Poisson Distribution Calculator
Calculate Poisson probabilities (PMF and CDF) with visualization for modeling rare events.
Average rate of occurrence (must be > 0)
Number of occurrences (non-negative integer)
Tulokset
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Theory & Formula
What is Poisson Distribution?
Poisson distribution models the number of events occurring in a fixed interval of time or space, given a known average rate.
Probability Mass Function
\(P(X = k) = \frac{\lambda^k e^{-\lambda}}{k!}\)
Where: λ = average rate, k = number of occurrences, e ≈ 2.718
Properties
• Mean equals variance: E[X] = Var[X] = λ: \(E[X] = Var[X] = \lambda\)
• λ is the only parameter (rate parameter)
Applications
• Counting rare events (accidents, defects)
• Queueing theory and traffic modeling
• Radioactive decay and particle counting