Deriving the Normal Distribution
It&#x27;s been years since I took probability, but why start from these particular set of assumptions?<p>You&#x27;ve shown that the correct form and constant factors falls out from assuming rotational invariance and independent components. But why is this particular set of assumptions intuitively what we call the &quot;normal distribution&quot;?<p>The same distribution should fall out starting from other more useful equivalent definitions right? (e.g., the maximum entropy distribution for some mean&#x2F;variance, or the limiting distribution under CLT assumptions, etc)