Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 207 / 2 / b

The hypotheses imply $a=1/5=0.2$ and $b=1/1.25=0.8$, so $a+b=1$. Conditional on the negative result at month 1, the likelihood is the probability of remaining in $S$ at month 2 and moving to $I$ by month 3. The supplied matrix exponential givesThe Markov property therefore gives