Let b be an estimator for in the model for GVFs in (9.13). Let B=ty /

Let b be an estimator for β in the model for GVFs in (9.13). Let B=ty / tx and Ḃ =ṫy / ṫx.
Suppose that Ḃ and ṫx are independent.
a. Using the model in (9.13) and the result in (9.2), show that we can estimate V (Ḃ) 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 Ṽ (Ḃ) = b Ḃ (1 − Ḃ)/ˆtx and that Ṽ (Ḃ) = Ṽ (1 − Ḃ).