20. At a certain university, suppose each student moves on to the next year of classes with probability p, stays in the same class with probability r, and leaves the university for reasons other than graduating with probability q. Assume there are 4 classes, and after moving on from class 4, the student graduates and becomes an alumni of the university. (a) Sketch a state diagram and determine the transition matrix. What are the absorbing states? (b) If p.7,q.2, r = .1, find out the average amount of time a student spends in college. Discuss your result. (c) Determine the probability a student currently in their third year of classes will graduate from the university.

20. At a certain university, suppose each student moves on to the next year of classes with probability p, stays in the same class with probability r, and leaves the university for reasons other than graduating with probability q. Assume there are 4 classes, and after moving on from class 4, the student graduates and becomes an alumni of the university. (a) Sketch a state diagram and determine the transition matrix. What are the absorbing states? (b) If p.7,q.2, r = .1, find out the average amount of time a student spends in college. Discuss your result. (c) Determine the probability a student currently in their third year of classes will graduate from the university.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 9EQ

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