By <Bayes theorem>, the <frailty distribution among survivors> has density
$$
g(u,t)
=\frac{\mathbb P(T>t\mid U=u)g(u)}{\overline S(t)}
=\{1+H_0(t)\}e^{-u\{1+H_0(t)\}},
\qquad u\geq0.
$$
It is an <exponential distribution> with rate $1+H_0(t)$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 207 / 6 / b / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-207/6/b/solution