04faex1

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

This preview shows pages 1–2. Sign up to view the full content.

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,

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 08/11/2008 for the course MATH 632 taught by Professor Seppalainen during the Spring '07 term at Wisconsin.

### Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online