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

In the fields of Probability Theory and Mathematical Statistics, leveraging methods/theorems often rely on common mathematical assumptions and constraints holding. Two such mathematical concepts are random variables (RVs) being “uncorrelated”, and RVs being “independent”. I’ve seen a good deal of confusion regarding these concepts (including on the Medium platform). These are well specified terms mathematically and they do not mean the same thing. For anyone interested in Statistics, Data Science, or Machine Learning, these are concepts absolutely worth understanding.

This article aims to:

• Mathematically specify the definitions for RVs being uncorrelated, and RVs being independent
• Prove that RVs that are independent are by definition also uncorrelated
• Prove that RVs can be uncorrelated but not independent (by example)

#data-science #statistics #probability #machine-learning #mathematics