# 173_FirstMidterm_Sol - IND ENG 173 Introduction to...

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IND ENG 173 First Midterm Solutions Introduction to Stochastic Processes February 20, 2017 Prof. Mariana Olvera-Cravioto Page 1 of 6 First Midterm Exam Place all answers on the question sheet provided. The exam is open textbook and open notes/handouts/ homework. You are allowed to use a calculator, but not a computer, tablet or smartphone. Write all answers clearly and in complete sentences. All answers should be supported by analysis or an argument. This exam has a total of 53 points. 1. Alan owns a store in the neighborhood and he believes that there are good days, when many customers come into his store, and bad days, when very few do. He models this customer behavior using a Markov chain, where he has estimated that a good day will be followed by another good day with probability 0.6, and a bad day will be followed by another bad day with probability 0.5, independently of previous days. Let X n = 1 if the n th day is a good day, and X n = 2 if it is a bad day. (a) [6 pts] Write the one-step transition probability matrix.
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