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5. A pressure transducer regulates a climate control system in a factory. The transducer fails according to an exponential distribution with rate one failure every five years on average. a. What is the cumulative distribution function of the time until failure? b. What is the probability that a transducer chosen at random functions for eight years without failure? 754 Chapter Thirteen Reliability and Maintainability c. What is the probability that a transducer that has functioned for eight years con- tinues to function for another eight years? 6. For the pressure transducer mentioned in Problem 5, use the failure rate function to estimate the likelihood that a transducer that has been operating for six years fails in the seventh year. How close is the approximation to the exact answer?

5. A pressure transducer regulates a climate control system in a factory. The transducer fails according to an exponential distribution with rate one failure every five years on average. a. What is the cumulative distribution function of the time until failure? b. What is the probability that a transducer chosen at random functions for eight years without failure? 754 Chapter Thirteen Reliability and Maintainability c. What is the probability that a transducer that has functioned for eight years con- tinues to function for another eight years? 6. For the pressure transducer mentioned in Problem 5, use the failure rate function to estimate the likelihood that a transducer that has been operating for six years fails in the seventh year. How close is the approximation to the exact answer?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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5. A pressure transducer regulates a climate control system in a factory. The transducer fails according to an exponential distribution with rate one failure every five years on average. a. What is the cumulative distribution function of the time until failure? b. What is the probability that a transducer chosen at random functions for eight years without failure? 754 Chapter Thirteen Reliability and Maintainability c. What is the probability that a transducer that has functioned for eight years con- tinues to function for another eight years? 6. For the pressure transducer mentioned in Problem 5, use the failure rate function to estimate the likelihood that a transducer that has been operating for six years fails in the seventh year. How close is the approximation to the exact answer?
Transcribed Image Text:5. A pressure transducer regulates a climate control system in a factory. The transducer fails according to an exponential distribution with rate one failure every five years on average. a. What is the cumulative distribution function of the time until failure? b. What is the probability that a transducer chosen at random functions for eight years without failure? 754 Chapter Thirteen Reliability and Maintainability c. What is the probability that a transducer that has functioned for eight years con- tinues to function for another eight years? 6. For the pressure transducer mentioned in Problem 5, use the failure rate function to estimate the likelihood that a transducer that has been operating for six years fails in the seventh year. How close is the approximation to the exact answer?
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