Axioms of Probability — Understanding the Foundations

Axioms of Probability — Understanding the Foundations

Foundations of Probability Theory & a few proofs. These three axioms form the foundations of Probability Theory, from which every other theorem or result in Probability can be derived.

This article is going to be a brief one. Regarding technical knowledge, I’m generally a proponent of having strong fundamentals and grounded understanding in the methods one is using. I don’t typically like memorizing anything and avoid doing so whenever possible. Rather I instead focus on developing strong fundamentals on concepts, from which I can later mathematically derive anything I may need.

Below are the Kolmogorov Axioms as presented by Andrew Kolmogorov in 1933. These three axioms form the foundations of Probability Theory, from which every other theorem or result in Probability can be derived. I’ve always found it interesting how regardless of how complex a Probability Theorem or Result can become, it can all be sourced-back to and derived from these three fundamental axioms. The simplicity I find fascinating. Also below are a few simple Probability Theorems derived from the three axioms. A quick search on Medium revealed these proofs and relations (to my knowledge) have yet to be simply curated in one article. These are concepts worth knowing.

So let’s jump in:

Three Probability Axioms:

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probability data-science statistics mathematics

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