Suggest an estimator of population mean in cluster sampling with unequal size clusters, which is based upon the means of selected clusters. Determine whether it is an unbiased estimator?

In cluster sampling with unequal size clusters, we aim to estimate the population mean using a method that appropriately accounts for the variability in cluster sizes. Let the finite population consist of NN clusters, where the ithi^{th} cluster has MiM_i elements, and the total number of elements in the population is M=∑i=1NMiM = \sum_{i=1}^N M_i. Suppose a simple random sample of nn clusters is selected without replacement. Let yˉi\bar{y}_i denote the sample ___ __________ _______ ________ __________ ______ ____ _____ _____.
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