~HW1_1_Sol

# ~HW1_1_Sol - ECEN-646 Homework 1 Part 1 Solutions 1 C...

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ECEN-646 Homework 1, Part 1 Solutions 1 C ¸inlar Exercise (4.1), Chapter 1 (a) Ω = { ( N, N, N ) , ( N, N, D ) , ( N, D, N ) , ( N, D, D ) , ( D, N, N ) , ( D, N, D ) , ( D, D, N ) , ( D, D, D ) } (b) A = { ( D, N, N ) , ( D, N, D ) , ( D, D, N ) , ( D, D, D ) } B = { ( N, D, N ) , ( N, D, D ) , ( D, D, N ) , ( D, D, D ) } B C = { ( N, N, D ) , ( D, N, D ) , ( N, D, N ) , ( N, D, D ) , ( D, D, N ) , ( D, D, D ) } A C = { ( N, N, D ) , ( N, D, D ) , ( D, N, N ) , ( D, N, D ) , ( D, D, N ) , ( D, D, D ) } A B C = { ( N, D, N ) , ( N, N, D ) , ( N, D, D ) , ( D, N, N ) , ( D, N, D ) , ( D, D, N ) , ( D, D, D ) } A B = { ( D, D, N ) , ( D, D, D ) } A c B c C = { ( N, N, D ) } A B c C = { ( D, N, D ) } ( A B c ) C = { ( N, N, D ) , ( D, N, D ) , ( D, D, D ) } ( A C ) ( B c C ) = { ( N, N, D ) , ( D, N, D ) , ( D, D, D ) } 2 C ¸inlar Exercise (4.3), Chapter 1 ω = ( ω 1 , ω 2 ), X ( ω ) = | ω 1 | , Y ( ω ) = | ω 2 | , Z ( ω ) = radicalBig ω 2 1 + ω 2 2 (a) X represents the distance from ω to the ordinate ( ω 1 = 0). Y represents the distance from ω to the abscissa ( ω 2 = 0). Z represents the distance from ω to the origin, (0 , 0). (b) P ( { ω : ω 1 a } ) = integraldisplay a -∞ integraldisplay -∞ 1 2 π exp bracketleftbigg - 1 2 ( x 2 + y 2 ) bracketrightbigg dxdy = 1 2 π integraldisplay a -∞ exp bracketleftbigg - 1 2 x 2 bracketrightbigg dx In the same way P ( { ω : ω 2 b } ) = integraldisplay b -∞ 1 2 π exp

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• Fall '16
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