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A sum of observations derived by a simple random sampling design from apopulation of independent random variables is studied. A procedure finding ageneral term of Edgeworth asymptotic expansion is presented. The Lindebergcondition of asymptotic normality, Berry-Esseen bound, Edgeworth asymptoticexpansions under weakened conditions and Cramer type large deviation resultsare derived.

Approximation by normal distribution for a sample sum in sampling without replacement from a finite population