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Mathematics, 07.03.2020 02:56 CameronVand21

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. Supposethat when both are working, one of the two will go out with probability 0.02 (eachhas probability 0.01 and we ignore the possibility of losing two on the same day).However, when only one is there, it will burn out with probability 0.05. (i) What isthe long-run fraction of time that there is exactly one bulb working? (ii) What is theexpected time between light bulb replacements?

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