  In this article, we consider the numerical approximation of far-field
statistics for acoustic scattering problems in the case of random obstacles. In
particular, we consider the computation of the expected far-field pattern and
the expected scattered wave away from the scatterer as well as the computation
of the corresponding variances. To that end, we introduce an artificial
interface, which almost surely contains all realizations of the random
scatterer. At this interface, we directly approximate the second order
statistics, i.e., the expectation and the variance, of the Cauchy data by means
of boundary integral equations. From these quantities, we are able to rapidly
evaluate statistics of the scattered wave everywhere in the exterior domain,
including the expectation and the variance of the far-field. By employing a
low-rank approximation of the Cauchy data's two-point correlation function, we
drastically reduce the cost of the computation of the scattered wave's
variance. Numerical results are provided in order to demonstrate the
feasibility of the proposed approach.
