# HW11 - ECE 302 Homework#11 Due date 4/13...

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ECE 302, Homework #11. Due date: 4/13 http://www.ece.purdue.edu/ chihw/ECE302 07.html Prof. Chih-Chun Wang Email: [email protected] Office: MSEE354 Office Hours: MWF: 12pm–1pm TA: Kamesh Krishnamurthy, Email: [email protected] Office: POTR 370 Office Hours: M: 10–11am TTh: 10:30am–12:30pm Question 1: 1. Problem 4.39(a). 2. Find f Z | X,Y ( z | x, y ), f Y | X ( y | x ) and f X ( x ). (Hint: Just like the 2-D case, f Z | X,Y ( z | x, y ) = f X,Y,Z ( x,y,z ) f X,Y ( x,y ) . So your goal is to find the marginal pdf f X,Y ( x, y ).) 3. Verify the “chain rule” that f X,Y,Z ( x, y, z ) = f Z | X,Y ( z | x, y ) f Y | X ( y | x ) f X ( x ). Question 2: Problem 4.45. Question 3: Problem 4.67. (Hint: You need to consider two cases: a > 0 and a < 0. Ignore the case a = 0.) Question 4: 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

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