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# hw3 - Markov chain(a Determine the transition matrix of the...

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IE 336 Handout #4 Sep. 19, 2008 Due Sep. 26, 2008 Homework Set #3 1. As in problem 4 from homework 1, let f ( x, y ) = 2 e - x - y , 0 y x < be the joint pdf of two random variables X and Y . Find E ( X ) and E ( Y | x ). 2. Solberg, Chapter 2 “Formulating Markov Chain Models”, exercise 1. 3. Solberg, Chapter 2 “Formulating Markov Chain Models”, exercise 4. 4. Consider a truck problem similar to the one that we considered in class. Assume that instead of 4 cities we now have 3 cities, Chicago, Dallas, and Philadelphia. There is a truck driver who makes one trip between these cities every day. He starts the trip in one of them and finishes in one of the other two. If he starts the trip in Chicago he will finish it in Dallas with probability 2 3 . On the other hand if he starts the trip in Dallas he will finish it in Philadelphia with probability 1 5 and if he starts in Philadelphia he will finish it in Chicago with probability 2 7 . Assume that the truck driving can be modeled as a stationary
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Unformatted text preview: Markov chain. (a) Determine the transition matrix of the Markov chain. (b) If a trip starts in Dallas ﬁnd the probability that it ﬁnishes in Chicago. (c) Assume that trips start in the morning and ﬁnish in the evening of the same day. If the driver is in Chicago on Wednesday morning ﬁnd the probability that he will be back in Chicago one day later, i.e. Thursday evening. 5. Consider the “college progression” example from class (section 2.7 in the book). Let p i = i 20 , 1 ≤ i ≤ 4 and q i = i 5 , 1 ≤ i ≤ 4. Assume that at some point a student (somebody who is still in college) is equally likely to be freshman, sophomore, junior or senior. (a) Compute the probability that a year later the same student is junior. (b) If during a school year a student is junior, ﬁnd the probability that during that same school year he/she will leave college. 1...
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