Let
be a set of Independent random variates and each
have an arbitrary probability distribution
with Mean and a finite Variance
. Then the normal form variate
(1) 
(2) 
(3) 

(4) 
(5) 
(6) 
(7) 
(8)  
(9) 
(10) 
(11) 
(12) 
(13) 
(14) 
The ``fuzzy'' central limit theorem says that data which are influenced by many small and unrelated random effects are approximately Normally Distributed.
See also Lindeberg Condition, LindebergFeller Central Limit Theorem, Lyapunov Condition
References
Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, 1972.
Spiegel, M. R. Theory and Problems of Probability and Statistics. New York: McGrawHill, pp. 112113, 1992.
Zabell, S. L. ``Alan Turing and the Central Limit Theorem.'' Amer. Math. Monthly 102, 483494, 1995.
© 19969 Eric W. Weisstein