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I have been studying ML for over a year and am actually a Bachelors of Statistics myself and am sick of not knowing the beauty of the Gaussian distribution and why it is so prevalent in nature. I've encountered it in machine learning, Bayesian estimation, mathematical approximation but have never found a great resource to really get it. All I find are hand-wavy introductions to it which state a theorem here and there but never expound on the full power.

I ask you guys to recommend me resources so I can fully understand the normal distribution, its origins and why it so prevalent. I also want to know what's the deal with covariance matrices in multivariate Gaussians and how its determinant ended up there. My professors, peers and almost everyone seem to take it for granted but it really want to 'get it'.

Would appreciate recommendations all forms, not wayyy mathematical, but a sure, giving a strong grasp.

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marked as duplicate by whuber♦ May 6 at 17:15

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ This and this and this and this are related. To be honest, I don't think we can improve especially on the last link without knowing more precisely what you struggle with. $\endgroup$ – S. Kolassa - Reinstate Monica May 6 at 17:14
  • $\begingroup$ The question about the determinant might not be covered in the duplicates. It shows up basically because all multivariate normals are rotated versions of collections of uncorrelated (and therefore independent) univariate normals; probabilities of independent variables multiply; scaling a univariate variable by $\sigma$ must introduce a factor of $1/\sigma$ in its density in order to keep the total probability at $1;$ and the product of these factors is precisely the determinant that appears in the multivariate normal density function. $\endgroup$ – whuber♦ May 6 at 17:23
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    $\begingroup$ Is there an explanation for why there are so many natural phenomena that follow normal distribution? $\endgroup$ – Glen_b May 6 at 17:39