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DNNs play a major role in the state-of-the-art ASR systems. They can be used for extracting features and building probabilistic models for acoustic and language modelling. Despite their huge practical success, the level of theoretical understanding has remained shallow. This paper investigates DNNs from a statistical standpoint. In particular, the effect of activation functions on the distribution of the pre-activations and activations is investigated and discussed from both analytic and empirical viewpoints.