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Beamforming with wireless acoustic sensor networks (WASNs) has recently drawn the attention of the research community. As the number of microphones grows it is difficult, and in some applications impossible, to determine their layout beforehand. A common practice in analyzing the expected performance is to utilize statistical considerations. In the current contribution, we consider applying the speech distortion weighted multi-channel Wiener filter (SDW-MWF) to enhance a desired source propagating in a reverberant enclosure where the microphones are randomly located with a uniform distribution. Two noise fields are considered, namely, multiple coherent interference signals and a diffuse sound field. Utilizing the statistics of the acoustic transfer function (ATF), we derive a statistical model for two important criteria of the beamformer (BF): the signal to interference ratio (SIR), and the white noise gain. Moreover, we propose reliability functions, which determine the probability of the SIR and white noise gain to exceed a predefined level. We verify the proposed model with an extensive simulative study.