Chapter 13

Poisson processes

Poisson processes serve as a simple model for events occurring in time or space: in one dimension, cars passing by a highway checkpoint; in two dimensions, flowers in a meadow; in three dimensions, stars in a region of the galaxy. Poisson processes are a primary building block for more complicated processes in time and space, which are the focus of a branch of statistics called spatial statistics.

Poisson processes are also useful in probability, as they tie together many of the named distributions and provide us with insightful story proofs for results that might otherwise be tedious to show. This leads to a new problem-solving strategy, which we will demonstrate: even when a problem makes no mention of Poisson processes, ...

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