exam3 - List of potentially useful facts [V,D]=eig([25 22;...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 2
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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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 .
Background image of page 4
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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 21

exam3 - List of potentially useful facts [V,D]=eig([25 22;...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online