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Introduction The Poisson distribution is usually introduced by its probability mass function (PMF). It is then tied back to the binomial distribution by showing that a particular parameterization of the binomial distribution converges to the Poisson distribution. This approach is somewhat unsatisfying: it does not give much insight into the Poisson distribution and, namely, why it is used to model certain phenomena. In this short post, we avoid motivating the Poisson distribution by its PMF and ...