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1. Reliable strategy?| Suppose you have a control system in a potentially dangerous facility [such as a nuclear power station]. The system has a very important control microchip. To increase system reliability, a reservation strategy known as \"active redundancy\" is sometimes used. Such a strategy suggests that a set of nil identical microchips are put into permanent operation, even though only one microchip of the set is used in the operation of the system. All other microchips are in "active status" for immediate replacement in the event of a component failure. If X1,X2, ,X,, denote the operating times {until their first failure) of the n microchips, suppose that Xkarexpl) with El > 0 for each in: = 1, ,n. a] Represent the random variable that measures the total time of operation ofthe redundant system with n microchips. Solution: Tn = mxXl,X2, ...,X,,) b) Find the distribution function Fix} of the random variable from the previous part. _ .l. n - , Solution: Frnbr) = [{1 9 '5) Si 1 2 0, 0 SE x