Consider an underlying population that is unimodal and

Question

Consider an underlying population that is unimodal and symmetric about its finite mean μ and suppose we are interested only in making inferences about μ using RSS data based on an odd set size k. Consider an unbalanced RSS of size n (see the "Unbalanced Ranked Set Sampling" discussion in this section) collected from this population, where the judgment sample median X_[(k+1)/2] is measured in each of the n sets of size k each. Thus, the collected RSS data will be of the formjth set sample median for each of the sets j = 1, 2, ... , n}. Letbe the average of these n RSS set medians. Show that  is an unbiased estimator for μ when the ranking process is perfect (See Ozturk and Wolfe (2000) for more discussion on such median unbalanced RSSs.)