Thorough examination of bias and variance in the linear regression

The connection between probability definition and machine learning explanation

Are variance and bias of an estimator mathematical definitions and machine learning explanations reconcilable? Source: Robot hand photo created by rawpixel.com — www.freepik.com

Why a new bias variance post?

I had trouble to clearly understand the connection between the definitions of the variance and the bias of an estimator in my probability courses and the explanation from the machine learning courses I then followed. In the first case, the mathematical definitions …

bias bias-variance-tradeoff linear linear regression math regression variance