Homework SourseA lamp uses one bulb with an average lifespan of 1300 hours
A lamp uses one bulb with an average lifespan of 1300 hours. We bought two bulbs, so once the first bulb burns out, we replace it with a second of the same type. Assuming we can model the probability of failure of these bulbs by an exponential density function with mean =1300, find the probability that we can keep the lamp lit longer than 1800 hours.
A lamp uses one bulb with an average lifespan of 1300 hours. We bought two bulbs, so once the first bulb burns out, we replace it with a second of the same type. Assuming we can model the probability of failure of these bulbs by an exponential density function with mean =1300, find the probability that we can keep the lamp lit longer than 1800 hours.
Solution
Let X and Y denote respectively the life hour of first and second bulb.
Assuming X,Y ~ Exp(mean = 1300) i.i.d.
Therefore X+Y ~ Gamma( 2,1300)
Required to find
P[X + Y > 1800]
= 1 - P[Gamma(2,1300) < 1800 ]
= 1 - 0.403 (using software)
= 0.597 (Answer)
