Let $u_j^{(1)}=u_j$ and $u_j^{(0)}=1-u_j$. Applying the <Nelson–Aalen estimator> separately to group $k$ gives
$$
\widehat H_j^{(k)}
=\sum_{\ell=1}^{j}\frac{u_\ell^{(k)}}{r_\ell^{(k)}},
$$
with a zero contribution when the event at $a_\ell$ occurs in the other group.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 207 / 4 / c / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-207/4/c/i/solution