Poisson distribution calculator
Calculate the probability of exactly k events occurring when the average rate is λ events per interval.
Average rate (λ)
Events (k)
Poisson formula
P(X = k) = (e^−λ × λᵏ) / k!
Where λ = average rate of occurrence, k = number of events, e ≈ 2.71828.
When to use Poisson
Events are independent, occur at a constant rate, and you're counting occurrences in a fixed interval. Examples: calls per hour, defects per batch, accidents per month.
Properties
Mean = λ. Variance = λ. Standard deviation = √λ. For large λ, Poisson approximates normal N(λ, λ).
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