ORIE3510Introduction to Engineering Stochastic ProcessesSpring 2010Homework 4: Discrete Time Markov ChainsDue 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 losesa game, it wins its next game with probability 0.35. If the team wins a game, then it has dinnertogether with probability 0.65, whereas if the team loses then it has dinner together with probability0.25. 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 itis Poisson distributed with mean 3. Suppose that any year’s weather conditions depends on pastyears only through the previous year’s condition. Suppose that a good year is equally likely to be
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Probability theory, Markov chain, positive recurrent, null recurrent