Poisson Distribution Calculator
Exact Poisson Probability P(X = k)
Probability of exactly k events in an interval
Poisson Range Probability
Probability of events in a range P(a ≤ X ≤ b)
Formula
P(X=k) = e^(-λ) × λᵏ / k! | Mean = λ | Variance = λ
Frequently Asked Questions
What is the Poisson distribution?
The Poisson distribution models the number of events occurring in a fixed interval of time or space, given a known average rate (λ). Examples: calls per hour at a call center, typos per page, or accidents per month.
When should I use Poisson vs Binomial?
Use Poisson when counting events in a continuous interval with a known average rate. Use Binomial for a fixed number of independent trials each with the same probability. Poisson approximates Binomial when n is large and p is small (λ = np).
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