Math 452/550: Stochastic processes
Homework assignment # 2
Due In Class, Oct. 8th, 2010
Submit all of your work for marking. You are permitted to collaborate on the homework; however,
you must write up your homework yourself. You should not copy somebody else’s homework: if you
choose to collaborate, you should be able to recreate all of the steps involved in solving a problem
yourself, and should do so in your writeup. Please list the names of your collaborators on the ﬁrst
page of each homework.
Assignments must be submitted by the given due date. No late homework will be accepted.
1.
Show that the product of two stochastic matrices is a stochastic matrix.
2.
Consider a Markov chain with three states 0,1,2 and a transition probability matrix
P
=
1
/
2 1
/
3 1
/
6
0
1
/
3 2
/
3
1
/
2
0
1
/
2
.
Find
E
[
X
4
] if
P
{
X
0
=
i
}
= 1
/
3
,i
= 0
,
1
,
2.
3.
Let (
X
n
)
n
≥
0
be a Markov chain with the probability transition matrix
P
= (
p
ij
)
i,j
≥
0
on the
discrete states 0,1,2,
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 Spring '11
 stephenlang
 Math, Calculus, Stochastic process, Markov chain, Stochastic matrix, transition probability matrix

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