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 ma] 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 XLXZ, ...,Xn denote the operating times {until their first failure) of the n microchips, suppose that kaexp) with El > U for each k = 1, ...,n. a) Represent the random variable that measures the total operating time of the redundant system with n microchips. b] Establish the distribution function F(x} of the random variable from the previous part. c) Establish the expected uptime of the redundant system. d] For a redundant system with n=10 microchips, determine the expected time. e} Com pare this average time (n=10} with the average time when you have only one microchip. f) Would you consider this strategy reliable? justify To count the exercise as correct, justify each step used