Poisson Distribution Calculator

Calculate probabilities for the Poisson distribution

Average Rate (λ):

Number of Events (k):

P(X = 2): 22.4042%

P(X ≤ 2): 42.3190%

P(X > 2): 57.6810%

Mean (λ): 3.0000

Variance (λ): 3.0000

Standard Deviation: 1.7321

The Poisson distribution models the number of events occurring in a fixed interval of time or space, given an average rate λ.

PMF: P(X = k) = (λ^k × e^(-λ)) / k!

Mean = Variance = λ

Examples: Number of emails per hour, calls to a call center, radioactive decay events.

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Formula Source: Standard Mathematical References

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ðŸ”„Last reviewed: May 2026

âœ“Formula checks are based on standard references and internal QA review.