Poisson Approximation to Binomial

Probability · Axiom Academy

LESSON Poisson Approximation to Binomial When n is large and p is small, Binomial converges to Poisson 1. When to Use the Approximation The Poisson approximation to the Binomial works well when: p is small (typically p ≤ 0.05) The product λ = np is moderate (typically λ < 10) We approximate Binomial(n,p) with Poisson(λ) where λ = np 2. Comparing the Distributions Let's visualize how closely the Poisson approximates the Binomial: The Poisson approximation simplifies calculations significantly: Binomial: Complex formula with large factorials and powers Poisson: Simple formula with just e^(-λ) and λ^k/k! Error is typically less than 1% when conditions are met

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