First-moment equation of a birth-death process
= First-moment equation of a birth-death process
Since births and deaths change the state by $+1$ and $-1$,
$$
\frac d{dt}\mathbb{E} N_t=\mathbb{E}[b_{N_t}-d_{N_t}].
$$
= First-moment equation of a birth-death process
Since births and deaths change the state by $+1$ and $-1$,
$$
\frac d{dt}\mathbb{E} N_t=\mathbb{E}[b_{N_t}-d_{N_t}].
$$