04fafin - 632 Introduction to Stochastic Processes Spring 2004 Final Exam Instructions Show calculations and give concise justifications for full

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 632 Introduction to Stochastic Processes Spring 2004 Final Exam Instructions: Show calculations and give concise justifications for full credit. Points add up to 200. 1. Four cages labeled A , B , C and D are connected by tubes as indicated in the diagram below. A rat runs from one cage to the other. Whenever it leaves a cage, it chooses at random among the tubes leading out of the cage. (So for example when the rat leaves A , it chooses one of B , C and D with equal probability, and when it leaves B , it chooses one of A and C with equal probability.) Let X n denote the n th cage the rat visits. Suppose the rat starts in A , so X = A . (a) (30 pts) What is the expected number of cages the rat visits until its first return to cage A , not counting the first and last visits to A ? (b) (25 pts) Find lim n →∞ P { X n = A, X n +1 = B, X n +2 = A } in other words the long-term limiting probability that we see the rat visit A- B- A ....
View Full 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

04fafin - 632 Introduction to Stochastic Processes Spring 2004 Final Exam Instructions Show calculations and give concise justifications for full

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online