The above link is what I used as the related reference that I got the same answer as mine
$Y_{i}$ = $\alpha$ + $\beta$$X_{i}$+ $errorterm_{i}$
Prove that the estimator of $\beta$ is unbiased
What I did is proving this thing without using any expectation at all, so I wonder why it works?!!
Basically, what unbiasedness is the expectation of the estimator equal to the true parameter we interest in which is beta here, but what I did I did not use any expectation so What I got still the true parameter?
Can I conclude that the expectation of what I got the constant is that true parameter?
My feeling is that I might get something wrong...
P.S.I wish to type all of those Math formattings but maybe next time and I wish to post this in mathematics but unfortunately, I do not have more than 10 reputations to post the picture !!
mean(rnorm(5))
will generally not be equal to zero. $\endgroup$