SA3-075_成果報告書.PDF

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1 SA ( ) X j 8 X ( j )

2 SA ( )

3 SA ( ) 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

4 SA ( ) 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

5 SA ( ) 1 S = ( X X) i k = 1 σ S 1 S = ( Xi X) 1 k = 1 ES ( ) σ = S 1 (1)=16p= PX ( = K) K= E( X ) = = 8.8 σ = p(1 p) = = 3.96 σ = p(1 p) = ()=16p= PX ( = K) K= E( X ) = = 8 σ = p(1 p) = = 4 σ = p(1 p) = PX ( = K) K E( X ) P K P 5

6 SA ( ) K P(X=K) = p= K P(X=K) = p= (1) () 3 (3) (4)=3p= P(1 X 3) = P(11 X 4) < < = = =

7 SA ( ) K P(X=K) = p= (3) (4) ( C =

8 SA ( ) X, X, X, X, X, X 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 H36 = C6 = d, d3, d4, d5, d6 1 d = d 1, d = d 1, d = d 1, d = d 1, d = d { d, d 3, d 4, d 5, d 6 } 6 X = d + d + d + d + d + d 4 d, d, d, d, d (6) d = d 1, d = d 1, d = d 1, d = d 1, d = d 1, d = d d 1+ d + d 3 + d 4 + d 5 + d 6 31 H31 = C31 = H31 = = = 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} = P( X1 KPX ) ( = K X1 K) = = o X1 X X3X PX ( = K) = P( X KPX ) ( K X KPX ) ( = KX K X K) = = o X, X, X PX ( = K) = =, K {1,,3, L,4} o

9 SA ( ) PX ( = K) = =, K {1,,3, L,4} o PX ( = K) = =, K {1,,3, L,4} o 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 K j j ( j) = K = 4 C6 P(X ) C CC 1 ( K 1)! (4 K)! = ( 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

10 SA ( ) ~ ~ (3) (4) L B(7, ) = p = = = p(1 p) = ( ) = ± , ( P X ) = PX ( 19) = , = , 18 ( P X ) = PX ( 19) = X j X ( j ) - ( ) 10

11 SA ( ) 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 j=1,,3,4,5,6 X j X (1) 37 X () 38 j X ( ) 36 j j i ( ) ( ) (7) : : : : : : : : : : : : : : : : : : : 9103 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 909 : : : : : : : : : : : : : : : : : : : 9061 : : : : : : : : : : : : : : : : : : : 9093 : : : : : : : : : : : : : : : : : : : 9301 ( ) B(7, ) 7 PX ( 5) = PX ( 7 6) = =

12 SA ( ) ± , 13 4 P(109 X ) = PX ( 7 140) = , (8) (5) (8) 15 - X (1) = X () = X (3) = X (4) = X (5) = X (6) = X (5) = (8)091001~ 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 D.F

13 SA ( ) 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, ) ± , p = = PX ( 19) - P(113 X ) B(7, ) ± , PX ( 117) = ( 4 133) PX = P(118 X 4 13) =

14 SA ( ) ± , PX ( 117) =0.1654( 4 14) P X (118 14) PX = = P(15 X 13) = , X = K X = K i k = 1 P i= 1 1 S = ( X X) i ( a± b) 11 X i X =

15 SA ( ) σ p(1 P) 1 S = 11 (1 X) (0 X ) 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, ) B(4, ) B(4, ) i [6, 7] ( X i ± σ ) 0.67 ( p ± σ ) i X (1) X (6) x = 1 X () X (5) X (3) X (4) x = X (1) = X () = X (3) = X (4) = X (5) = X (6) = X (1) X (6) X (3) X (4) X () X (5) X () X (5) X (1) X (6) X (1) X (6)

SA3-075- ( ) X (1) X (5) X (1) X (5) X (1) X (6) X () X (5) X (1) X () X

(4) 36530364 X () X (3) X (1) X () X (3) X (6) X (5) X (4) X (1) X (6) X

16 SA ( ) 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) X () X (3) X (4) 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)

17 SA ( ) 6 36 C C C = = = = C C C = = C Berard W. Lidgre, Statistical Theory, 3 rd ed., Taiwa 1 st ed.,, p.43-48, NIST SEMATECH, Egieerig Statistics Hadbook, Chi-Square Goodess-of-Fit Test, 8.Robert V. Hogg Ad Elliot A. Tais, Probability ad Statistical Iferece, 4 th ed., NY, Macmilla Publishig Compay, P.589-P.594, William Kight, Calculators for Chi Square Distributio,

18 SA ( )

19 SA ( )

20 SA ( )

21 SA ( )

22 SA ( )

23 SA ( )