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Suppose a chandelier has 2019 bulbs, each has independent random lifetimes that is uniformly distributed on...

Suppose a chandelier has 2019 bulbs, each has independent random lifetimes that is uniformly distributed on an interval [0,β] with the same variance as an exp(1/4) variable. (You have to figureout the value of β.) Find the expected time until 2001 bulbs have burned out.

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Answer #1

The lifetimes of the bulbs are uniformly distributed on an interval . That is .

The variance of the random variable is

Also .

It is given that variance is equal to . Thus,

The time until 2001 bulbs have burned out is the random variable .

The expected value is

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