  We compute exactly the mean perimeter and area of the convex hull of N
independent planar Brownian paths each of duration T, both for open and closed
paths. We show that the mean perimeter < L_N > = \alpha_N, \sqrt{T} and the
mean area <A_N> = \beta_N T for all T. The prefactors \alpha_N and \beta_N,
computed exactly for all N, increase very slowly (logarithmically) with
increasing N. This slow growth is a consequence of extreme value statistics and
has interesting implication in ecological context in estimating the home range
of a herd of animals with population size N.
