ORIE3510
Introduction to Engineering Stochastic Processes
Spring 2010
Homework 4: Discrete Time Markov Chains
Due 2:30pm, February 24, 2010 (drop box)
Be sure to write your name and section number or day&time on your homework.
In all questions, be sure to give the justification for your answers.
There are 3 problems for 100 total points.
Problem 1 (20 points)
Every time a team wins a game, it wins its next game with probability 0.75; every time it loses
a game, it wins its next game with probability 0.35. If the team wins a game, then it has dinner
together with probability 0.65, whereas if the team loses then it has dinner together with probability
0.25. What proportion of games result in a team dinner?
Problem 2 (30 points)
In a good weather year the number of storms is Poisson distributed with mean 1; in a bad year it
is Poisson distributed with mean 3. Suppose that any year’s weather conditions depends on past
years only through the previous year’s condition. Suppose that a good year is equally likely to be
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 Spring '10
 LEWIS
 Probability theory, Markov chain, positive recurrent, null recurrent

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