# Predicting the failure of components that follow a bivariate distribution

• November 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?

$f(x, y) = \frac{x + y}{27}$ for 0 < x < 3 and 0 < y < 3.