RP-HW2 - Kyung Hee University Department of Electronics and Radio Engineering C1002900 Random Processing Homework 2 Spring 2010 Professor Hyundong

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Kyung Hee University Department of Electronics and Radio Engineering C1002900 Random Processing Homework 2 Spring 2010 Professor Hyundong Shin Issued: April 14, 2010 Due: April 28, 2010 Reading: Course textbook Chapter 7 HW 2.1 Consider the following 33 matrices: .       ABC D EF G 10 3 1 10 5 2 10 5 2 10 5 2 250 533 5 33 531 102 232 2 32 2 12 10 5 2 10 0 0 2 1 1 53 1 030 12 1 21 2 0 0 2 1 1 2 Your answers to the following questions may consist of more than one of the above matrices or none of them. Justify your answers. (a) Which of the above could be the covariance matrix of some random vector? (b) Which of the above could be the cross-covariance matrix of two random vectors? (c) Which of the above could be the covariance matrix of a random vector in which one com- ponent is a linear combination of the other two components? (d) Which of the above could be the covariance matrix of a random vector with statistically independent components? Must a random vector with such a covariance matrix have sta- tistically independent components? HW 2.2 For each of the following statements, determine whether it is TRUE or FALSE. Make sure you give a sufficient but brief justification of your answers. Note that each statement is independent of the others, so you cannot use the assumptions of one in the others. (a) If random vectors X and Y are jointly Gaussian and  | EE XY X , then X and Y are statistically independent.
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 (b) Given two random variables X and Y , if  | EXY EX , then for all functions g ,      E Xg Y E X E g Y . (c) Given two random variables X and Y , if   E Xg Y E X E g Y for all functions g , then | . HW 2.3 We wish to estimate a random variable X by some constant ˆ x . There are many ways to meas- ure how good an estimate ˆ x is. Here you will derive an important property of the minimum mean square error estimation (MMSE) . Define the mean square estimation error by   ˆˆ () ex E X x  2 .
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 06/10/2010 for the course ELECTRONIC C1002900 taught by Professor Hyungdongshin during the Spring '10 term at Kyung Hee.

Page1 / 7

RP-HW2 - Kyung Hee University Department of Electronics and Radio Engineering C1002900 Random Processing Homework 2 Spring 2010 Professor Hyundong

This preview shows document pages 1 - 3. Sign up to view the full document.

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