Binomial / Poisson / Normal relationships

Definition

Binomial: n independent trials, success probability p — X~Bin(n,p). Poisson: counts of rare events — λ=rate. Normal: continuous bell curve; approximates Binomial when n large and p not extreme (rule of thumb np,n(1−p)≥10).

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Poisson can limit Binomial as n→∞, p→0, np→λ.

Normal is determined by (μ,σ²). Standardize Z=(X−μ)/σ.

Know E/Var for each named family cold.

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1.When is Poisson a better model than Binomial for counting?

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