The central limit theorem in the mathematical theory of probability may be expressed as follows:

“If Xi (I = 1,2,3,……n) be independent random variables such that E(Xi) =µi and V(Xi) =

Then it can be proved that under certain very general conditions, the random variable is asymptotically normal with mean µ and standard deviation σ where

and

This theorem was first stated by Laplace in 1812 and a rigorous proof under fairly general conditions was given by Liapounoff in 1901. Below we shall consider some particular cases of this general central limit theorem.

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