Question
Asked Dec 3, 2019
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You are given two components, component A and component B, and suppose their lifetimes, in hours, are expo-
nential with parameters XA and AB, respectively. Further, assume that their lifetimes are independent.
(a) If AA AB = 1/25, how many hours, on average, does the component that lives longer outlive the other
component by?
(b) If AA 1/25 and AB = 1/20, what is the probability component A outlives component B?
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You are given two components, component A and component B, and suppose their lifetimes, in hours, are expo- nential with parameters XA and AB, respectively. Further, assume that their lifetimes are independent. (a) If AA AB = 1/25, how many hours, on average, does the component that lives longer outlive the other component by? (b) If AA 1/25 and AB = 1/20, what is the probability component A outlives component B?

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Expert Answer

Step 1

According to the provided data,

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А exp В ~ еxp(23)

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Step 2

a. The concept of memory less property is used here, that is, if X~exp(λ), then P(X>t+s|X>s) = e-dt. Therefore, even elapsing or expanding ‘s’ unit of time X still follows exponen...

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E(X) 1 1/25 = 25 hours

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