For iid X₁,…,Xₙ with mean μ and finite variance σ², the normalised sum √n (X̄ₙ - μ)/σ converges in distribution to N(0,1). Universality class of additive noise.
Central limit theorem
Related concepts
- Law of large numbers
- Expectation E[X]
- Random variable
- Gaussian (normal) distribution
- Law of iterated logarithm
- Large deviations & Cramér theorem
- Strong / weak law of large numbers
- Slutsky's theorem
- Large-scale structure (LSS)
- Pareto power-law (1896)
- R_mix = f·R_A + (1−f)·R_B: linear 2-component isotope mixing
- Flory polymer statistics (1953)
- Flory-Huggins chi (1942)
- Drake log-CLT: log N = Σ log(factor); 7-term sum; product-of-iids asymptote
- RNA-seq
- Population viability analysis (PVA)
- RNA polymerase elongation kinetics framework
- Kimura neutral theory framework