Unformatted text preview: 2. Suppose there are only two domains in a population, defined by indicator variable X i = ቄ 1 if unit ݅ is in domain 1 if unit ݅ is in domian 2 Then, the two population domain means of variable Y are given by, respectively, ܻ ത ଵ = ∑ ܺ ே ୀଵ ܻ / ∑ ܺ ே ୀଵ and ܻ ത ଶ = ∑ ሺ1 െ ܺ ሻ ே ୀଵ ܻ / ∑ ሺ1 െ ܺ ே ୀଵ ሻ If a simple random sample with replacement sample of size n is selected. Let ݕ and ݔ be the observations of Y and X of the selected i ‐ th unit. Define the two estimators of ܻ ത ଵ and ܻ ത ଶ as ݕ ത ଵ = ∑ ݔ ݕ ୀଵ / ∑ ݔ ୀଵ and ݕ ത ଶ = ∑ ሺ1 െ ݔ ሻݕ ୀଵ / ∑ ሺ1 െ ݔ ୀଵ ) Show that the covariance of ݕ ത ଵ and ݕ ത ଶ is approximately equal to zero....
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 Spring '16
 Simple random sample

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