A system consists of two components with independent lifetimes X1 and X2, where X1 is exponentially distributed with rate λ, and X2 has a uniform distribution on [0, 1]. The components operate in...

A system consists of two components with independent lifetimes X1 and X2, where X1 is exponentially distributed with rate λ, and X2 has a uniform distribution on [0, 1]. The components operate in parallel, and the system lifetime is max{X1, X2} (the system is operational if and only if at least one component is working). When the system fails, it is replaced by another system with an identical and independent lifetime, and this is repeated indefinitely. The number of system renewals over time forms a renewal process N(t). Find the distribution and mean of the system lifetime. Find the distribution and mean of N(t) (reduce your formulas as much as possible). Determine the portion of time that (a) two components are working, (b) only type 1 component is working, and (c) only type 2 component is working.