestep transition probability matrix.
±
²
³
±
²
³
g
0.1
0.2
0.7
0.3
0.4
0.3
0.2
0
0.8
G
a.
What is the probability of going from A to C in exactly one step? (1 point)
b.
What is the probability of going from C to B in exactly two steps? (2 points)
c.
Draw the transition probability graph for this Markov chain. (1 point)
d.
Identify which the states are recurrent. (1 point)
e.
Find the longterm probabilities of being in state A, B, or C in a given step. (3 points)
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 Spring '11
 a
 Operations Research, Markov chain, transition probability, Diliman Department of Industrial Engineering and Operations Research

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