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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IND ENG 173, First Midterm Solutions