For $T=$ age at death minus $60$, the observations are
$$
2,\ 7,\ 14^+,\ 15,\ 19^+,\ 21^+.
$$
There are three distinct event times and hence three independent discrete hazards $q_2,q_7,q_{15}$. Their risk-set sizes are $6,5,3$, so
$$
\boxed{L(q_2,q_7,q_{15})
=q_2(1-q_2)^5q_7(1-q_7)^4q_{15}(1-q_{15})^2.}
$$
The <maximum-likelihood estimates> are $\widehat q_2=1/6$, $\widehat q_7=1/5$, and $\widehat q_{15}=1/3$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 207 / 4 / b / ii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/iii/paper-207/4/b/ii/solution