(Answered) Suppose that 5 components are sequentially connected in a

Statistics

Suppose that 5 components are sequentially connected in a such a way that the whole system works as long as all of them work. Assume that the lifetime of each component has an Exponential distribution with mean 100. Furthermore, assume that these components work (and fail) independently from each other. Let X be the time at which the system fails.

a) Show that P(X >or =x) = exp(- x/20)

b) Find the cumulative distribution function F(x) of X.

c) Find the expected failure time of the system

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