HW10 - (0 2 π Let X = cos(Θ and Y = sin(Θ 1 Find E Y 2...

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ECE 302, Homework #10, due date: 3/30/2011 http://cobweb.ecn.purdue.edu/ chihw/11ECE302S/11ECE302S.html Question 1: [Basic] Problem 5.25(b,c). Question 2: [Basic] Problem 5.27(a,c,d). Question 3: [Basic] Problem 5.28. Question 4: [Intermediate/Exam Level] Suppose X is a uniform random variable with parameters a = 1 ,b = 2. Given X = x 0 , the conditional probability density function of Y , is an exponential random variable with λ = x 0 . 1. Find the sample space of ( X,Y ). 2. What is the joint probability density function of X and Y ? 3. What is the probability that P ( X < 1 . 5 and Y 2)? Question 5: [Intermediate/Exam Level] Suppose Θ is uniformly distributed in the interval
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Unformatted text preview: (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 6: [Basic] Problem 5.31. Question 7: [Basic] Problem 5.41. Question 8: [Basic] Problem 5.47. Question 9: [Basic] Problem 5.48(a,b,d). Question 10: [Intermediate/Exam Level] Problem 5.58. Question 11: [Intermediate/Exam Level] Problem 5.18. Question 12: [Basic] Problem 5.20....
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This note was uploaded on 02/12/2012 for the course ECE 302 taught by Professor Gelfand during the Spring '08 term at Purdue.

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HW10 - (0 2 π Let X = cos(Θ and Y = sin(Θ 1 Find E Y 2...

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