. If the machine is running smoothly, there is 1% chance that by the next morning it will have exploded (this will destroy the machine), there is also a 9% chance that some part of the machine will break leading to it being temporarily broken. If neither of these things happen then the next morning there is an equal probability of it running smoothly or running but needing adjustment. • If the machine is temporarily broken in the morning then an engineer will attempt to repair the machine that day, there is an equal chance that they succeed and the machine is running smoothly by the next day or they fail and cause the machine to explode. . If the machine is running but needing adjustment there is a 20% chance that an engineer will repair it so it is running smoothly the next day and otherwise it will remain in the same state for the next day. Taking X₂ to be the state of the machine on the morning of day i for i E N we get a Markov chain which models the state of the machine. (a) Write down the transition matrix for this Markov chain.

. If the machine is running smoothly, there is 1% chance that by the next morning it will have exploded (this will destroy the machine), there is also a 9% chance that some part of the machine will break leading to it being temporarily broken. If neither of these things happen then the next morning there is an equal probability of it running smoothly or running but needing adjustment. • If the machine is temporarily broken in the morning then an engineer will attempt to repair the machine that day, there is an equal chance that they succeed and the machine is running smoothly by the next day or they fail and cause the machine to explode. . If the machine is running but needing adjustment there is a 20% chance that an engineer will repair it so it is running smoothly the next day and otherwise it will remain in the same state for the next day. Taking X₂ to be the state of the machine on the morning of day i for i E N we get a Markov chain which models the state of the machine. (a) Write down the transition matrix for this Markov chain.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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