For constant hazards $h_A=\theta$ and $h_B=\phi$,
$$
F_A(t)=\int_0^t\theta e^{-(\theta+\phi)u}\,du
=\frac{\theta}{\theta+\phi}
\left(1-e^{-(\theta+\phi)t}\right).
$$
Its limit $\theta/(\theta+\phi)$ is the probability that $A$ occurs before $B$.


Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 207 / 6 / a / v / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-207/6/a/v/solution