SA3-075- ( ) 3 3 3 3 4 4 4 1 5 5 3 6 4 6 7 X j 8 X ( j ) 9 10 11 13 16 17 091001 09305 17 1
SA3-075- ( ) 0-1 3 0-0-30-4 4 1 7 34 8 4-1 9 5 10 6 11 7 1 8 13 9 14 1011 15 113 17
SA3-075- ( ) 91 1 091001 p N K N K N K C p (1 p) 1 K N N j N j (1-p)q 1 ( p+ q) = C p q j=k B(,p) p X P = K B(,p) K PX ( P = K) X = K P PX ( = K) = C p K (1 p) K P K p µ µ = E( X ) = k = 0 P k C p (1 p) k k k 1 k 1 k = p Ck 1 p (1 p) k= 1 1 k 1 k = p C k 1 p (1 p) k= 1 N j= 0 j 3
SA3-075- ( ) 1 = p( p (1 p)) + = p 3 σ σ = E X µ [( p )] = E[( X ) µ E( X ) + µ ] p = E[( X )] µ p p! EX [ p( X 1)] = p kk ( 1) p (1 p) k!( k)! k k = k = 0 k =! k p (1 p) ( k )!( k)! ( )! k k k = ( 1) p p (1 p) k = ( k )!( k)! = ( 1) p [ ( 1)] [( ) ] ( ) ( ) ( p p p p p p p ) EX X = E X X = EX EX = EX µ EX ( ) = ( 1) p + µ p σ = [( E X )] µ = ( 1) p + µ µ = p(1 p) 4 p σ = p(1 p) p X p X i 1, i = 0, i X = K X = K P X X = X i= 1 i 1 i i = 1 σ 4
SA3-075- ( ) 1 S = ( X X) i k = 1 σ S 1 S = ( Xi X) 1 k = 1 ES ( ) σ = S 1 (1)=16p=0.55 16 16 PX ( = K) K=9 0.55 E( X ) = 16 0.55= 8.8 σ = p(1 p) =16 0.55 0.45= 3.96 σ = p(1 p) = 1.98997487 ()=16p=0.5 16 16 PX ( = K) K=8 0.5 0.55 E( X ) = 16 0.5 = 8 σ = p(1 p) =16 0.5 0.5= 4 σ = p(1 p) = 0.5 1 PX ( = K) K E( X ) P K P 5
SA3-075- ( ) K P(X=K) = p= K P(X=K) = p= (1) () 3 (3) (4)=3p=0.556888 3 P(1 X 3) = P(11 X 4) 3 0.556888 < < = 1-0.01388-0.019598 =0.968014 3 0.556888 0.556888 1 3 0.968014 1 3 0.01388+0.019598=0.031986 6
SA3-075- ( ) K P(X=K) = p= (3) (4) (3 4 6 4 1 4 6 C = 545786 6 6 7
SA3-075- ( ) X, X, X, X, X, X 1 3 4 5 6 X, X, X, X, X, X (1) () (3) (4) (5) (6) d1 = X(1) N, d = X X N, j =,3,4,5,6 j ( j) ( j 1) o 5 1 d j 37, j = 1,,3,4,5,6 6 X (6) = d 1 + d + d 3 + d 4 + d 5 + d 6 4 7 4 H36 = C6 = 545786 d, d3, d4, d5, d6 1 d = d 1, d = d 1, d = d 1, d = d 1, d = d 1 0 3 3 4 4 5 5 6 6 { d, d 3, d 4, d 5, d 6 } 6 X = d + d + d + d + d + d 4 d, d, d, d, d (6) 1 3 4 5 6 3 4 5 6 d = d 1, d = d 1, d = d 1, d = d 1, d = d 1, d = d 1 1 1 3 3 4 4 5 5 6 6 7 37 d 1+ d + d 3 + d 4 + d 5 + d 6 31 H31 = C31 = 34784 7 545786 H31 = 545786 34784 = 9100 6 9100 545786 = 0.556888 7 X j 4 X 1 1 PX ( 1 = K) =, K {1,,3, L,4} 8 4 X1 X X PX ( = K) = PX ( = K X K), K {1,,3, L,4} 1 41 1 1 = P( X1 KPX ) ( = K X1 K) = = o 4 41 4 9 X1 X X3X 3 41 40 1 1 PX ( = K) = P( X KPX ) ( K X KPX ) ( = KX K X K) = = o 10 3 1 1 3 1 4 41 40 4 X, X, X 4 5 6 41 40 39 1 1 PX ( = K) = =, K {1,,3, L,4} o 11 4 4 41 40 39 4 8
SA3-075- ( ) 41 40 39 38 1 1 PX ( = K) = =, K {1,,3, L,4} o 1 5 4 41 40 39 38 4 41 40 39 38 37 1 1 PX ( = K) = =, K {1,,3, L,4} o 13 6 4 41 40 39 38 37 4 X ( j ) 1. X ( j) = K, X (1), L, X ( j 1) {1,, L, K 1} X ( k + 1), L, X (6) { K + 1, K +, L,4} j = 1,,3,4,5,6, K = j j+ 1, j+, L, j+ 36 K 1 1 4 K j 1 1 6 j ( j) = K = 4 C6 P(X ) C CC 1 ( K 1)! (4 K)! = 545786 ( j 1)!( K j)! (6 j)!(36 + j K)!. (5) X j ( ) 14 (5) K X(1) X() X(3) K X(1) X() X(3) K X(1) X() X(3) X(6) X(5) X(4) k X(6) X(5) X(4) k X(6) X(5) X(4) k 3. (6) X j ( ) (6) 9
SA3-075- ( ) 91 1 091001 93 3 6 09305 4 7 4 3 193 1 091001~09103 09100~091033 6 0.556888 (3) (4) 3 1 3 0.968014 3 113L3 0.968014 3 1 3 0.031986 3 7 1718 3 1 091001 09103 09100 091033 133659719161193 B(7, 0.968014) = p =4 0.556888 = 14.73 7 16 4 11 = p(1 p) = 4 0.556888 (1 0.556888) =7.43484 11± 7.43484 113.565176, 18.43484 (113 4 4 P X ) = 0.066 PX ( 19) = 0.307 114, 18 0.556888 0.556888 1-0.066-0.307 = 0.67 0.67 114, 18 (113 4 4 P X ) = 0.066 PX ( 19) = 0.307 0.556888 0.556888 4 X j X ( j ) - ( ) 10
SA3-075- ( ) X ( j) 36+ j ( fi 4 πi), j 1,,3,4,5,6 i= j 4π i 15 = = 15i j j f i 4 X j =i πi 4 X ( j ) =i 4 π i 14 (5) X ( j) π 4 X ( j ) =i f i 8-15 f i 15-4 5 4 168 10 4 j=1,,3,4,5,6 X j 37 4 1 X (1) 37 X () 38 j X ( ) 36 j j i ( ) + 4 37 6 ( ) (7) 0.968 1 0 3 91001 9100 : : : : : : : : : : : : : : : : : : : 9103 : : : : : : : : : : : : : : : : : : : 91053 91054 : : : : : : : : : : : : : : : : : : : 91064 : : : : : : : : : : : : : : : : : : : 91096 : : : : : : : : : : : : : : : : : : : 909 : : : : : : : : : : : : : : : : : : : 9061 : : : : : : : : : : : : : : : : : : : 9093 : : : : : : : : : : : : : : : : : : : 9301 ( ) - 15 1 36 133659719161193 7 7 B(7, 0.968014) 7 PX ( 5) = 0.01930157 PX ( 7 6) = 0.035647 6 7 0.968014 0.968014 1-0.01930157 = 0.98069843 7 0.98069843 0.01930157 11
SA3-075- ( ) 7 16 4 11 1 14.73 ± 7.43484 118, 13 4 P(109 X ) = 0.00538514PX ( 7 140) = 0.093704 0.556888 0.968014 0.0 110, 139 11 0.95654446 - (8) (5) (8) 15 - X (1) = 4.868009 X () = 40.6985 X (3) = 3.0097X (4) = 34.76984X (5) = 49.998X (6) = 5.89596 9 36 X (5) = 49.998 0.95 - (8)091001~093054 X(1) X() X(3) X(4) X(5) X(6) X(1) X() X(3) X(4) X(5) X(6) X(1) X() X(3) X(4) X(5) Cumulative probability 0.0050.0100.05 0.05 0.10 0.5 0.50 0.75 0.90 0.95 0.975 0.99 0.995 D.F. 34 16.5 17.8 19.8 1.7 4.0 8.1 33.3 39.1 44.9 48.6 5.0 56.1 59.0 35 17. 18.5 0.6.5 4.8 9.1 34.3 40. 46.1 49.8 53. 57.3 60.3 36 17.9 19. 1.3 3.3 5.6 30.0 35.3 41.3 47. 51.0 54.4 58.6 61.6 37 18.6 0.0.1 4.1 6.5 30.9 36.3 4.4 48.4 5. 55.7 59.9 6.9 38 19.3 0.7.9 4.9 7.3 31.8 37.3 43.5 49.5 53.4 56.9 61. 64. 1
SA3-075- ( ) This public table is i the public domai. It was produced usig APL programs writte by the author, William Kight / Uiv. of New Bruswick / Caada 4 4 B(7, 0.9680) 3 7 7 16 4 11 11± 7.4348 113.565, 18.4348 p =4 0.5568 = 14.73 4 4 1- PX ( 19) - P(113 X ) 0.67 11 103 4 3 B(7, 0.9680) 3 30 3 14.73± 7.43484 117.95, 13.1648 PX ( 117) =0.1654 ( 4 133) 4 0.5568 0.5568 0.5568 PX = 0.1479 P(118 X 4 13) =0.6867 0.6867 0.7 10 0.5568 0.5568 13
SA3-075- ( ) 10 11 14.73± 7.4348 117.95, 13.1648 0.68 0.34 PX ( 117) =0.1654( 4 14) 4 0.5568 4 P X 0.5568 (118 14) 0.3654 PX =0.4867 0.5568 4 =0.48670.16540.313P(15 X 13) =0.68670.313 0.556888 117.95, 13.1648 0.68 0.34 X = K X = K i k = 1 P i= 1 1 S = ( X X) i ( a± b) 11 X i X = 0.54 4 14
SA3-075- ( ) σ p(1 P) 1 S = 11 (1 X) + 103 (0 X ) 0.48386 4 S ( p ± σ ) ( X i ± σ ) ( p± S ) ( Xi ± S ) ( p ± σ ) ( X ± σ ) ( p ± σ ) ( X ± σ ) σ ( p± S ) ( X ± S ) i ( X ± S ) p i 4 B(7, 0.9680) B(4, 0.556888) B(4, 0.556888) i [6, 7] 0.98069843 ( X i ± σ ) 0.67 ( p ± σ ) 0.6867 i - 14 5 6 X (1) X (6) x = 1 X () X (5) X (3) X (4) x = 1 5 8 15 X (1) = 4.8680 X () = 40.699 X (3) = 3.0097X (4) = 34.7698X (5) = 49.998X (6) = 5.8960 X (1) X (6) X (3) X (4) X () X (5) X () X (5) X (1) X (6) X (1) X (6) 15-113 15
SA3-075- ( ) X (1) X (5) X (1) X (5) X (1) X (6) X () X (5) X (1) X () X () X (3) X (3) X (4) X (5) X (6) 3565364 5 10 X () X (3) 36105364 5 30 X (4) 36530364 X () X (3) X (1) X () X (3) X (6) X (5) X (4) X (1) X (6) X () X (5) X (3) X (4) - 4 5 4 37 6-15 4 448 15 4 6 - - 0.556888 6 36 5 16
SA3-075- ( ) 6 36 C C 6 37699 C 545786 1 5 = = 0.431194105 0 6 = = 0.371306035 4 6 6 36 C C C 4 6 194779 545786 1-0.431194105-0.371306035 = 0.19749986 1-0.371306035 = 0.68693965 6 36 1 5 6 4 C 6 1. 91. 9 3. 9 4. http://episte.math.tu.edu.tw/articles/sm/sm_16_06_1/ 5. http://www.roclotto.com.tw 6. Berard W. Lidgre, Statistical Theory, 3 rd ed., Taiwa 1 st ed.,, p.43-48, 1978 7. NIST SEMATECH, Egieerig Statistics Hadbook, 1.3.5.15. Chi-Square Goodess-of-Fit Test, http://www.itl.ist.gov/div898/hadbook/eda/sectio3/eda35.htm 8.Robert V. Hogg Ad Elliot A. Tais, Probability ad Statistical Iferece, 4 th ed., NY, Macmilla Publishig Compay, P.589-P.594,1993 9.William Kight, Calculators for Chi Square Distributio, http://www.math.ub.ca/~kight 091001 09305 3 0.968 1 0 09100 09100 17
SA3-075- ( ) 09100 09100 09100 09100 09100 09100 09100 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 0910 18
SA3-075- ( ) 0910 0910 0910 091049 091051 091053 091055 091057 091059 091061 091063 091065 091067 091069 091071 091073 091075 091077 091079 091081 091083 091085 091087 19
SA3-075- ( ) 091089 091091 34 091093 091095 091097 091099 09001 0 09003 09004 09005 09006 09007 09008 09009 09010 09011 0901 09013 09014 09015 09016 09017 09018 09019 0900 0901 090 0903 0904 0905 0906 0907 0908 0909 09030 09031 0
SA3-075- ( ) 0903 09033 09034 09035 09036 09037 09038 09039 09040 09041 0904 09043 09044 09045 09046 09047 09048 09049 09050 09051 0905 09053 09054 09055 09056 09057 09058 09059 09060 09061 0906 09063 09064 09065 09066 09067 09068 09069 09070 09071 0907 09073 09074 1
SA3-075- ( ) 09075 09076 09077 09078 09079 09080 09081 0908 09083 09084 09085 09086 09087 09088 09089 09090 09091 0909 09093 09094 09095 09096 09097 09098 09099 09100 09101 0910 09103 09104 093001 09300 093003 093004 093005 093006 093007 093008 093009 093010 093011 09301 093013
SA3-075- ( ) 093014 093015 093016 093017 093018 093019 09300 09301 0930 09303 09304 09305 3