ols regression - classical derivation

Derivation

{% \mathbb{E}(\vec{b}|X) = \vec{\beta} %} :

{% \mathbb{E}(\vec{b} - \vec{\beta}|X) = \mathbb{E}((X^TX)^{-1} \epsilon|X) %}

{% = (X^TX)^{-1} \mathbb{E}(\epsilon|X) = 0 %}