2.1.3 Poisson Distribution

The Poisson distribution is used to model the number of occurrences of an event in a fixed time period or space, e.g. every 5 minutes or every square mile.

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  $\theta$ is the rate of occurrence.

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  Mean = $\theta$.

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  Variance = $\theta$.

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  PMF: $p(r)=\frac{{\theta }^r\exp (-\theta )}{r!}$.

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  Events must occur at random, be independent and occur evenly over space/time.

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  If events are not random and are regular then the variance mean. If events are clustered / clumped together then the variance $>$ mean.