= Solution
In the <Yule process>, each of $k$ branches gives birth independently at rate $\lambda$ per generation. The next birth therefore has total rate $k\lambda$. Its waiting time has an <exponential distribution>, so the mean <phylogenetic epoch> duration is
$$
\boxed{E_k^{\rm Yule}=\frac1{k\lambda}}.
$$
For the ensuing calculation use $E_2=1/(2\lambda)$, $E_3=1/(3\lambda)$ and $E_4=1/(4\lambda)$. This is the inter-event waiting-time convention requested in the question, including an observation interval with four branches. Stopping the forward process immediately when the fourth branch is born would instead leave a zero terminal interval and describe a different sampling convention.
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