Consider the Following Alternative Estimator for the Population Mean Prove That

question 52

Essay

Consider the following alternative estimator for the population mean: $$\tilde { Y } = \frac { 1 } { n } \left( \frac { 1 } { 4 } Y _ { 1 } + \frac { 7 } { 4 } Y _ { 2 } + \frac { 1 } { 4 } Y _ { 3 } + \frac { 7 } { 4 } Y _ { 4 } + \ldots + \frac { 1 } { 4 } Y _ { n - 1 } + \frac { 7 } { 4 } Y _ { n } \right)$$
Prove that $\tilde { Y }$ is unbiased and consistent, but not efficient when compared to $\bar { Y }$ .

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Definitions:

Price Elasticity

A measure of how much the quantity demanded of a good responds to a change in the price of that good.

Fresh Fish

Fish that have been recently caught and have not been frozen or processed.

Total Revenue

Total Revenue is the full amount of money received by a company for its goods or services, before any expenses are subtracted.

Equilibrium Price

The price at which the quantity of goods supplied is equal to the quantity of goods demanded in a market.