A lightbulb has a lifetime that is exponential with a mean of 200 days. When it burns out a janitor replaces it immediately. In addi- tion there is a handyman who comes at times of a Poisson process at rate 0.01/day and replaces the bulb as "preventive maintenance." (a) Consider the process of times when the bulb is replaced. What is this process? (b) What is the probability that the next two bulb replacements are done by the handyman? (c) In the long run what fraction of the replacements are due to failure