Okay, so I guess my first question is if the main utility of the normal distribution ##f(x)## is to provide a probability measure for any subspace of the measurable space ##(\mathbb{R},\mathcal{B})## (where ##\mathcal{B}## is the borel σ-algebra on the real numbers) by defining the measure as(adsbygoogle = window.adsbygoogle || []).push({});

[tex] P(A)=\int_Af(x)\,dx\;\;\; \forall{}A\in\mathcal{B}. [/tex]

Then my second question is: where does the normal distribution come from? What is the derivation of it that uses the least amount of assumptions (i.e. assume I am NOT throwing darts at a target)? Can you derive it from combinatorics alone? Or are there some assumptions that have to be made?

Thanks

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# Where does the normal distribution come from?

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