fetime 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 1 MA6.101 Probability And Statistics ASSIGNMENT 3 Due by : 11:59 PM, Nov 4th 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 replacements 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
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
1
MA6.101
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 replacements
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
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