I'm studying CTMC (Continuous Time Markov Chains). I came across the following slide
I don't understand how they got
$M(t+h) = M(t) + \alpha h + M(t)\lambda h - M(t) \mu h +o(h)$
Could anyone please explain how to derive this expression for $M(t+h)$.
If I define $T(t)$ = Sojourn Time at $t$ and want to compute $N(t)=E(T(t))$
Then can I write $N(t)= M(t)/\lambda$ ?
How can I write a similar expression like $M(t+h)$ for $N(t+h)$?
Update: I found a similar question here which is already answered but my second question about computing $E[N(t+h)]$ still holds.