# Predicting the failure of components that follow a bivariate distribution

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• Nov 22nd 2009, 03:48 PM
Intsecxtanx
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
• Nov 23rd 2009, 01:07 AM
mr fantastic
Quote:

Originally Posted by Intsecxtanx
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).