Thread: Simple linear regression model

The OLS estimator for the simple linear regression model can be written as
where

In the case for a sample size of three observations (T=3), this estimator can be written as:
where

Assume that the full set of assumption of the SLRM hold.
Without using summation notation, use the fact that to find .

Explain how the assumptions of the model are used to arrive at your answer.

i started by equating (definition of variance),
then using known results to



would greatly appreciate if anyone could help me derive without using any summation notation.

i suppose the end resut of [using a proof that uses summation notation) would be



and,



and