On the total heights of random rooted binary trees (Q1333336)

The height of a vertex in a rooted binary tree is the distance from the vertex to the root. The total height of a rooted binary tree is the sum of the heights of its vertices. This paper computes the distribution and moments of the height of a rooted binary tree chosen uniformly at random from the set of all such trees with \(n\) unlabelled vertices. The study of such a random variable is motivated by applications in computer science and neuroscience. Previous papers on the subject focused only on the mean height of rooted binary trees.