Problem 3. For i = 1,2, let Xi1,,Xịn consistute a sample of size n; from a population having unknown mean u and known variance ož. For X; = +E Xij, i = 1,2, a biostatistician suggests that the "optimal" estimator of the unknown parameter u is û = w,X1+W2X2, where the weights are chosen so that the following two conditions are simultaneously satisfied: • E[i] = µ, i.e., the estimator is unbiased • Varſi], the variance of the estimator, is minimized. Derive explicit expressions for the particular choices of wi and wz that simultaneously satisfy these two conditions, and then interpret your findings.

Problem 3. For i = 1,2, let Xi1,,Xịn consistute a sample of size n; from a population having unknown mean u and known variance ož. For X; = +E Xij, i = 1,2, a biostatistician suggests that the "optimal" estimator of the unknown parameter u is û = w,X1+W2X2, where the weights are chosen so that the following two conditions are simultaneously satisfied: • E[i] = µ, i.e., the estimator is unbiased • Varſi], the variance of the estimator, is minimized. Derive explicit expressions for the particular choices of wi and wz that simultaneously satisfy these two conditions, and then interpret your findings.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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