Poisson Distribution
A discrete distribution with parameter λ > 0 where P(X = k) = e^(-λ) × λ^k / k! for k = 0, 1, 2, ... The mean is E(X) = λ and the variance is Var(X) = λ. The Poisson distribution is an approximation to the binomial distribution when n is large, p is small, and np = λ is moderate.
Real World
The UK's National Grid monitors lightning strikes per hour using a Poisson model, since strikes occur independently and randomly at a roughly constant rate across a region.
Exam Focus
Always verify the two conditions — events independent and constant average rate — before stating X ~ Po(λ) in your answer.
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