Solution
= Solution
The <probability density function> is the negative derivative of the <survivor function>:
$$
\boxed{f(t)=-F'(t),\qquad F(t)=\int_t^\infty f(s)ds.}
$$
Indeed the <probability> in a short interval is $F(t)-F(t+\varepsilon)$, and division by its width gives the derivative relation.