How does the Poisson Distribution work?

P(X=k) = (e^−λ × λᵏ) / k! Then: λ = average number of events per interval Then: Events must be independent and occur at constant average rate.

Can you give an example of how to use the Poisson Distribution?

Example: Input λ=3 calls/min · P(exactly 5 calls) gives a result of P = e^−3 × 3⁵/120 ≈ 10.1% (Classic Poisson application).

Is the Poisson Distribution free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Poisson Distribution?

Our Poisson Distribution uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Poisson Distribution

📊Poisson Distribution Calculator

λ (mean rate)

Average events per interval

k (exact events)

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

›Poisson distribution — Wikipedia

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