A) The time until a component is taken out of service is uniformly distributed on 0 to 8 hours. Two such independent components are put in series, and the whole system goes down when one of the components goes down. If Xi (i=1,2) represents the component run times, then Y=min(X1,X2) represents the system lifetime. Devise two distinct ways to generate Y. [Hint: One way is relatively straightforward using the random numbers. For the other method, compute the CDF of Y and then use the independence of the component times].

B) Assume the component lifetimes are exponentially distributed, one with mean 2 hours and the other with mean 6 hours. Rework the above problem (in a) under this assumption.

Please show all work.