 Poisson central limit theorem

ID: poisson-central-limit-theorem

Codex  0 Created 2026-09-24 Updated 2026-10-03

N_{λ} \sim Pois (λ)

and

λ \to \infty

, then

\frac{N _{λ} - λ}{λ} d N (0, 1) .

exp (λ (e^{i t / λ} - 1 - \frac{i t}{λ})) ⟶ e^{- t^{2} /2} .

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