Measure time in years after age 70. Residence in the care home begins at time 3, so inclusion is conditional on $T>3$: this is <left truncation>, also called delayed entry. Exact death at time 13 contributes
$$
\mathbb P(T=13\mid T>3)
=\frac{F(13)-F(13^-)}{S(3)}
=\frac{S(13^-)-S(13)}{S(3)}.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 207 / 6 / a / vi / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-207/6/a/vi/solution