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Let $Y_1,\ldots,Y_n$ be independent and identically distributed
random variables with finite $\mu = E(Y)$ and $\sigma^2 = V(Y)$.
Let $U_n = {\overline{Y} - \mu\over \sigma/\sqrt{n}}$.  Then 
as $n \to\infty$, $U_n$ converges to a standard normal random
variable in distribution.
 
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