The lifetime in hours of a certain component of a machine has the continuous probability density function f (x) = 1 e-/1000 1000 x 2 0. The machine contains five similar components, the lifetime of each having the above distribution. The makers are considering offering a guarantee that not more than two of the original components will have to be replaced during the first 1000 hours of use. Find the probability that such a guarantee would be violated, assuming that the components wear out independently, and that if a component does fail then the replacement used is of particularly high quality and will certainly last for the 1000 hours.
The lifetime in hours of a certain component of a machine has the continuous probability density function f (x) = 1 e-/1000 1000 x 2 0. The machine contains five similar components, the lifetime of each having the above distribution. The makers are considering offering a guarantee that not more than two of the original components will have to be replaced during the first 1000 hours of use. Find the probability that such a guarantee would be violated, assuming that the components wear out independently, and that if a component does fail then the replacement used is of particularly high quality and will certainly last for the 1000 hours.
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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