The mean number of extreme lines in a convex hull of lines (Q1611060)

Write \(L(g)\) and \(R(g)\) for the left and right halfplane determined by an oriented line \(g\) in the plane. Given a set of oriented lines \(g_1,\dots,g_r\), their convex hull, \(H_0\), is the set of all oriented lines \(g\) such that \(\bigcap L(g_i) \subset L(g)\) and \(\bigcap R(g_i) \subset R(g)\). Choose \(n\) random, uniform, and independent lines, \(G_1,\dots,G_n\), from \(H_0\). The paper under review investigates the expected number of extreme lines of the convex hull of these random lines.