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Math Help - Help predicting future lifetime of a component w/ a joint pfd. thanks for looking.

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    Post Help predicting future lifetime of a component w/ a joint pfd. thanks for looking.

    The future lifetimes (in months) of two components of a machine have the following joint density function:
    f(x,y)=\left\{\begin{array}{lr}(6/125,000)(50-x-y)&0 < x < 50-y < 50\\0&otherwise\end{array}\right.

    What is the probability that both components are still functioning 15 months from now? thanks for your help
    Last edited by Intsecxtanx; November 16th 2009 at 05:49 PM.
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    Quote Originally Posted by Intsecxtanx View Post
    The future lifetimes (in months) of two components of a machine have the following joint density function:
    f(x,y)=\left\{\begin{array}{lr}(6/125,000)(50-x-y)&0 < x < 50-y < 50\\0&otherwise\end{array}\right.

    What is the probability that both components are still functioning 15 months from now? thanks for your help
    Drawing the region of integration helps.

    \Pr(X \geq 15, Y \geq 15) = \int_{y=15}^{y=35} \int_{x=15}^{x=50-y}  f(x, y) \, dx \, dy.
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