Question: Please show all work and all steps. A light bulb in a room has a lifetime that is independent identically distributed with a mean of

Please show all work and all steps.

A light bulb in a room has a lifetime that is independent identically distributed with a mean of 4 months. A janitor comes at times of a rate 2 (per month) Poisson processes to check the bulb and will replace the bulb immediately if it burns out.

(1) What is the rate for replacing a bulb?

(2) What is the limiting fraction of time that the light bulb works?

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