Based on the assumption that most probability densities in real life can be approximated by a mixture of Gaussian densities, the authors propose a set of algorithms for training a multi-layered perceptron as a parallel distributed processing network (PDP) to estimate various probability densities and to serve as a Bayes classifier. The effectiveness of a PDP density estimator was measured in terms of the relative difference between the target p.d.f. and the network output representing the estimation. The classification rate of the PDP network was effectively identical to that of the Bayes classifier. for invoking these algorithms.Although the p-persistent protocol introduces a longer packet delay, the difference is small.