The lifetime of a lightbulb can be modeled with an exponential random variable with an expected lifetime of 700 days. (a) Find the probability that the lightbulb will function for more than 1400 days. (b) Find the probability that the lightbulb will function for more than 1400 days, given that it is still functional after 500 days.

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The lifetime of a lightbulb can be modeled with an exponential random variable with
an expected lifetime of 700 days.

Please help with parts a and b:

 

The lifetime of a lightbulb can be modeled with an exponential random variable with
an expected lifetime of 700 days.
(a) Find the probability that the lightbulb will function for more than 1400 days.
(b) Find the probability that the lightbulb will function for more than 1400 days, given
that it is still functional after 500 days.
Transcribed Image Text:The lifetime of a lightbulb can be modeled with an exponential random variable with an expected lifetime of 700 days. (a) Find the probability that the lightbulb will function for more than 1400 days. (b) Find the probability that the lightbulb will function for more than 1400 days, given that it is still functional after 500 days.
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