Consider a system containing n components, where the lifetimes of the components are independent random variables and each has pdf fY(y) = λe^(-λy), y > 0. Show that the average time elapsing before the first component failure occurs is 1/(nλ).
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Step 1
Given that the pdf of the component lifetimes is fY(y) = λe^(-λy), we have: P(Y > y) = 1 - P(Y ≤ y) = 1 - ∫[0 to y] λe^(-λt) dt = 1 - (1 - e^(-λy)) = e^(-λy) Show more…
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