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The estimator determined in Exercise 8.1.10 is also unbiased for µ 2 when the statistical model…

The estimator determined in Exercise 8.1.10 is also unbiased for µ2 when the statistical model comprises all continuous distributions on R1 that have a finite first moment. Is this estimator still UMVU for µ

Exercise 8.1.10

Suppose a statistical model comprises all continuous distributions on R1 that have a finite second moment. Based on a sample of n, determine a UMVU estimator of µ2where E is the true mean. Justify your answer