The lifetimes of six major components in a copier are independent exponential random variables with means of
Question:
(a) What is the probability that the lifetimes of all the components exceed 5000 hours?
(b) What is the probability that at least one component lifetime exceeds 25,000 hours?
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Step by Step Answer:
a Let Xx2X6 denote the lifetimes of the six components respectively Because of independence PX1 5000 X2 5000 X6 5000PX 5000PX2 5000PX6 5000 If X is exponentially distributed with mean 8 then 1 and PX x et dt e 025 025 0 02 2325 e 1 ex8 Therefore the answer is X 00978 b The probability that at least one component ...View the full answer
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Related Book For 
Applied Statistics And Probability For Engineers
ISBN: 9781118539712
6th Edition
Authors: Douglas C. Montgomery, George C. Runger
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