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Spring 2009 OR3510/5510
Problem Set 3
Due Monday Feb 16 at 10am. You may insert in the homework box between Rhodes and Upson
or give it to me in PHL 101 at the beginning of class by 10:10am. If you intend to give it to me,
please make sure to arrive in good time so as not to interfere with the lecture.
Reading: By Wednesday we will be in section 4.7 of the text and then will come back to 4.6.
x/y=page x, problem y in Ross.
(1) 266/20
(2) 268/30
(3) Let
{
X
n
}
and
{
Y
n
}
be two independent Markov chains, each with the same discrete state
space
S
and same transition probabilities. Deﬁne the process
{
Z
n
}
=
{
(
X
n
,Y
n
)
}
with state
space
S
×
S
.
(a) Show
{
Z
n
}
is a Markov chain and give the transition probability matrix.
(b) If
{
X
n
}
has stationary distribution
π
X
= (
π
X
(
i
)
,i
∈
S
}
and
{
Y
n
}
has stationary
distribution
π
Y
= (
π
Y
(
i
)
,i
∈
S
}
, does
{
Z
n
}
have a stationary distribution and if so,
what is it?
(4)
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 Summer '09
 RESNIK

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