# exam3 - List of potentially useful facts[V,D]=eig[25...

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List of potentially useful facts [V,D]=eig([25 22; -9.4 -9.4]) V = 0.94 -0.64 -0.33 0.77 D = 17.2 0 0 -1.64 [V,D]=eig([25 -4; -4 22]) V = -0.57 -0.82 -0.82 0.57 D = 19.2 0 0 27.8 [V,D]=eig([25 -9.4; -9.4 22]) V = -0.65 -0.76 -0.76 0.64 D = 14.0 0 0 33.0 [V,D]=eig([5 -9.4; -9.4 4.7]) V = -0.70 -0.71 -0.71 0.70 D = -4.55 0 0 14.25
EEL 5544 Examination Number 3-A December 10, 2010 The time for this test is 2 hours. This is a closed book test, but you are allowed three formula sheets. The formula sheets cannot contain any examples. You should write your name on the formula sheets and turn them in with your exam. You may use a calculator on this test. You must show your work to receive credit for a problem. Note that some problems are worth more points than other problems, and the problems are not necessarily sorted in order of difﬁculty or point value. You must sign the honor statement at the end of the test in order to receive any credit. Bonus points may be offered for exceptionally good answers. Exam III-3

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Exam III-4 1. (14 points) X and Y are jointly Gaussian random variables with zero mean, variances σ 2 X = 25, σ 2 Y = 22, and covariance -9.4. Part I. (a) Find the correlation coefﬁcient ρ XY . (b) Specify the covariance matrix for [ X Y ] 0 . (c) If U = X + 3 Y and V = 2 X - Y , ﬁnd the covariance matrix for [ U V ] 0 .
Part II. Now consider Principal Components Analysis for lossy compression of ( X , Y ) . (d) Find a unitary linear transformation ± W Z ² = A ± X Y ² such that W and Z are uncorrelated random variables with σ 2 W > σ 2 Z . (e) Give the covariance matrix for

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## This note was uploaded on 01/29/2012 for the course ECE 101 taught by Professor Wang during the Spring '11 term at Iowa State.

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exam3 - List of potentially useful facts[V,D]=eig[25...

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