ORIE 3510 – Homework5
Instructor: Mark E. Lewis
due 2PM, Wednesday February 29, 2012 (ORIE Hallway drop box)
1. Consider a Markov chain on the states
{
1
,
2
, . . . ,
9
}
with transition matrix
0
.
5
0
0
.
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
(a) Is this chain irreducible?
(b) Find the period of state 1 and state 8.
2. If
{
X
n
, n
≥
0
}
is an irreducible Markov chain with period
d
≥
2. Is
{
X
dn
, n
≥
0
}
irreducible?
Justify your statement by proof (for YES) or by a counterexample (for NO).
3. Harry plays semipro basketball where he is a defensive specialist.
His scoring productivity
per game fluctuates between three states: 1 (scores 0 or 1 points), 2 (scores between 2 and 5
points), 3 (scores more than 5 points). Inevitably, if Harry scores a lot of points in one game,
his jealous teammates refuses to pass him the ball in the next game, so his productivity in the
next game will be nil. These transitions could be modeled by a Markov chain with transition
matrix
P
=
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 Spring '10
 LEWIS
 Harry, Markov chain

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