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Unformatted text preview: ECE 302, Homework #3, due date: 2/2/2011 http://cobweb.ecn.purdue.edu/ ∼ chihw/11ECE302S/11ECE302S.html Review of Calculus: Question 1: Compute the following integrals. Z 2 π a cos( ωt + θ ) dθ Z 2 π a cos( ωt + θ ) da Question 2: Define a 2-D function f ( x,y ) as follows. f ( x,y ) = ( x/y 2 if y ∈ [1 , 2] and x ∈ [0 ,y ] 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 3: Define a 1-D function f X ( x ) as follows. f X ( x ) = x if x ∈ [0 , 1] 1 2 if x ∈ (1 , 2] otherwise Another function F ( x ) can be defined based on the integral of f X ( x ) as follows: F ( x ) = Z x s =-∞ f X ( s ) ds. 1. Find the expression of F ( x ) for the case of x < 0. 2. Find the expression of F ( x ) for the case of x ∈ [0 , 1]. 3. Find the expression of F ( x ) for the case of x ∈ (1 , 2]. 4. Find the expression of F ( x ) for the case of x > 2. 5. Write down the complete expression of F ( x ) by considering the above four different cases. Your answer is simply a piecewise function that considers four different cases. Question 4: [Basic] Problem 2.62. Please assume the die is fair. Question 5: [Basic] Consider a best-of-three series between teams A and B. The condi- tional distributions are as follows. P ( A wins the next game | B is leading in the series ) = 0 . 7 P ( A wins the next game | A and B are tied in the series ) = 0 . 5 P ( A wins the next game | A is leading in the series ) = 0 . 4 1. Construct the weight assignment for the sample space1....
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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.
- Spring '08