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Unformatted text preview: The system will fail if either of the two components fails. Let T be the time at which the system fails Let X 1 and X 2 be the lifetimes of the two components. Assume that X 1 and X 2 are independent and that each has the Weibull distribution with α = 2 and β = 0.2. (a) Find P( X 1 > 5). (b) Find P( X 1 > 5 and X 2 > 5). (c) Explain why the event T > 5 is the same as the event { X 1 > 5 and X 2 > 5}. (d) Find P( T ≤ 5). (e) Let t be any positive number. Find P( T ≤ t ), which is the cumulative distribution function of T . (f) Does T have a Weibull distribution? If so, what are its parameters. 4. Let X Geom( p ). Find the Maximum Likelihood Estimator (MLE) of p ....
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 Spring '12
 Dr.Kwok

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