Formalized neuron: probabilistic description and asymptotic theorems

The aim of the present paper is to study a formalized neuron from a probabilistic point of view. Some simple situations are taken into account; particular attention is then given to the case when the number of input lines becomes very large and sufficient conditions to apply some asymptotic theorems are made explicit. In particular, the central limit theorem is studied, and under the hypothesis of its applicability the probability for the neuron to fire k times in a fixed time interval Nτ is finally calculated.