ORIE3510
Introduction to Engineering Stochastic Processes
Spring 2010
Homework 2: Discrete Time Markov Chains
Due February 10, 2010 (drop box)
In all questions, be sure to give the justiﬁcation for your answers.
There are 5 problems, each equally weighted for 100 total points.
1. Let
{
X
n
:
n
≥
0
}
be a Markov chain and suppose
P
ii
>
0. Let
η
i
be the exit time from state
i
:
η
i
= inf
{
n
≥
1 :
X
n
6
=
i
}
.
Derive the distribution of
η
i
.
2. Suppose that whether or not an NFL team wins the Super Bowl depends on the number of
Super Bowl wins for that team in the last three seasons.
(a) How would you analyze this using a Markov chain? Specify the state space.
(b) Suppose that if a team has won the Super Bowl three years in a row, then they will
win the fourth one with probability 0.7. Else, if a team has not won any Super Bowls
in the last three years, they will win this one with probability 0.3. Else, the team will
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 Fall '08
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 Probability theory, Stochastic process, Markov chain, Super Bowls

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