Variance of Estimator: Learn How to Calculate

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The discussion centers on calculating the variance of an estimator, specifically for the model Y_i=βX_i+ε_i, where the estimator β is defined as \bar{Y} / \bar{X}. The user initially calculated the mean of the estimator as n*β but expressed uncertainty about the variance calculation. Participants in the thread encouraged defining terms for clarity and provided assistance in understanding the variance concept. Ultimately, the user confirmed finding a solution to their question. The conversation highlights the importance of understanding both mean and variance in statistical estimators.
trenekas
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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!
 
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It would help if you could back up one step and define your terms.
 
I found a solution :) Thank you.
 

Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
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