B4C3

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1 3-, S ( ) a S A S {a} ( ) ( ) S A B AB A B AB A A A =S A A B AB= Ex.,,,3,4,5,6, () S AsS={,,3,4,5,6} () 4 A A AsA={,,3}A ={4,5,6} (3) B B AsB={,3,5}B ={,4,6} (4) C C AsC={,4,6}C ={,3,5} (5) 7 D D AsD= D ={,,3,4,5,6} (6) AB,A,B AsAB={,,3,5}AB={,3} (7) BC,B,C AsBC={,,3,4,5,6}BC= (8) CD,C,D AsCD={,4,6}CD= (9)S A As63 A B A,B Ex. S{,,3,4,5,6} A{,} ()S?()A As646 Ex3. 6 SA (S)(A) As /9

2 Ex4. 3 A B,C ()AAs{(,,),(,,),(,,),(,,)} ()BAs{(,,),(,,),(,,)} (3)CAs{(,,),(,,)} (4)A,B As{(,,),(,,),(,,),(,,),(,,)} (5)A,B As{(,,),(,,)} (6)A As{(,,),(,,),(,,),(,,)} (7)A,B As (8)B,C As Ex5. SA B ()(S)=As4 ()(AB)=As3 (3)(AB)=As5 (4)S ( S )=As 4 Ex6., S As79 Ex () As: C ()A 0 (A)=As C 0 C /9

3 3- Ex8. (Laplace) S A S A A ( A) ( A) P( A) = = ( S). () () () () 5(3) 5As Ex9. 35 As Ex0. () As4 () As3 (3) ( ) As4 (4) ( ) As3 (5) ( ) As (6) ( ) As Ex. 3 [88]As /9

4 Ex. As S AB S ()P( )=0P(S)=0P(A) () P(A )= P(A) (3) P(AB)=P(A)+P(B) P(AB) AB= P(AB)=P(A)+P(B) (4) A B P(A)P(B) (5) ABC S ABC P(A B C)=P(A)+P(B)+P(C) P(A B) P(B C) P(C A)+P(A B C) (6) P(A B)=P(A B )=P(A) P(A B) Ex [88]As 9 5 Ex4. A B 3 p A B p 5 5 () p () < p (3) < p < (4) p (5) p > [87]As Ex5. 6 (6 ) [87]As 5 9 Ex6. 7 ( ) [86] As 6 35 Ex [85]As /9

5 Ex [84]As 4 Ex [8]As 33 Ex [8]As 3 Ex () 0 () 0 9 [80]As Ex. ()3 ()34 [77]As 5 Ex [76]As 7 Ex () () [76] As Ex [73] As /9

6 .A S P(A)>0B S A P B P(B A) P(B A)= ( A B ) PA ( ) P. P(B A)= ( A B ) A ( B) = PA ( ) A ( ) 3. ABC S P(C)>0 ()P( C)=0 ()P(C C)= (3)0 P(A C) (4)P(A C)= P(A C) (5)P(AB C)=P(A C)+P(B C) P(AB C) (6)A B P(A C) P(B C) 4. ()P(AB)=P(A)P(B A) ()P(ABC)=P(A)P(B A)P(C AB) (3)P(A A...A )=P(A )P(A A )...P(A A A...A - ) Ex () () As Ex ( 4 6 ) 5 [89]As 7 8 Ex8. [87]As 3 7 Ex9. 4 [86]As (Partitio) A A A r S ()A A A r =S ()A i A j = i jij=r {A A A r } S /9

7 Ex [90]As40% Ex % [79]As0.6.{A A A r } S B P(B)>0 ()P(B)=P(B A )+P(B A )+ +P(B A ) =P(A ) P(B A )+P(A ) P(B A )++P(A ) P(B A ) = = P( A )( B A ) P( A B) j ()P(A j B)= = PB ( ) PA ( ) PB ( A) j j = P( A ) P( B A ) ( ) (3) P(B) P(A j B) 5 ( ) 96 Ex As 96 As 6 A A A 3 A B Ex ( ) [89]As /9

8 Ex34. A B 30%70%A % B 5% (A) A (B) B (C) A 3/38 (D) A 30/0000 (E) B 350/0000[85]AsBC. AB S () P(A B)=P(A) P(B) AB () AB A B A B A B. ABC ABC S () ABC P(A B C)=P(A) P(B) P(C) P(A B)=P(A) P(B) P(B C)=P(B) P(C) P(C A)=P(C) P(A) P(A B C)=P(A) P(B) P(C) S={,,}A={,4,6,8,0,}B={3,6,9,}C={,5,6,7,,} () ABC ABC AB C A BC AB C A BC A B C A B C 3. p () p () ( p) ( p) (3) C p ( p) =3 Ex [86]As0.83 Ex ( ) = p (A)0.4 p<0.5(b)0.5 p<0.6(c)0.6 p<0.7(d)0.7 p<0.8(e)0.8 p<0.9 log3=.494log3=.505log.83=0.45[86]asd /9

9 Ex [84]As Ex38. 3 [83]As 30 Ex ( ) () As () As 9 4 Ex40. P(A)=aP(B)=bP(AB)=c abc () P( A B ) =As c () P( A B) =Asb c (3) P( A B) =As a+c (4) P( A B ) =As a b+c Ex4. () 5 () As 6 Ex4. 3 abc ()a<b<c()abc (3)a+b+c=(4)(a-b)(b-c)=0(5)(a-b)(b-c)=As Ex43. As 5 96 Ex44. () () 4 AsC 9 ( ) 3 ( ) 7 3 ( )( ) Ex45. () 6 () (3) As /9

10 Ex46. A P(A)>99.8% (log=0.300log3=0.477)as35 Ex47. A B Ax + By = 3 As x + y = Ex48. a b f(x)=3x +ax+b 3 As 3 Ex49. f(x)=x +ax+b ab ()f(x)=0 As 9 36 ()f(x)=0 As 7 36 (3)f(x)=0 As 7 36 (4) x f(x) As 7 36 Ex () () (3) 3 (4) 4 (5) 5 (6) 8 As Ex As0 Ex5. 5 () () 50 0 As 7 8 Ex As /9

11 Ex54. 3 P(A) P(B) A B As As Ex () 6 73 () As 65 Ex56. 3 (3 ) 5 (345 ) 6 (3456 ) 4 9 () () (3) As Ex As0.33 Ex () () 4 As 5 5 Ex As 66 Ex60. 5 () () (3) (4) (AKQ J)As Ex As /9

12 3 Ex6. ABC p( B) = p ( C) = 5 3 p ( A B ) = p ( B C) = p ( C A) = p ( A B C) = p( A B C) = ()p(abc )=()p(a)=as Ex63. ABC P(A)=P(B)=P(C)=0.P(A B)=0. P(B C)=P(C A)=0 As0.5 Ex64. AB P(A B)= 3 4 P(A )= 3 P(A B)= 4 ()P(A)()P(B)(3)P(A B)As 3 3 Ex65. AB P(A)=0.P(B)=0.4 P(A )P(A B ) As0.80. Ex66. AB P(A B)=0.3P(A B )=0.5 P(A)P(B) As0.0.3 Ex () () As Ex As Ex As Ex As Ex7. ( ) As /9

13 Ex7. ABCDE () () 4 (3) 3 (4) (5) (6) 3 As Ex73. 4 () () (3) As Ex74. 0 A 4 B 3 C 3 () A () As Ex75. AB As 8 Ex76. 0 As 0 8 Ex77. As Ex78. As 35 Ex79. ax +bx+c=0 abc { } As Ex As /9

14 3-3 E. p m p m. S{A A...A } S A i p i i=3... A i m i i=3... p m =pm +p m +---+p m = Ex As 4 Ex8. 3- (=3) 7 5 As 4 Ex As0 Ex As E E Ex85. As Ex86. As /9

15 Ex As 5 As 44 5 As 44 5 Ex As 3 5. Ex89. 0 As Ex As =0 Ex9. 00 As0 Ex9. ( /) P =0.3 P =0. P 3 =0.4 P 4 =0. ( )[89]AsE()=E()=7E()= /9

16 Ex [88]As 63 0 Ex94. 5 [85]As 9 Ex () ()3 (3) 8 [8]As Ex (00 ) 9 [80]As Ex ( ) [86]As 7 6 Ex [88]As 4 3 Ex99. 5 As Ex As5 Ex As45 Ex As /9

17 Ex As9 Ex As75 Ex05. () () 50 0 As Ex06. As 3 6 Ex As 5 8 Ex () () 90 As78 Ex As 65 Ex As6 Ex Ex As /9

18 Ex As0 3 Ex4. ABC,, As46 Ex5. ( ) a + b(a>b) a b As 3 Ex As Ex As 3 0 Ex As 0 Ex As Ex As00 Ex. () 8 () ( ) 6 As /9

19 3-4 ( ) () ( ) () ( ). N N = N ()N=+c0<c< c () N (N+) ( r )r r+r+...r+(-) ( ) Ex [89]As /9

20 Ex ( ) As 7 Ex4. () As () As (3) As (4) As Ex As68.4cm Ex () ( ) 0 () 4 3 ( 458 ) 393 (3) Ny + N y + N3 y3 y =, N + N + N3 = N 999 N 75 N i i yi i 607 y = ( ) (4) ~56~0~56~0 ~5 ( ) (5) As Ex As /9

21 3-5 () () ( ) ( ) () (). =. 5~5 3. = 4. ( ) ( ) () () () () (3) L ~U f f f +f ++f L ~U f f +f f ++f L ~U f f +f ++f f (4) Ex () 5 () 0 (3) 5 As.764% /9

22 Ex9. ()60 () 70 (3) 80 ~90 As807 Ex30. 5 ( ) 35~38 38~4 4~ ~ ~ ~ ~ /9

23 3-6 M(Mea)X. ( ) M = ( x + x + + x ) = x i i= Ex As75.7. ( ) M = ( fx + f x + + f x ) = f i xi i= () M = fi xi = fi[ A + ( xi A)] = A + i= i= i= f ( x x () i A h M = fixi = fi[ A+ h )] = A+ h i= i= i i A) i= xi A fi ( ) h Ex3. 0 =As Ex33. 0,, ( ) =As75 3. () () i= ( x M) = 0 i 50~55 55~60 60~65 65~70 70~75 75~80 80~85 85~ ( xi M) ( xi p) i= i= p (3) X + a = X + a, bx = bx, bx + a = bx + a (4) ( y )M( ) W x x x w w w w x + wx + + w x W = w + w + + w Ex As /9

24 G.M. x x x G. M. = x x SMAMGMHM( ) Ex As6 x Ex ( log=0.300log.07=0.030)as7.% Me(Media). ( ) ( ) M L f f e i. i = i M = L + ( U L ) U L f e i f i i i i i 3. Ex37. 0 =As68.33 i Ex38. 0,, ( ) =As ~55 55~60 60~65 65~70 70~75 75~80 80~85 85~ Mo ( fi fi ) 3 M o = Li + ( Ui Li) ( f f ) ( f f ) i i i+ i Ex As Ex a b a b=[77]as /9

25 Ex4. 00 ( ( ( ( ( = =[83] ( ( As Ex4. 50 ( ) (A) (B) (C) 85 (D) (E) [89]AsACDE Ex43. ( ) (A) 0 (B) 00 (C) (D) 7080 (E) [8]AsADE /9

26 3-7 (R) (Q.D.) (σs) (R) MAX MIN ( ) Q.D.=Q 3 Q ( ) Q ( ) 3 Q 3 3 Q Q Q Q 3 (Me) () Q 4 4 () [ ] Q 4 4 (3)Q 3 = = = σ + M = ( ) S + M. (σ) σ = ( x M) = x i i M i= i= σ = f ( x M) = h f d M i i i i M x i i = = ( i= i= ) xi A d i = ( )M h Ex ,80,80,80,86 [86]As6 Ex45. 48, 70 σ σ σ σ [89] (A)σ <σ 5(B)σ 5 σ <σ(c)σ =σ(d)σ<σ σ+5(e)σ+5<σ AsB Ex [79]As /9

27 Ex ,5,53,54,56,57,60,6 As5463. (S) S ( ) ( ) ( ) ( x M i x M i x M = = = = σ i i= i= i= S = f ( x M) = h ( f d i i i i i= i= = h f d M ( ) i i i = M ) ( )M Ex48., 8 ( ), 67,58,6,75,70,8,64,66( ), RQ.D.MS As ) Ex49. As Ex As = 4. = Ex5. 9,8,,4,0,8,7,0,3,0 RMQ.D. As Ex5. 9,8,,4,0,8,7,0,3,0 RM Q.D. As Ex53. x =6S x =4 x=4y 3 y As /9

28 Ex54. x, x,, x 6 3 3x+ 3x + 3x 3 + 3x + RMMeQ.D.SAs Ex55. 9 ( ).43,.46,.4,.45,.44,.48,.46,.47, ,6,,5,4,8,6,7,5? (A) 5(B) (C).45(D) 0. (E).45[88]AsABCE (M+,M ) 68.6% (M+,M ) 95.44% (M+3,M 3) 99.73% M 3σ M σ M σ M M + σ M + σ M + 3σ Ex ()?() 90?(3) 80?As60560 Ex57.,,3,, As Ex58. 5 ( 0 ) A,,,,,0,0,0,0,0 B,,,,,5,5,5,5,5 C4,4,4,5,5,5,5,6,6,6 D,,,,3,3,4,4,5,5 E,,3,4,5,6,7,8,9,0 [89]AsA Ex As660.4 Ex60. 0 A,B A B A,B As /9

29 30( X X ) Ex6. X X S Y = + 70 S () Y Y As70 () Y S Y As30 Ex6., 5 ( ),, (A) (B) (C) (D) (E) [88]AsCE Ex63. 30,40,60,50,70,80,60,90, () As60 3 () () 60? As64 () 60? As46 (3) 70 60?[84]As /9

Microsoft Word - 新1.doc

Microsoft Word - 新1.doc . 80% E E E 0 0 E E 4 E E ω E E Ω E E Ω ={} E 0 0 =,, L, 0 E Ω= {,, L, 0} ω = ω = Ω= { ω, ω } E k k =,, L,, L E Ω= {,, L,, L} 4 E 4 t 0 t