= Solution
Under the independent-site <Jukes-Cantor model>, the number of differences from a known ancestor has a <binomial distribution> with mismatch probability
$$
p(t)=\frac34(1-e^{-\mu t}),\qquad d\sim\operatorname{Binomial}(L,p(t)).
$$
For an interior estimate, <maximum likelihood estimation> gives $\widehat p=d/L$. Equating this to the model probability and rearranging gives
$$
1-\frac{4d}{3L}=e^{-\widehat\mu t},\qquad\boxed{\widehat\mu=-\frac1t\ln\left(1-\frac{4d}{3L}\right)}.
$$
This is finite for $0\leq d/L<3/4$. At $d/L=3/4$, the estimate tends to infinity: the endpoint distribution has reached its limiting saturation and no finite rate can reproduce it exactly. For $d/L>3/4$, the displayed <logarithm> is not defined as a real number; within this model the constrained likelihood is maximized only as $\mu\to\infty$. For $d=0$ the boundary estimate is zero. The corresponding estimate of the actual event <mutation rate> is $\widehat r=3\widehat\mu/4$.
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