= Solution
The deterministic equation has solution $n(t)=n(0)e^{(B-D)t}$ and is identical in form to the equation for the stochastic <expected value>. It therefore identifies only the net rate
$$
r=B-D.
$$
The <variance> equation also contains the total event rate $s=B+D$. Once $r$ and $s$ are inferred,
$$
\boxed{\ B=\frac{s+r}{2},\qquad D=\frac{s-r}{2}\ }.
$$
The deterministic trajectory cannot distinguish frequent births and deaths that nearly cancel from infrequent events with the same net growth, whereas fluctuations can.
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