Your Textbook States That an Implication of the Gauss-Markov Theorem $\bar { Y }$

question 12

Essay

Your textbook states that an implication of the Gauss-Markov theorem is that the sample average, $\bar { Y }$ , is the most efficient linear estimator of $E \left( Y _ { i } \right)$ when $Y _ { 1 } , \ldots , Y _ { n }$ are i.i.d. with $E \left( Y _ { i } \right) = \mu _ { Y }$ and $\operatorname { var } \left( Y _ { i } \right) = \sigma _ { Y } ^ { 2 }$ . This follows from the regression model with no slope and the fact that the OLS estimator is BLUE.
Provide a proof by assuming a linear estimator in the $Y$ 's, $\tilde { \mu } = \sum _ { i = 1 } ^ { n } a _ { i } Y _ { i }$ . (a)State the condition under which this estimator is unbiased.

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Definitions:

Operating Activities

Activities related to the core business functions of a company, including production, sales, and delivery of its products or services.

Net Income

The final earnings of a business once all costs and taxes are removed from the overall revenue.

Indirect Method

A way of reporting cash flows from operating activities in the statement of cash flows by adjusting net income for changes in balance sheet accounts.

Operating Activities

Activities that relate directly to the running of a business for profit, including production, sales, and distribution.