Suppose that a certain system contains three components that function independently of each other and are connected in series, as defined in Exercise 5 of Sec 3 7, so that the system fails as soon as one of the components fails Suppose that the length of life of the first component, measured in hours, has the exponential distribution with parameter 0 001, the length of life of the second component has the exponential distribution with parameter 0 003, and the length of life of the third component has the exponential distribution with parameter 0 006 Determine the probability that the system will not fail before 100 hours

Question: Suppose that a certain system contains three components that function independently of each other and are connected in series, as defined in Exercise 5 of

Suppose that a certain system contains three components that function independently of each other and are connected in series, as defined in Exercise 5 of Sec. 3.7, so that the system fails as soon as one of the components fails. Suppose that the length of life of the first component, measured in hours, has the exponential with parameter β = 0.001, the length of life of the second component has the exponential with parameter β = 0.003, and the length of life of the third component has the exponential with parameter β =0.006. Determine the probability that the system will not fail before 100 hours.

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