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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.
 Spring '10
 HyungdongShin
 Electrical Engineering

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