The elevator of a building with a ground floor and two floors makes trips from one floor to another. The floor at which the nth elevator trip ends follows a Markov chain. It is known that half of the trips that leave from the ground floor go to each of the other two floors, while if a trip starts on the first floor, only 25% of the time it ends on the second. Finally, if a journey begins on the second floor, it always ends on the ground floor. How many trips on average will a person who is on the ground floor and wants to get to the second floor make?

The elevator of a building with a ground floor and two floors makes trips from one floor to another. The floor at which the nth elevator trip ends follows a Markov chain. It is known that half of the trips that leave from the ground floor go to each of the other two floors, while if a trip starts on the first floor, only 25% of the time it ends on the second. Finally, if a journey begins on the second floor, it always ends on the ground floor. How many trips on average will a person who is on the ground floor and wants to get to the second floor make?

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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