  The path-difference metric is one of the oldest distances for the comparison
of fully resolved phylogenetic trees, but its statistical properties are still
quite unknown. In this paper we compute the mean value of the square of the
path-difference metric between two fully resolved rooted phylogenetic trees
with $n$ leaves, under the uniform distribution. This complements previous work
by Steel and Penny, who computed this mean value for fully resolved unrooted
phylogenetic trees.
