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The lifetime of a lightbulb can be modeled with an exponential random variable with an expected lifetime of 1000 days. (a) Find the probability that

The lifetime of a lightbulb can be modeled with an exponential random variable with an expected lifetime of 1000 days.

(a) Find the probability that the lightbulb will function for more than 2000 days.

(b) Find the probability that the lightbulb will function for more than 2000 days, given that it is still functional after 500 day

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