A manufacturer of electrical components has determined that the length of time t (in hundreds of hours)

Question:

A manufacturer of electrical components has determined that the length of time t (in hundreds of hours) before a certain one of its components fails has probability density function

f(t) = 2t e^-t2

Find the probability that a randomly selected one of these components lasts

(a) More than 150 hours.

(b) More than 150 hours given that it lasts more than 100 hours.

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