This is from my lecture on classic linear regression model:
$$ \text { Assumption 1: } E\left(\varepsilon \mid x_{1}, \ldots, x_{K-1}\right)=0 $$
Q: I am able to follow this fine until "Assumption 1 applies ... so that upon substitution". Where is that longer equation coming from? Where is he substituting the previous result of the correlated error vector to get that last lengthy equation?
You should have a model assumption that $$y_i = \beta_0 + \beta_1 x_{i1} + \cdots + \beta_{K-1} x_{i, K-1} + \varepsilon_i.$$ Substituting in the expression for $\varepsilon_i$ yields the long equation you are asking about.