Poisson probability

Poisson probability: use expected count λ, observed count k. Review the formula, worked example and calculation steps.

Inputs

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RESULT
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Formula & explanation
P(X=k) = exp(−λ) λᵏ/k!

Variables & units

Expected count λ
Numeric value · minimum 0, maximum 1000
Observed count k
Numeric value · minimum 0, maximum 1000

Worked example

λ=3 and k=2 gives approximately 0.224042.

Assumptions

Counts independent events with constant expected intensity over the interval.

Formula version 1.0.0. JavaScript floating-point arithmetic applies. Results display up to 6 decimal places; stored values retain available precision. Use the units shown.

Practice with an example

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