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20082ee131A_1_131AHW2SOL

# 20082ee131A_1_131AHW2SOL - EE 131A 1 a b c d 2 a b c d e...

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EE 131A Homework #2 Spring 2008 Solution K. Yao 1. a. F E . b. E . c. . d. { O ∪ { 4 , 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 , 26 , 28 , 30 }} . 2. a. All kings or all clubs. b. King of clubs. c. All kings and all the spades, hearts, and diamonds. d. All spades, hearts, and diamonds except their three kings. e. All kings. 3. i. S = { ( g 1 , g 2 ) , ( g 1 , g 3 ) , ( g 1 , d 1 ) , ( g 1 , d 2 ) , ( g 2 , g 1 ) , ( g 2 , g 3 )( g 2 , d 1 ) , ( g 2 , d 2 ) , ( g 3 , g 1 ) , ( g 3 , g 2 ) , ( g 3 , d 1 ) , ( g 3 , d 2 ) , ( d 1 , g 1 ) , ( d 1 , g 2 )( d 1 , g 3 ) , ( d 1 , d 2 ) , ( d 2 , g 1 ) , ( d 2 , g 2 ) , ( d 2 , g 3 ) , ( d 2 , d 1 ) } ii. a. E 1 = { ( g 1 , d 1 ) , ( g 1 , d 2 ) , ( g 2 , d 1 ) , ( g 2 , d 2 ) , ( g 3 , d 1 ) , ( g 3 , d 2 ) , ( d 1 , g 1 ) , ( d 1 , g 2 ) , ( d 1 , g 3 ) , ( d 2 , g 1 ) , ( d 2 , g 2 ) , ( d 2 , g 3 ) } . b. E 2 = S - { ( d 1 , d 2 ) , ( d 2 , d 1 ) } . c. E 3 = { ( g 1 , d 1 ) , ( g 1 , d 2 ) , ( g 2 , d 1 ) , ( g 2 , d 2 ) , ( g 3 , d 1 ) , ( g 3 , d 2 ) , ( d 1 , g 1 ) , ( d 1 , g 2 ) , ( d 1 , g 3 ) , ( d 1 , d 2 ) , ( d 2 , g 1 ) , ( d 2 , g 2 ) , ( d 2 , g 3 ) , ( d 2 , d 1 ) } , or E 3 = S - { ( g 1 , g 2 ) , ( g 1 , g 3 ) , ( g 2 , g 1 ) , ( g 2 , g 3 ) , ( g 3 , g 1 ) , ( g 3 , g 2 ) } . d. E 4 = { ( d 1 , d 2 ) , ( d 2 , d 1 ) } 4. a. The total number of ways in which the coats can be returned is 4!. There is only one outcome that is favorable, so the probability is 1/4!. b. For any one person, the total number of ways is 4, and there is only one favorable outcome. Thus, the answer is 1/4. 5. a. The sample space is S = { ( S 1 , S 2 ) : S 1 , S 2 [0 , 1] } . b. The sample space is S = { ( S 1 , S 2 ) : S 1 + S 2 1 . 5 }

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c. The sample space is S = { ( S 1
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20082ee131A_1_131AHW2SOL - EE 131A 1 a b c d 2 a b c d e...

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