Parameter estimation is an important problem in mathematical statistics.Inspired by an exercise in the textbook,a class of linear unbiased estimators is constructed for the population mean and variance under the condition of single population group sample and multi-population sample.The validity of this kind of estimation is discussed by using Lagrange condition extremum method,and the most effective estimation is given.The processing methods and techniques have certain methodological significance,broaden students' thinking,and can be promoted and used in research-based teaching of mathematical statistics.
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