  We study random convex cones defned as positive hulls of $d$-dimensional
random walks and bridges. We compute expectations of various geometric
functionals of these cones such as the number of $k$-dimensional faces and the
sums of conic quermassintegrals of their $k$-dimensional faces. These
expectations are expressed in terms of Stirling numbers of both kinds and their
$B$-analogues.
