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Central Limit Theorem

The key theorem in probability and statistics.
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The statement of the theorem

The distribution of the sum (or average) of a large number of independent, identically distributed variables approaches a normal distribution.\nSn−nμσn→dN(0,1)\frac{S_n - n\mu}{\sigma\sqrt{n}} \xrightarrow{d} N(0,1)
Source: Wikipedia