ind the expected total illumination time (in years), given you do exactly 3 bulb re- placements 2. Your replacements are now probabilistic. If your current bulb breaks, you replace it with a bulb of type A with probability p, and with type B with probability (1 – p). Find the expected total illumination time (in years), given you do exactly n bulb replacements, and start with bulb of type A
The lifetime of a bulb is modeled as a Poisson variable. You have two bulbs types A and
B with expected lifetime 0.25 years and 0.5 years, respectively. When a bulb’s life ends, it stops working. You start with new bulb of type A at the start of the year. When it stops
working, you replace it with a bulb of type B. When it breaks, you replace with a type A
bulb, then a type B bulb, and so on.
1. Find the expected total illumination time (in years), given you do exactly 3 bulb re-
placements
2. Your replacements are now probabilistic. If your current bulb breaks, you replace
it with a bulb of type A with
p). Find the expected total illumination time (in years), given you do exactly n bulb
replacements, and start with bulb of type A
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