Question: The lifetimes of six major components in a copier are independent exponential random variables with means of 8000, 10,000, 10,000, 20,000, 20,000, and 25,000 hours,

The lifetimes of six major components in a copier are independent exponential random variables with means of 8000, 10,000, 10,000, 20,000, 20,000, and 25,000 hours, respectively.
(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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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 full answer

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