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5. Let X1,..., X„ ~ iid N(0, T). (a) Find the MSE for the usual unbiased estimator of T: ↑ = 4E X?. Show that this is unbiased and find (X; - X)?. (b) Consider the alternative estimator 8(x) = E the MSE. n Li=1 (c) Why does it make sense for (b) to be better than (a) in this case?

5. Let X1,..., X„ ~ iid N(0, T). (a) Find the MSE for the usual unbiased estimator of T: ↑ = 4E X?. Show that this is unbiased and find (X; - X)?. (b) Consider the alternative estimator 8(x) = E the MSE. n Li=1 (c) Why does it make sense for (b) to be better than (a) in this case?

MATLAB: An Introduction with Applications
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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5. Let X1,..., X„ ~ iid N(0, T). (a) Find the MSE for the usual unbiased estimator of T: ↑ = 4E X?. Show that this is unbiased and find (X; - X)?. (b) Consider the alternative estimator 8(x) = E the MSE. n Li=1 (c) Why does it make sense for (b) to be better than (a) in this case?
Transcribed Image Text:5. Let X1,..., X„ ~ iid N(0, T). (a) Find the MSE for the usual unbiased estimator of T: ↑ = 4E X?. Show that this is unbiased and find (X; - X)?. (b) Consider the alternative estimator 8(x) = E the MSE. n Li=1 (c) Why does it make sense for (b) to be better than (a) in this case?
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