  We study an inverse scattering problem associated with a Schr\"odinger system
where both the potential and source terms are random and unknown. The
well-posedness of the forward scattering problem is first established in a
proper sense. We then derive two unique recovery results in determining the
rough strengths of the random source and the random potential, by using the
corresponding far-field data. The first recovery result shows that a single
realization of the passive scattering measurements uniquely recovers the rough
strength of the random source. The second one shows that, by a single
realization of the backscattering data, the rough strength of the random
potential can be recovered. The ergodicity is used to establish the single
realization recovery. The asymptotic arguments in our study are based on the
theories of pseudodifferential operators and microlocal analysis.
