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# h4color - ECE 580 Math 587 SPRING 2011 Correspondence 9...

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Unformatted text preview: ECE 580 / Math 587 SPRING 2011 Correspondence # 9 March 7, 2011 ASSIGNMENT 4 Reading Assignment: Text: Chapter 4. Suggested Reading: Curtain & Pritchard: Chp 5 (pp. 75-84). Review probability theory and stochastic processes from any (graduate) text of your choice. Notice : This is the last homework assignment before the midterm exam, which is scheduled for March 17. Problems (to be handed in): Due Date: Tuesday, March 15 . The problems in this set are all on the topic of Hilbert Spaces of Random Variables and Stochastic Processes. 29. Let (Ω , F , P ) be a probability space, and L 2 (Ω , P ; R n ) be the Hilbert space of second-order random vectors (of dimension n ) defined on (Ω , F , P ), with inner product ( x,z ) = E [ x T Qz ] where Q is a given (fixed) positive-definite matrix of dimension n × n . Let { y ,. . ., y i } be m − dimensional random vectors defined on (Ω , F , P ), which are uncorrelated and have zero mean. Let M nm be the class of all n × m matrices with bounded entries, and consider the following optimization problem for a given...
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h4color - ECE 580 Math 587 SPRING 2011 Correspondence 9...

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