The future lifetimes (in months) of two components of a machine have the following joint density function:
![](https://www.beanactuary.org/wp-content/uploads/2020/10/eq.40.1-300x60.jpg)
What is the probability that both components are still functioning 20 months from now?
Correct Answer
Solution: B
We are given that:
and we want to determine .
In order to determine integration limits, consider the following diagram:
![](https://www.beanactuary.org/wp-content/uploads/2020/10/eq.40.8.jpg)
We conclude that =
![](https://www.beanactuary.org/wp-content/uploads/2020/10/eq.40.9.jpg)