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

• Nov 16th 2009, 04:29 PM
Intsecxtanx
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:
$\displaystyle f(x,y)=\left\{\begin{array}{lr}(6/125,000)(50-x-y)&0 < x < 50-y < 50\\0&otherwise\end{array}\right.$

What is the probability that both components are still functioning 15 months from now? thanks for your help
• Nov 16th 2009, 06:22 PM
mr fantastic
Quote:

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

What is the probability that both components are still functioning 15 months from now? thanks for your help

Drawing the region of integration helps.

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