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sts of five identical components connected in series as shown 2 3 4 As soon...

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sts of five identical components connected in series as shown 2 3 4 As soon as one components fails the entire system will fail Suppose each component has a lifetime that is exponentially distributed with 0 01 and that components fail independently of one another Define events A ith component lasts at least t hours i 1 5 so that the A s are independent events Let X the time at which the system fails that is the shortest minimum lifetime among the five components a The event X t is equivalent to what event involving A A UA n A3 U A4 A5 A UA U A3 UA4 UA5 A A A3 A4 A5 n n A n A U A3 n A4 U A5 b Using the independence of the A s compute P X t P X t Obtain F t P X t F t Obtain the pdf of X 500 A5

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