Question: Let b be an estimator for Î² in the model for GVFs in (9.13). Let B=ty / tx and á¸ =á¹«y / á¹«x. Suppose that

Let b be an estimator for Î² in the model for GVFs in (9.13). Let B=ty / tx and á¸‚ =á¹«y / á¹«x.
Suppose that á¸‚ and á¹«x are independent.
a. Using the model in (9.13) and the result in (9.2), show that we can estimate V (á¸‚) by

b. Now let B be a proportion for a subpopulation, where tx is the size of the subpopulation and ty is the number of units in that subpopulation having a certain characteristic. Show that á¹¼ (á¸‚) = b á¸‚ (1 ˆ’ á¸‚)/Ë†tx and that á¹¼ (á¸‚) = á¹¼ (1 ˆ’ á¸‚).

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