hw2 - EE 562a Homework Set 2 Due Monday 5 Feb 2007 1 (The...

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Unformatted text preview: EE 562a Homework Set 2 Due Monday 5 Feb 2007 1 (The following well-defined problems come from different sources, and the notation used may vary. Dont let that bother you!) 1. Let y ( u ) be a random vector with second-moment description m y = K y = 3- 1- 1 3 3 . (a) What is the mean squared length of y ( u )? (b) For what unit vector b max does y t ( u ) b max have maximum variance? (c) For what unit vector b min does y t ( u ) b min have minimum variance? (d) Upper bound the P {| y ( u ) | > 10 } . (Here P {} denotes the probability of the event {} .) 2. Find the biased linear transformations of a random vector w ( u ), composed of mean-zero, unit-variance, uncorrelated random variables, which will yield random vectors having the following second moment descriptions: (a) m x = 1 2 3 K x = 1 1 1 1 2 2 1 2 3 (b) m y = 1 1- 1- 1 K y = 1- 1- 1 1 2- 2- 2 2 (c) m z = 1 1 1 K z = 9 6 3 6 13 8 3 8 14 Hint: Parts (a) and (c) are most easily done with triangular-matrix transformations of w ( u )....
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This note was uploaded on 05/06/2008 for the course EE 562a taught by Professor Toddbrun during the Spring '07 term at USC.

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hw2 - EE 562a Homework Set 2 Due Monday 5 Feb 2007 1 (The...

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