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Consider the following two-stage stratified sampling plan. In the first stage, the population is stratified into H strata and kh clusters are selected from stratum h with probability proportional to cluster size, where sampling is independent across strata. In the second stage, a sample of mhi units is selected from sampled cluster i in stratum h, and sampling is independent across clusters. Find π_i and the Horvitz Thompson estimator Y_ht of the population total.

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