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According to central limit theorem, irrespective of the distribution of the original/population dataset, the sampling distribution will follow normal distribution.

My Question is if the means of n samples of the population data follow normal distribution, what is this helping us in ? I tried to find examples in the context of Ml but found no good example. It would be of great help if you could help me understand the significance of CLT ( basically application of knowing that sampling distribution will have bell curve) in the context of ML with an example.

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Are you familiar with hypothesis testing? Confidence Intervals ? Statistical Significance ? All of these concepts typically rely on the central limit theorem.

One concrete example I can think of relating to ML: Regression

Most approaches to regression typically assume that the error term that appears follows a Gaussian distribution. How do we justify this assumption ? Well the idea is that we can think of the error term as a sum of multiple different error terms. Now even if these individual error terms do not follow a Gaussian distribution, we can model their sum as a Gaussian because of the Central Limit Theorem.

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