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Consider a system with one component that is subject to failure, and suppose that we have...

Consider a system with one component that is subject to failure, and suppose that we have 90 copies of the component. Suppose further that the lifespan of each copy is an independent exponential random variable with mean 30 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 3600 days.
Probability ≈≈

(b) Now, suppose that the time to replace the component is a random variable that is uniformly distributed over (0,0.5)(0,0.5). Approximate the probability that the system is still working after 4500 days.
Probability ≈≈

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