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Math Help - Probability mean lifetime

  1. #1
    Junior Member
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    Probability mean lifetime

    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.
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  2. #2
    MHF Contributor
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    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.
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