📊Poisson Distribution Calculator
Average events per interval
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.
- 1P(X=k) = (e^−λ × λᵏ) / k!
- 2λ = average number of events per interval
- 3Events must be independent and occur at constant average rate
λ=3 calls/min · P(exactly 5 calls)=P = e^−3 × 3⁵/120 ≈ 10.1%Classic Poisson application
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Fun Fact
Bortkiewicz used the Poisson distribution in 1898 to model Prussian cavalry soldiers killed by horse kicks — demonstrating it fits rare independent events perfectly.
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