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In this article, we deal with the numerical solution of acoustic scattering problems in case of random obstacles. We compute the second order statistics, i.e. the expectation and the variance, of the solution's Cauchy data on an artificial, deterministic interface by means of boundary integral equations. As a consequence, 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 using adoi:10.5451/unibas-ep70079 fatcat:5co7xwrvejfx5gb6ljqydk37cy