# Una dimostrazione diretta della legge di probabilit\`a di Poisson (A direct proof of the Poisson probability law)

## TL;DR

This paper provides an elementary, direct proof of the Poisson probability law as an alternative to the traditional binomial limit derivation, and applies it to a problem in statistical mechanics.

## Contribution

It introduces a simple, direct proof of the Poisson law and demonstrates its application to statistical mechanics problems.

## Key findings

- Elementary proof of Poisson law presented
- Alternative derivation from binomial distribution shown
- Applied to a statistical mechanics problem

## Abstract

The purpose of this paper is to prove directly, by an elementary method, the Poisson probability law. This proof is offered as an alternative to the more usual derivation from binomial distribution in the limit of small probabilities. The same proof is then applied to the solution of a problem in statistical mechanics. --- Lo scopo di questo articolo \`e dimostrare direttamente, con un metodo elementare, la legge di probabilit\`a di Poisson. Questa dimostrazione \`e proposta in alternativa alla pi\`u consueta derivazione dalla distribuzione binomiale nel limite delle piccole probabilit\`a. La stessa dimostrazione viene quindi applicata alla soluzione di un problema di meccanica statistica.