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If anyone was frustrated like me on this concept of "moments" I found the following insightful and fascinating:

https://gregorygundersen.com/blog/2020/04/11/moments/

I have no idea how I got through undergrad and graduate school without internalizing this concept that seems so foundational. Whacky

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I thought I had a pretty good grasp on this, but the idea that an infinite sum of higher order moments uniquely defines a distribution in a way analogous to a Taylor series, was new and super interesting! It gives credence to the shorthand that the lower order moments (mean, variance, etc) are the most important properties of a distribution to capture, and is how you should approximate an unknown distribution given limited parameters.

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