20065ee131A_1_EE131AF06HW1Solution

20065ee131A_1_EE131AF06HW1Solution - Solution of Assignment...

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Unformatted text preview: Solution of Assignment 1, EE 131A Due: Wednesday October 11, 2006 Problem 1. (a) S = { ( F,F ) , ( F,R ) , ( F,K ) , ( R,F ) , ( R,R ) , ( R,K ) , ( K,F ) , ( K,R ) , ( K,K ) } . (b) A = { ( F,F ) , ( F,R ) , (( R,F ) , ( R,R ) } . Problem 2. (a) ( A B c C c ) uniontext( B A c C c ) uniontext( C A c B c ) . (b) ( A B C c ) uniontext( A C B c ) uniontext( B C A c ) . (c) A B C . (d) ( A B ) uniontext( A C ) uniontext( B C ) . (e) A c B c C c . Problem 3. We use the identity P [ A B ] = P [ A ] + P [ B ]- P [ A B ] , for the sets A = { a,c } and B = { b,c } . The result is 1 = P [ { a,b,c } ] = 5 8 + 7 8- P [ c ] . Therefore, P [ c ] = 1 2 . Since, P [ { a,c } ] = P [ a ] + P [ c ] and P [ { b,c } ] = P [ b ] + P [ c ] , thus P [ a ] = 1 8 and P [ b ] = 3 8 . Problem 4. (a) We use the inequality P [ X Y ] P [ X ] + P [ Y ] , then P bracketleftbig A B C bracketrightbig = P bracketleftbig ( A...
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This note was uploaded on 06/09/2010 for the course EE 131A taught by Professor Lorenzelli during the Spring '08 term at UCLA.

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20065ee131A_1_EE131AF06HW1Solution - Solution of Assignment...

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