HW4-2

# HW4-2 - ECE 302 Homework#4 Due date 2/9...

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ECE 302, Homework #4. Due date: 2/9 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 Review of Calculus: Question 1: Define a 2-D function f ( x, y ) as follows. f ( x, y ) = ( x/y 2 if y [0 , 2] and x [0 , y ] 0 otherwise Compute the values of the following 2-dimensional integrals. Z 4 / 3 y =2 / 3 Z 3 / 2 x =1 / 2 f ( x, y ) dxdy Z 4 / 3 y =2 / 3 Z x = -∞ f ( x, y ) dxdy Z y = -∞ Z 3 / 2 x =1 / 2 f ( x, y ) dxdy. Question 2: Problem 2.51. You have to assume that the outcomes of the first and the second tosses are independent . Why do you need this independence assumption? Question 3: Problem 2.63. Question 4: Problem 2.64. Question 5: Problem 2.91. Answer the following questions before trying to solve Problem 2.91:

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1. What is the sample space? Hint: S = { (0 , 0) , (0 , 1) , (0 , 2) , (0 , 3) , (1 , 0) , · · · } 2. This problem cannot be solved without assuming independence. What are the independence assumptions?
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