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Two components operate in parallel in a device, so the device fails when and only when
Chapter 5, Problem 5.3-19(choose chapter or problem)
Two components operate in parallel in a device, so the device fails when and only when both components fail. The lifetimes, X1 and X2, of the respective components are independent and identically distributed with an exponential distribution with = 2. The cost of operating the device is Z = 2Y1 + Y2, where Y1 = min(X1, X2) and Y2 = max(X1, X2). Compute E(Z).
Questions & Answers
QUESTION:
Two components operate in parallel in a device, so the device fails when and only when both components fail. The lifetimes, X1 and X2, of the respective components are independent and identically distributed with an exponential distribution with = 2. The cost of operating the device is Z = 2Y1 + Y2, where Y1 = min(X1, X2) and Y2 = max(X1, X2). Compute E(Z).
ANSWER:Step 1 of 2
The pdf is,
Given,