A estimate the population total using the horvitz-thompson

Question

For the design and data of Exercise 1:

(a) Estimate the population total using the Horvitz-Thompson estimator.

(b) Give an unbiased estimate of the variance of the estimator. (This may be compared to the value of

Exercise 1

An unequal probability sample of size 3 is selected from a population of size 10 with replacement. The y-values of the selected units are listed along with their draw-by-draw selection probabilities: y₁ = 3, p₁ = 0.06; y₂ = 10, p₂ = 0.20; y₃ = 7, p₃ = 0.10. (a) Estimate the population total using the Hansen-Hurwitz estimator. (b) Estimate the variance of the estimator.