HW10-2

# HW10-2 - h x Question 3 Problem 4.35(Hint You should use...

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ECE 302, Homework #10. Due date: 4/6 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: Problem 4.29. You are welcome to design any joint distribution that satisﬁes the description. Question 2: 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 h ( x ) = E ( Y | X = x ) where x is a number between ( - 1 , 1). Plot the function
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Unformatted text preview: h ( x ). Question 3: Problem 4.35. (Hint: You should use techniques similar to Example 4.26.) Question 4: Consider two random variables 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 5: Problem 4.61....
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