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Thread: exponential distribution

  1. #1
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    exponential distribution

    The lifetime of a brake has an exponential distribution with mean BETA? What is the probability the
    brake lasts more than twice its expected lifetime?

    I would think it would be something like this. Am I close? How would I solve for two unknowns?

    1 - e^(-y/BETA) = 1 - e^(-y/BETA)
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  2. #2
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    Re: exponential distribution

    exponential distribution w/parameter $\lambda$ has mean $\lambda^{-1}$

    so your distribution has parameter $\beta^{-1}$

    the CDF with parameter $\lambda$ is given as

    $1-e^{-\lambda x}$ which here translates to

    $F(x) = 1 - e^{-\frac x \beta}$

    You want to know the probability the brakes last $2\beta$ or longer so evaluate

    $1 - F(2 \beta)= e^{-2}$
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