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What is the Central Limit Theorem in statistics and did I spell it right?

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What is the Central Limit Theorem in statistics and did I spell it right?

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The central limit theorem is one of the most remarkable results of the theory of probability. In its simplest form, the theorem states that the sum of a large number of independent observations from the same distribution has, under certain general conditions, an approximate normal distribution. Moreover, the approximation steadily improves as the number of observations increases. The theorem is considered the heart of probability theory, although a better name would be normal convergence theorem.

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