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

1. ## 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

2. Originally Posted by Intsecxtanx
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.

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