# hw5 - UCSD ECE 153 Prof. Young-Han Kim Handout #18...

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UCSD ECE 153 Handout #18 Prof. Young-Han Kim Thursday, November 6, 2008 Homework Set #5 Due: Thursday, November 20, 2008 1. Work on the midterm problems to make sure you understand everything clearly. 2. Read Sections 6.1–6.5 in the text. Try to work on all examples. 3. Which of the following matrices can be a covariance matrix? Justify your answer either by constructing a random vector X , as a function of the i.i.d. zero mean unit variance random variables Z 1 , Z 2 , and Z 3 , with the given covariance matrix, or by establishing a contradiction. (a) 1 2 0 2 (b) 2 1 1 2 (c) 1 1 1 1 2 2 1 2 3 (d) 1 1 2 1 2 3 2 3 3 4. Given a Gaussian random vector X N ( μ , Σ), where μ = (1 2 3) T and Σ = 9 0 0 0 4 1 0 1 1 . (a) What is P ( X 1 + X 2 + 2 X 3 < 0)? (b) Find the joint pdf on Y = A X , where A = 1 1 - 1 2 - 1 1 . 5. Packet switching. Let N P( λ ), i.e., Poisson with parameter λ , be the number of packets arriving at a switch per unit time. Each packet is routed to Output Port 1

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## This note was uploaded on 10/26/2011 for the course MATH 180C taught by Professor Eggers during the Winter '09 term at Aarhus Universitet.

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hw5 - UCSD ECE 153 Prof. Young-Han Kim Handout #18...

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