The Poisson distribution models the number of events in a fixed interval given average rate λ. P(X=k) = (e^−λ × λᵏ) / k!. Both the mean and variance equal λ.
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Did You Know?
Bortkiewicz used the Poisson distribution in 1898 to model Prussian cavalry soldiers killed by horse kicks — demonstrating it fits rare independent events perfectly.
References
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