A smartphone manufacturer is so certain of its quality control that it offers a complete replacement warranty if the smartphone fails within 3 years. Based upon compiled data, the company notes that there is a 2 percent chance that its smartphone will fail during the first year, a 10 percent chance that a smartphone that survives the first year fails during the second year, and a 20 percent chance that a smartphone that survives the first two years fails during the third year. The warranty does not cover replacement smartphones after the third year. (a) Formulate the evolution of the status of the smartphone as a Markov Chain whose states include two abosrbing states that involve needing to honor the warranty or having the smartphone survive the warranty period. Construct the transition probability matrix and draw the transition probability diagram. (b) Determine the probability that: (a) the manufacturer will have to honor the warranty and (b) the manufacturer will not have to honor the warranty. Provide any equations that were used to calculate these probabilities along with (briefly) describing how you solved these equations (for example, you could show the steps in an excel file).
A smartphone manufacturer is so certain of its quality control that it offers a complete replacement warranty if the smartphone fails within 3 years. Based upon compiled data, the company notes that there is a 2 percent chance that its smartphone will fail during the first year, a 10 percent chance that a smartphone that survives the first year fails during the second year, and a 20 percent chance that a smartphone that survives the first two years fails during the third year. The warranty does not cover replacement smartphones after the third year. (a) Formulate the evolution of the status of the smartphone as a Markov Chain whose states include two abosrbing states that involve needing to honor the warranty or having the smartphone survive the warranty period. Construct the transition probability matrix and draw the transition probability diagram. (b) Determine the probability that: (a) the manufacturer will have to honor the warranty and (b) the manufacturer will not have to honor the warranty. Provide any equations that were used to calculate these probabilities along with (briefly) describing how you solved these equations (for example, you could show the steps in an excel file).
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
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Question
A smartphone manufacturer is so certain of its quality control that it
offers a complete replacement warranty if the smartphone fails within 3 years. Based upon
compiled data, the company notes that there is a 2 percent chance that its smartphone will
fail during the first year, a 10 percent chance that a smartphone that survives the first year
fails during the second year, and a 20 percent chance that a smartphone that survives the first
two years fails during the third year. The warranty does not cover replacement smartphones
after the third year.
(a) Formulate the evolution of the status of the smartphone as a Markov Chain whose states
include two abosrbing states that involve needing to honor the warranty or having the
smartphone survive the warranty period. Construct the transition probability matrix
and draw the transition probability diagram.
(b) Determine the probability that: (a) the manufacturer will have to honor the warranty
and (b) the manufacturer will not have to honor the warranty. Provide any equations
that were used to calculate these probabilities along with (briefly) describing how you
solved these equations (for example, you could show the steps in an excel file).
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