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Math Help - Predicting the failure of components that follow a bivariate distribution

  1. #1
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    Post Predicting the failure of components that follow a bivariate distribution

    A device runs until either of two components X and Y fails, at which point the device stops running. The joint density function of the lifetimes of the two components, both measured in hours, is
    f(x, y) = \frac{x + y}{27} for 0 < x < 3 and 0 < y < 3.

    how can you calculate the probability that the device fails during its first half hour of operation?

    thank you for your help
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    Quote Originally Posted by Intsecxtanx View Post
    A device runs until either of two components X and Y fails, at which point the device stops running. The joint density function of the lifetimes of the two components, both measured in hours, is
    f(x, y) = \frac{x + y}{27} for 0 < x < 3 and 0 < y < 3.

    how can you calculate the probability that the device fails during its first half hour of operation?

    thank you for your help
    Calculate 1 - Pr(X > 1/2, Y > 1/2).
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