tut07_sol - Massachusetts Institute of Technology...

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Massachusetts Institute of Technology Department of Electrical Engineering & Computer Science 6.041/6.431: Probabilistic Systems Analysis (Spring 2005) Tutorial 7 Solutions Week of March 28, 2005 1. (a) a b for all possible values of X , Y .S ince a is the mean squared estimation error of the least squares estimator of X based on Y ,and b is the mean squared estimation error of the linear least squares estimator of X based on Y ,wemust have a b , because removing the linearity constraint can only improve the optimization, not make it worse. (b) ρ X,Y = ± 1 X (1 ρ 2 Explanation: Since b = σ 2 X,Y ), it is evident that the only way to pick ρ X,Y to get b =0 is ρ X,Y = ± 1. For these two values of
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This note was uploaded on 06/10/2010 for the course ELECTRONIC C1002900 taught by Professor Hyungdongshin during the Spring '10 term at Kyung Hee.

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