How to analyze this expected value of a random tree?

Revision en1, by Y25t, 2021-09-30 10:26:42

In a rooted tree $$$T$$$, let $$$dep_u$$$ be the distance from $$$u$$$ to the root, $$$dis_u$$$ be the distance from $$$u$$$ to the deepest leaf in $$$u$$$'s subtree.

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en4 English Y25t 2021-09-30 12:18:42 0 (published)
en3 English Y25t 2021-09-30 12:13:56 1 Tiny change: 'ooted tree.\n\nHow t' -> 'ooted trees.\n\nHow t' (saved to drafts)
en2 English Y25t 2021-09-30 10:51:01 216 Tiny change: 's subtree.' -> 's subtree.\nLet $f(T)=\sum_{u\in T} dep_u\times dis_u$, ' (published)
en1 English Y25t 2021-09-30 10:26:42 194 Initial revision (saved to drafts)