Poisson Distribution
Statistics & ProbabilityCalculate Poisson probability P(X = k), cumulative probability P(X ≤ k), and rate distribution for events occurring randomly at a known average rate λ over time or space.
P(X ≤ 4) = 0.62884 · P(X > 4) = 0.37116
About this calculator
The Poisson distribution models the frequency of independent events occurring within a fixed interval of time, area, or volume when the average arrival rate (λ) is constant (e.g., website visitors per minute, customer arrivals at a bank, or radioactive decay clicks).
This tool computes exact and cumulative Poisson probabilities, expected mean (μ = λ), variance (σ² = λ), and distribution tables.
How It Works & Formula
P(X = k) = (λᵏ × e⁻λ) / k!. For large k or λ, calculations evaluate via natural logarithms ln(P) = k·ln(λ) - λ - ln(k!) to prevent numerical floating-point overflow.
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