Solution
= Solution
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 $\widehat q_{15}=1/3$.