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Distribution of a sample average
As first application of the theorem, let us remind ourselves that
a sample average
of independent variables,
is normally distributed, since it is a linear combination
of variables , with . Then,



(4.75) 



(4.76) 



(4.77) 



(4.78) 
This result, we repeat, is independent of the distribution
of and is already approximately valid for small values of .
Giulio D'Agostini
20030515