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Prob13

# Prob13 - Let(2’2{1,2,3,4 and o a{a,b,d F a{on{1,2,4{3 g...

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Unformatted text preview: Let (2’2 {1,2,3,4} and o a {a,b,d} F a {on {1,2,4}, {3}, g} Note that F is a o—field Let X(1)= a X(2) = b X(3) = a ‘ X(4) = d It follows that X{F’}E{X(A) : A EF}E{Q, {a}, (25} note that {a} EXU‘.’ } however, {a}c E{b,d} €73 X‘LP} Therefore, X{f’ } is not a d—field. //‘\\ 9- Zl=Y(X1)2+(X2)2 \$3 .7:(Z1)”G{Z1'1A°A€B} , {Wm mt (on) @éi M3 as}: m = g{(x1,X2): F? + (X2)2 6 (—oo, a] } E 1.,»ng MEL:WO:C~:W:E 50mm): (xl)2+ (x92 6 {Gal} Sim) (”53 @‘Wwwwwnfmm E O{(X1,X2) 34(X1)2+ (X2)2 5 a} f)? 3 8653?) Z a: 2»; (*3) 6 a cum»: (x1)2+ (X2) 2 s a2} note that a is any real number implies that a2 is any real number Therefore, 13(21) is a G-ﬁeld generate by a class of sets where each set can be represented as disc with an arbitrary radius a2 V 0 S a2 S 00. X}. [a /’/ 2‘ \x 4/ E'“\ E z’ 3 ‘\ ' i \‘ é , 2 K My / \x 6‘ y/ ‘ -1 3 ‘1 § (awal) V has} U [aq1a5§} What z 0&3 2, 7336 3 darts M am Web #135 3 Ozﬁ‘tﬂ’TJ/WGL P35" (70,0) Job/{:3 x} M duwmf M 3 6 Z: 3 a) @ M mjf m EFKZQ Number 9 continued 22 = sign(x1— X2) = 1 if x1> X2 corresponds to region III 0 if x1= X2 corresponds to region II —1 if X1< x2 corresponds to region I 73(22) E o{ 22'1 A : AEB} E0{22'1{1},22'1{0},22'1{-1},22'1{1,0},22"{1,-1},22'1{0,—1},Z2l{1,0,1}} 50{ III ,II ,I ,IIIuII ,IIIUI ,IIUI , IIIwIIuI} Ks, 97L)” i“ Q 1,5} #5; 7 f W23, 274572 895% 552/137) _ Efﬁ'tjla “ti/1% Pal/{7:5 57'} U}- f U 7a?! 75/12 fGﬁﬁiﬁt/zg 1}] Q 7 I DOD If; (X—nl<3%’fw 50W ”'6 W7 : EWW M-h7<§%7 So A(§T555[,><—55l<:ﬁ 7) :AL‘: M/Wn jx—Mc—o >55 7: E .2? : 7:5: .29» <0) 37 8w<¢7=0 . 855(5),?! @ 5557,10 A574,}, Anm 641. 00577555542 _ we need ~60 5/50th 85555137455) 5> 555635455, S52 :“5’555655/ :22 55,55pr W'xgﬂ“ 50 5M (3 '55): 5552045555): 7’ \$8M) (54557 \$185554”) ‘5 Sax/45550) - 0+5 3 5 ’5 5555 (\$74”) 3'” Aggy; (A55) ”9 “Q @A" * 5509730774557 255-3375551455) :0 so 5555 Agga £55 5.5 55 05 From/9555555 555mm €719“ [mfggg \$95 5:57 Meagwg 283/0 5‘ s awn)? Q5552, {mi-=35, 5:550 0:5“ mama i ‘53 J2. ...
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