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Hw4_ORIE3510_S10

# Hw4_ORIE3510_S10 - ORIE3510 Introduction to Engineering...

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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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