= Solution
The first departure from the no-symptoms state has an <exponential distribution> with rate $\lambda$. Spending the entire interval there means no departure at all, so
$$
\boxed{\mathbb P(\text{no symptoms throughout }[0,t]\mid X(0)=1)=e^{-\lambda t}.}
$$
This is the <holding time> survival <probability>. The <transition probability> $p_{11}(t)$ only says that the patient is symptom-free at the endpoint, allowing an onset and recovery in between, and is therefore not the answer. The formula also covers $\lambda=0$, when state 1 is absorbing.
Back to article page
