Solution

Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 34 / 6 / Solution

Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 4 / 14B / iii / Solution

{title2=$f_\tau(t)$}

When a <first-passage time> $\tau$ has an absolutely continuous distribution, its density is $f_\tau(t)=-S'(t)$, where $S(t)=\mathbb P(\tau>t)$ is its <survival function>. In a <continuous-time Markov chain>, this density is the total probability flux from surviving states into the absorbing set.

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 Incoming links: First-passage-time density