04faex1 - 632 Introduction to Stochastic Processes Spring...

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632 Introduction to Stochastic Processes Spring 2004 Midterm Exam I Instructions: Show calculations and give concise justifications for full credit. Don’t forget that theoretical ideas can help avoid tricky computations. The points add up 100. General notation: P x ( A ) is the probability of the event A when the chain starts in state x , P μ ( A ) the probability when the initial state is random with distribution μ . T y = min { n 1 : X n = y } is the first time after 0 that the chain visits y , or if no visit to y ever happens. ρ x,y = P x ( T y < ) is the probability that the chain visits y some time after time 0, given that it started at x . N ( y ) is the number of visits to state y , not counting a possible visit at time 0. 1. Imagine a road traveled by two kinds of vehicles, trucks and cars. Three out of every four trucks are followed by a car, while one of every five cars is followed by a truck. (a) (20 pts) Construct a Markov chain model with two states,
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This note was uploaded on 08/11/2008 for the course MATH 632 taught by Professor Seppalainen during the Spring '07 term at Wisconsin.

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04faex1 - 632 Introduction to Stochastic Processes Spring...

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