# hw1 - ECE 562 Fall 2011 HOMEWORK ASSIGNMENT 1 Reading...

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Unformatted text preview: ECE 562 Fall 2011 August 28, 2011 HOMEWORK ASSIGNMENT 1 Reading: Madhow, Appendix A, Section 3.1, 2.1 and 2.2, Class notes 1 and 2. Due Date: September 6, 2011 (in class) 1. Use your knowledge of Gaussian and jointly Gaussian pdfs to get the answers to the following directly (without resorting to integration). (a) Find the variance of the random variable that has density f X ( x ) = 1 √ 4 π e- ( x- 3) 2 4 , for all x. (b) Suppose f X,Y ( x,y ) = 1 2 πλ 2 e- x 2 + y 2 2 λ 2 . Find E[ X 2 + Y 2 ]. 2. Let X 1 ,X 2 ,...,X n be i.i.d. random variables each with pdf f X ( x ). (a) Find the pdf of Y = min { X 1 ,X 2 ,...,X n } . (b) Find the pdf of Z = max { X 1 ,X 2 ,...,X n } . 3. Random variables X and Y are jointly Gaussian with means m X = 1, m Y = 2, variances σ 2 X = 4, σ 2 Y = 9, and Cov( X,Y ) = − 4. (a) Find the correlation coefficient between X and Y . (b) If Z = 2 X + Y and W = X − 2 Y , find Cov( Z,W )....
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hw1 - ECE 562 Fall 2011 HOMEWORK ASSIGNMENT 1 Reading...

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