Consider a system with one component that is subject to failure, and suppose that we have 120 copies of the component. Suppose f
urther that the lifespan of each copy is an independent exponential random variable with mean 10 days, and that we replace the component with a new copy immediately when it fails. a. Approximate the probability that the system is still working after 1300 days.
b. Suppose that the time to replace the component is a random variable that is uniformly distributed over ( 0 , 0.5 ). Approximate the probability that the system is still working after 1100 days.
