A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Question 3)
A video cassette recorder manufacturer is so certain of its quality control that it is offering a
complete replacement warranty if a recorder fails within 2 years. Based upon compiled data,
the company has noted that only 1 percent of its recorders fail during the first year, whereas 5
percent of the recorders that survive the first year will fail during the second year. The warranty
does not cover replacement recorders.
a) Formulate the evolution of the status of a recorder as a Markov chain whose states
include two absorption states that involve needing to honor the warranty or having the
recorder survive the warranty period. Then construct the one-step transition matrix.
b) Find the probability that the manufacturer will have to honor the warranty.
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Transcribed Image Text:Question 3) A video cassette recorder manufacturer is so certain of its quality control that it is offering a complete replacement warranty if a recorder fails within 2 years. Based upon compiled data, the company has noted that only 1 percent of its recorders fail during the first year, whereas 5 percent of the recorders that survive the first year will fail during the second year. The warranty does not cover replacement recorders. a) Formulate the evolution of the status of a recorder as a Markov chain whose states include two absorption states that involve needing to honor the warranty or having the recorder survive the warranty period. Then construct the one-step transition matrix. b) Find the probability that the manufacturer will have to honor the warranty.
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