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# HW2 - ECE 302 Homework#2 due date...

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ECE 302, Homework #2, due date: 1/26/2011 http://cobweb.ecn.purdue.edu/ chihw/11ECE302S/11ECE302S.html Question 1: Deﬁne a 2-D function f ( x,y ) as follows. f ( x,y ) = ( 1 x e - 2 y x if x (0 , 2] and y [0 , ) 0 otherwise Compute the value of the following 2-dimensional integral. Z x = -∞ Z y = -∞ xyf ( x,y ) dydx. Question 2: Deﬁne a 2-D function f ( x,y ) as follows. f ( x,y ) = ( ce - x e - y if 0 y x < 0 otherwise Determine the c value such that Z x = -∞ Z y = -∞ f ( x,y ) dydx = 1 . Question 3: Consider f X ( x ) and f Y ( y ) as follows. f X ( x ) = ( e - x if x 0 0 otherwise f Y ( y ) = 0 . 5 e -| y | Compute the following two integrals Z y = -∞ Z x = -∞ ( x + y ) f X ( x ) f Y ( y ) dxdy Z y = -∞ Z x = -∞ e - 0 . 1( x + y ) f X ( x ) f Y ( y ) dxdy

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Question 4: [Basic] Consider a best-of-three baseball series between two teams A and B , namely, the team that wins 2 games wins the whole series. (No game will be played after
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HW2 - ECE 302 Homework#2 due date...

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