Question: i need a little more help with this question give...
I need a little more help with this question:
Give an unbiased estimate of the variance of the estimator. (This may be compared to the value of the simpler alternative estimator.)
The answer to this question is 62.46, but I need to see a proof to understand how to calculate it myself.
Note - Below is the previous information(i.e answers) to help with the problem. Please do not provide me with answers or proofs to the questions below. I already have calculated those. I am only interested in seeing a proof of the answer above. I have no idea what a proof of this kind of question looks like and the textbook is unhelpful.
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.
The population total using the Hansen–Hurwitz estimator is 56.667
The variance of the estimator is 44.444
The population total using the Horvitz–Thompson estimator is:
Pi 1 = .1694, Pi 2 = .488, Pi 3 = .271, Population = 64.03