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A professor has two light bulbs in his garage when both are

Question: A professor has two light bulbs in his garage. When both are burned out, they are replaced, and the next day starts with two working light bulbs. Suppose that when both are working, one of the two will go out with probability .02 (each has probability .01 and we ignore the possibility of losing two on the same day). However, when only one is there, it will burn out with probability .05.

(i) What is the long-run fraction of time that there is exactly one bulb working?

(ii) What is the expected time between light bulb replacements?

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