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The question is:
The number of car accidents an insured person faces depends on their experience. The rate at which Liam will have car accidents is given by: $$R(e) = \frac{(e+0.5)^{-2}}{200},$$ where $e$ is the experience in years.

I am required to find probabilities related to this, but the solution starts out with:
The rate at which Liam will have a car accident is a non-homogenous (continuous time) Poisson process.
How is this in any way a Poisson process? Like, what does the function have to do with it? Is this just assumed?

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    Indeed the formulation is sloppy. Rather, one should say that the set of times when Liam has a car accident is a non-homogenous Poisson process. – Did Aug 21 '17 at 12:37

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