The lifetime of a component computer is exponentially distributed with mean 1 year. Management hopes to increase the reliability by replacing the component with a new one if it has not failed after 2 years.

Compute the mean lifetime of the components used in the computers with the replacement policy.

2. Fun way...

$\int_{0}^{2}e^{-x}\;dx = 1 - \frac{1}{e^{2}}$

$\int_{2}^{\infty}e^{-x}\;dx = \frac{1}{e^{2}}$ -- Well, that was pretty obvious.

$\int_{0}^{2}x*e^{-x}\;dx = 1 - \frac{3}{e^{2}}$

Then

$\left(1 - \frac{1}{e^{2}}\right)*\left(1 - \frac{3}{e^{2}}\right) + \frac{1}{e^{2}}*3$

I think the '3' on the end is the hardest part.

I'm rather surprised by the result. Maybe it's wrong. Think it through.