Variance of the estimator β̂ = Ȳ/X̄

[trenekas]

Hi there. I would like to ask you one question about variance of estimator.

Suppose that $Y_i=βX_i+ε_i$ and β estimator is $\bar{Y}$ / $\bar{X}$.

I calculated mean of estimator. I am not sure if it's correct, but i got that its equal to n*β. But how about variance.
Any help would be appreciated!

 

[mathman]

It would help if you could back up one step and define your terms.

 

[trenekas]

I found a solution :) Thank you.