  The path-difference metric is one of the oldest and most popular distances
for the comparison of phylogenetic trees, but its statistical properties are
still quite unknown. In this paper we compute the expected value under the Yule
model of evolution of its square on the space of fully resolved rooted
phylogenetic trees with n leaves. This complements previous work by Steel-Penny
and Mir-Rossell\'o, who computed this mean value for fully resolved unrooted
and rooted phylogenetic trees, respectively, under the uniform distribution.
