HW13 - ECE 302, Homework #13, due date: 4/20/2011

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ECE 302, Homework #13, due date: 4/20/2011 http://cobweb.ecn.purdue.edu/ chihw/11ECE302S/11ECE302S.html Question 1: [Basic] Problem 6.68(a,b). Question 2: [Basic] Problem 6.69(a,b). Question 3: [Intermediate/Exam Level] Problem 6.72(a,b). Question 4: [Intermediate/Exam Level] Suppose the means and variances of random variables X and Y is m X = 1, σ 2 X = 2, m Y = - 2, and σ 2 Y = 3 respectively. Suppose we also know that the covariance between X and Y is Cov ( X,Y ) = 1. Let Z = X + Y . 1. Find the mean and the variance of Z . Note: X and Y are not independent this time. 2. Find Cov ( X,Z ) and the correlation coefficient ρ X,Z . 3. What is the minimum mean square error estimator of Z given X = x ? Question 5: [Intermediate/Exam Level] Continue from the previous question. 1. What is the linear minimum mean square error estimator of Z given X = x ? 2. What is the linear minimum mean square error estimator of X given Z = z ? Question 6:
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HW13 - ECE 302, Homework #13, due date: 4/20/2011

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