# HW11 - X and Y with means and variances being m X,σ 2 X...

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ECE 302, Homework #11, Due 4/8 http://www.ece.purdue.edu/ chihw/ECE302 09S.html Question 1: [Basic] Problem 5.40. Question 2: [Basic] Problem 5.61. Question 3: [Basic] Problem 5.65. Question 4: [Intermediate/Exam Level] Suppose Θ is uniformly distributed in the interval (0 , 2 π ). Let X = cos(Θ) and Y = sin(Θ). 1. Find E ( Y ). 2. Find E ( XY ). 3. Let h ( x ) = E ( Y | X = x ), where x is the input parameter that is between ( - 1 , 1). Find out the expression of h ( x ) and h ( x ). 4. Does E ( h ( X )) = E ( Y )? Question 5: [Intermediate/Exam Level] Continue from the previous question. 1. Are X and Y orthogonal? 2. Are X and Y correlated? 3. Find out the covariance and the correlation coeﬃcient of X and Y . Question 6: [Intermediate/Exam Level] Consider two random variables

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Unformatted text preview: X and Y with means and variances being ( m X ,σ 2 X ) and ( m Y ,σ 2 Y ) respectively. We further assume that X and Y are independent. 1. Find out the value of E ( XY ) in terms of ( m X ,σ 2 X ) and ( m Y ,σ 2 Y ). 2. Let Z = X + Y . Find out the values of E ( Z ) and E ( Z 2 ). 3. Find out the value of Var( Z ). Question 7: [Intermediate/Exam Level] Problem 5.71. Question 8: [Basic] Problem 5.76(a). Question 9: [Intermediate/Exam Level] Problem 5.80(a,b,d). Also ﬁnd E ( Y ) and E ( h ( X )) where h ( x ) = E ( Y | X = x ). Question 10: [Basic] Problem 5.111. Question 11: [Basic] Problem 5.112....
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## This note was uploaded on 05/02/2009 for the course ECE 302 taught by Professor Gelfand during the Spring '08 term at Purdue.

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HW11 - X and Y with means and variances being m X,σ 2 X...

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