Solution
= Solution
The <transition probability matrix> has entries
$$
P_{rs}(u)=\mathbb P(X(t+u)=s\mid X(t)=r)
$$
under the <time-homogeneous Markov property>. For the finite-state model in part d, the <transition semigroup of a continuous-time Markov chain> is
$$
P(u)=e^{uQ}.
$$