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Téorema central limit mangrupa hasil susunan konvergen-lemah dina teori probabilitas. Ieu téorema keur ngagambarkeun yén jumlah unggal variabel acak nu kasebar bébas sacara normal (independent identically distributed atawa i.i.d) ngadeukeutan sebaran normal. Hasil ieu nerangkeun kaunikan sebaran normal.

Hasil nu penting jeung kawentar éta disebutna Teorema Central Limit Theorem; nu museurkeun kana variabel bébas nu pasipatan sebaranna bébas tur nilai eksptasi jeung varianna terhingga.

Several generalizations exist which do not require identical distribution but incorporate some condition which guarantees that none of the variables exert a much larger influence than the others. Two such conditions are the Lindeberg condition and the Lyapunov condition. Other generalizations even allow some "weak" dependence of the random variables.

The réader may find it helpful to consider this illustration of the central limit theorem.