2. A hard drive in a data center lasts k periods before failing with probability a, for k = 1,2,... Let X, be the remaining life of the hard drive in service at the end of period t. Thus, X,- 0 means that X4+1 will be the total operating lifetime of the next hard drive installed. Is (X,} a Markov chain? Explain your answer. If it is a Markov chain, give the transition probabilities; if it is not, give an example where the Markov property is violated.

2. A hard drive in a data center lasts k periods before failing with probability a, for k = 1,2,... Let X, be the remaining life of the hard drive in service at the end of period t. Thus, X,- 0 means that X4+1 will be the total operating lifetime of the next hard drive installed. Is (X,} a Markov chain? Explain your answer. If it is a Markov chain, give the transition probabilities; if it is not, give an example where the Markov property is violated.

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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