# Thread: Predicting component failture with joint density functions

1. ## Predicting component failture with joint density functions

A device contains two components. The device fails if either component fails. The joint density function of the lifetimes of the components, measured in hours, is f(s, t) , where $0 < s < \infty$ and $0 < t < \infty$. What is the probability that the device fails during the first half hour of operation, expressed in terms of the cumulative distribution function F (s, t)? Thanks for your help

2. Originally Posted by Intsecxtanx
A device contains two components. The device fails if either component fails. The joint density function of the lifetimes of the components, measured in hours, is f(s, t) , where $0 < s < \infty$ and $0 < t < \infty$. What is the probability that the device fails during the first half hour of operation, expressed in terms of the cumulative distribution function F (s, t)? Thanks for your help
You need to express Pr(S < 1/2 or T < 1/2) = 1 - Pr(S > 1/2 and T > 1/2) in terms of the cdf.