A system consists of two components connected in series. The system will fail when either of the

Question:

A system consists of two components connected in series. The system will fail when either of the two components fails. Let T be the time at which the system fails. Let X1 and X2 be the lifetimes of the two components. Assume that X1 and X2 are independent and that each has theWeibull with α = 2 and β = 0.2.
a. Find P(X1 > 5).
b. Find P(X1 > 5 and X2 > 5).
c. Explain why the event T > 5 is the same as the event {X1 > 5 and X2 > 5}.
d. Find P(T ≤ 5).
e. Let t be any positive number. Find P(T ≤ t), which is the cumulative function of T .
f. Does T have a Weibull If so, what are its parameters?
Distribution
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