Question: Let X be the time to failure (in years) of a computer chip, and suppose that the chip has been operating properly for a years.

Let X be the time to failure (in years) of a computer chip, and suppose that the chip has been operating properly for a years. Then, it can be shown that the probability that the chip will fail within the next b years is Pr(aX a + b) Pr (a X) (6)

Compute this probability for the case when X is an exponential random variable with density function f (x) = ke^-kx, and show that this probability equals Pr (0 ≤ X ≤ b). This means that the probability given by (6) does not depend on how long the chip has already been operating. Exponential random variables are therefore said to be memoryless.

Pr(aX a + b) Pr (a X) (6)

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