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Probability Distributions Cheat Sheet

By Dr. Iris Vaughan, Mathematics Editor·Published 1 November 2025·Last reviewed 10 February 2026

Binomial, normal, Poisson, geometric, and hypergeometric distributions — with parameter definitions, mean/variance formulas, and when each applies.

Key Formulas
Binomial(n,p): P(X=k)=C(n,k)pᵏ(1−p)ⁿ⁻ᵏ
Normal(μ,σ²): continuous, symmetric
Poisson(λ): P(X=k)=e⁻λλᵏ/k!
Geometric(p): P(X=k)=(1−p)ᵏ⁻¹p

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