3978 30866 4 3 43 [] 3 30 4. []
.
. 98
.3 ( ) 06 99 85 84 94 06 3 0 3 9 3 0 4 9 4 88 4 05 5 09 5 8 5 96 6 9 6 97 6 05 7 7 03 7 07 8 07 8 06 8 8 9 9 95 9 0 05 0 06 30 0
.5 80 90 3 90 00 7 00 0 3 0 0 5 0 30 30.6 0 6 0 6 7 7 7 7 8 59 8 54 60 55
X X X + X + = + X N (. ) N X.3 30. = 3 N = N = N N X 06 + 84 + 0 + X = + + 0 30 305 = 30 035. ( ) X X f X f X f + + + k = f + f + + f (. ) X f. 5 k k = 85 3 + 95 7 + 05 3 + 5 5 + 5 X = 3 + 7 + 3 + 5 + 30 = = 03. 67 ( ) 30 k = k = X f f
k Xf = Xf + Xf + + Xk f X = k = k f f = t= X f X f = k + k + + X f f k X f = k (. 3) = f f (. 3) X k f = k f k f = = = = X f k f k N ( X X) = 0 ( X X) f = 0 (. 4) = N = k ( X X ) > ( X X) (. 5) = 0 N = X X N + k =
Σf L + Sm Me = (. 6) f m Σf 30 0 M e = 00 + 0 = 0385. ( ) 3 M0 = L + (. 7) + 3 7 M 0 = 00 + 0 = 04. 9( ) ( 3 7) + ( 3 5) N Mg = X X X N (. 8)
a a a 3 a 4 a N a N N a a a a a (.8) N a a a 3 a N M g = N = a a a a 0 0 N a a N N 0 3 N N M H = N = N (. 9) = X = X N N M H = (. 0) Σf X X X + X + + X ([ a] + ) ([ a] + ) ( [ a ]) Xa = (. ) [ a]
X + X + + X ([ ] + ) ([ ] + ) ( [ ]) = [ ] X( ) + X( 3) + + X( 0) = 9. 0 + 9. + + 9. 30 = 9 = 9. 6 X ( ) + X( ) + X( ) X0 = = 96. 5 X 0 = X a = X( 6) 5 X = = X ( 6) = 95.
N ( X X) = σ = ( 3. ) N σ N ( X X) = σ = ( 4. ) N ( x x) = S = (. 5) σ ( x x) = S = (. 6) k ( x x) f σ = = k ( 7. ) f =
k ( X X) f = S = k ( 8. ) f = N σ = ( X ) X = N N = + N = = = ( X X X + X X ) N N N N = = = N N = N = = N X = ( X X X NX ) ( X X X ) = ( X) (. 9) N k X f σ = = k ( X) (. 0) f = ( X X) σ = = = 0. 8( ) N N
.8 Xf X f X f 80 90 90 00 00 0 0 0 0 30 85 95 05 5 5 3 7 3 5 5 665 365 575 50 675 6375 4335 665 350 30 30 35550 X f Xf = = σ = k ( k ) f f = = 35550 30 = ( ) 30 30 = 04. ( ) k k
N + 30 + = = 55.
.9 98 98 98 03885 744739 9 003937078 4780450 5400885 930687 59990 77644 3640960 53005875 997330 59389 855997 97479 355387 357693 89393 560053 890443 3665546 95696 859748 3895706 6054 3895578 38884603 30868 4966574 587359 4380 338487 870749 7449054 537867
φ φ Ω Ω 6
P A A m ( ) = = ( 3. ) m 3. m m f(a)= 4040 048 0.5069 K. 000 609 0.506 K. 4000 0 0.5005
5 5 5 P( A ) = P( A ) ( 3. ) = =
φ φ φ φ 3 C3 C7 3 C3 C7 P( B) = 4 =, P( B) = 4 = C 0 C 30 P( B) = P( B + B ) = P( B ) + P( B ) 0 3 = + = 0 30 3 φ A A A A 0
A φ B P( A) = P( B) = P( B) = = 3 3 0 4 3 C3 C7 C3 C7 3 P( A) = 4 + 4 = + = C C 6 6 3 0 0 A φ 5 0 5 7 P( AB) P( AB) = ( 36. ) P( B)
3 P( A ) =, P( A A ) = 0 9 P( A A ) = 3 P( A ) P ( A A ) = 0 9 5 P ( AB ) P( B) P ( AB ) P( A) 3 3 9 P( AA ) = P( A ) P( A ) = = 0 0 00 P(B) = P(A B) + + P(A B) k k = P(A )P(BA ) (3.0) =
P( A P A B ) P( BA) ( ) = k, =, k ( 3. ) P( A ) P( BA ) = P( AB) P( A B) = P( B) P( A ) P( BA ) = P( A B) + + P( A B) P( A ) P( B A) = P( A ) P( BA ) + + P( A ) P( BA ) P( A ) P( BA ) = k P( A ) P( B A ) = P( A) P( BA) P( AB) = 3 P( A ) P( BA ) = 0. 30 0. 03 = 0. 0 0. 04 + 0. 30 003. + 050. 0. 0 0. 009 = 0. 07 = 3 033. k k k
ξ C8 8 P( X = 0) = = C 45 0 CC8 P( X = ) = = C 0 6 45 C P( X = ) = = C 45 0 5 P( X = ) = C p ( p), = 0,,, 5 5 X = 0
p =,, k f( x) = ( 3. ) 0 ( ) f( x ) = p = ( ) = = 8 pl = P( X = 0) = 45 6 p = P( X = ) = 45 p3 = P( X = ) = 45 3. X X=x x =0 x = x = P(X=x )=p 8 45 6 45 45
x P( x X x ) = f ( x) dx x, x (, + ) ( 33. ) x ()f(x) 0 () + - f( x) dx = F( x) = P( X < x ) = f( x ) x F( x) = P( X < x) = f ( x ) dx k k =
() 0 F(x) ( F(x) ) () F(+ ) = x m + p( X < x) = m F( ) = x + p( X < x) = 0 ( ) x = a, x = b, 3 b a f ( x ) dx = F ( b ) F ( a ) f( x ) = F( b) F( a) a x < b k 3.3 X=x X p =P(X=x ) F(x )=P(X<x ) 0 8 0 45 6 45 8 45 45 44 45 3 0
X = 0 P( X x) p x = = = p x = ( 35 0. ) x x C CN M P( X = x) = x = 0,, m(, M) ( 36. ) C N x x x P( X = x) = C p ( p) x = 0,,, ( 37. ) N λ x λ λ P( X = x) = e x ( 38. ) x = 0,,, λ > 0 λ 4 P( X = ) = e 4 = 05.
( x µ ) f( x) = e < x < + σ > 0 ( 39. ) σ π σ µ σ µ σ µ σ µ µ ± µσ σ σ σ µ µ σµ σ µσµσ µσµσ µ σ X µ z = ( 3. 0) σ z ϕ( z) = e ( 3. ) π z ΦΦ z z t Φ( z) = ϕ( z) dz = e dt ( 3. ) π Φ Φ
7 0 ( ) P ( X < 7) = F( 7) = φ( ) 3 = φ( ) = 0587. 5 0 ( ) P ( X 5) = F( 5) = φ( ) 3 φ( 67. ) = 0. 955 x 0 ( 3) P ( X < x) = F( x) = φ( ) = 00. 3 Z = x 0 =. 8 x = 66. 3 µσ σ λt λe f t t 0, ( ) = λ > 0 ( 3. 3) 0 t < 0 λ λ 05. t 05. 4t P( T 05. ) = 0 λe λ dt = 0 4e dt 4t 05. = e 0 = e + = 08647.
f x b a a < x < b ( ) = ( 3. 4) 0 000 < r < 500 f( r) = 500 00 0 300 P( 00 < R < 300) = 00 dr = 0. 500
F( x, y) = P( X = a, Y = b j) ( 36. ) a < xb j < y x y F(x,y) = - f ( u, v) dudv - ( 37. ) F( x, y) f( x, y) = ( 38. ) x y 4 3.4 X,Y X=x Y=y P(x) 0 0 4 0 4 4 4 4 0 4 4 P(y)
P( X = a ) = P( X = a, Y = b ) = p j j j j P( Y = b ) = P( X = a, Y = b ) = p j j j
E(X) = x p ( 39. ) D( X) = ( x E( X)) p ( 330. ) E( X) = + xf( x) dx ( 33. ) D( X) = + [ x E( X)] f( x) dx ( 33. ) f Σf f Σf
3.5 x x P( X = x) = p ( p) p pq x = 0, 0 < p < x CM C P( X = x) = C N x N x = 0,, m(, M) P( X = x) = C p ( p) x x x x = 0 0 < p < x λ P( X = x) = e x x = 0 λ > 0 ( x µ ) f( x) = e σ πσ < µ <, σ > 0 f( t) λe λt t 0, λ > 0 f( x) = b a @<x<b, λ a p p λ pq N N pq λ µ σ λ + b λ ( b a) ρ xy = Cov( X, Y) D( X) D( Y)
(/) 300 400 400 500 500 600 600 700 700 800 800 900 900 000 () 36 64 35 94 683 8 4
X µσ x = x4 µ σ = x = x µ E( x) = E( x Ex ) = = = µ = = σ σ D( x) = D( x D x ) = ( ) = = = = x (, ) µ σ x + x + + x x x e x > 0 f( x) = Γ( ) ( 4. ) 0 x 0 Γ( ) Γ Γ β Γ x a x ( ) f( x) dx = a a x a
()x x x x x ~ x, x ~ x, ( x x ) ~ x + + x µσ x = x S = x x ( ) = = x ~ N( µ, σ ) ( x x) = ( ) S = ~ x σ σ x = ( x x) ~ x X T = Y + Γ( ) t f( t) = ( + ) +, < t < ( 4. ) πγ( ) t f( t) e π E( t) = 0 D( t) = ( > )
t f t dt = a( ) ( ) a X / F = Y / + Γ( ) + ( )( z) ( + z) f( z) = Γ( ) Γ( ) 0 E( z) = ( > ) ( + ) D( z) = ( > 4) ( ) ( 4) F f z dz = a a (, )` ( ) F F Y / X / F ( + ) a = F a (, ) σ = σ F S = ~ F(, ) S
θ σ σ σ θ θ θ θ θ θ µ σ µ σ µσ x x σ µ x = µ x = µ + σ = =
µσ µ = x σ = x x = ( x x) ( 4. 4) = = σ σ σ = ( x x) (4. 5) = θµ σ c = σ µ µσ θ µ µ k µ k = x f( xθ ) dx k =,, s ( 4. 6) θ k µ k = x f ( xθ,, θ m ) dx = h( θ,, θ m ) k =,, m ( 4. 7) θ θ µ µ θ θ µ µ θ θ j = f j( µ,, µ m ) =,,, m ( 48. ) k x µ θ = θ j θ j θ θ θ θ g( θ) = g( θ,, θ m ) µ σ c = σ µ µσ c = σ / µ µ µ µσ µ µ µ σ µ µ µ σ µ µ µ µ
µ = x, σ = x x = ( x x) = = µ σ c = σ / µ c = ( x x) / x = θ θ θ θ θ θ θ θ L( θ x,, x ) = f( x θ) ( 4. 9) = θ θ θ θ x x x x x00 x00 L( p x x ) = p ( p) p ( p) p ( p) 00 = p x ( p) x 00 = 00 00 = 0 90 = p ( p) p 9 90 0 89 L( p x x ) = 0p ( p) 90p ( p) = 0 0 p = = 0. 00 µ σ µ σ ( x µ ) σ L( µ, σ x x) = ( e ) = σ π ( x µ ) σ = = ( ) e σ π
l L( µ σ x x ) = l π l σ ( x σ = µ ) ll = ( x µ ) = 0 µ σ = ll = + ( x µ ) 4 = 0 σ σ = σ µ = x = x σ = = ( x x) = µσ µ = xσ = ( x x) = θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ
θ θ θ θ x ~ N(, ) P x θ ( ) = 0. 9545 σ P( x ( 4. ) θ 3) = 0. 9973 σ σ x θ 3 θ σ
σ σ σ x 3 x + 3 x 3 x σ θ θ [, + 3 ] θ θ P( θ θ θ) = a θ θ θ θ x x ~ N(, ) θ σ x ~ N(, ) σ ( x θ 3 ) θ x σ σ σ σ 3, 3 0 99 θ 3 θ 3 x + ]., = x, = x + θ σ x Z = x µ N σ ~ ( 0 ) ( 4. ) x µ P( Z a Z a ) = a σ σ σ P( x Z a µ x + Z a ) = a σ
x S P( x Z x Z S a µ + a ) = 0. 95.. P( 3. 3. 96 0 98 µ 3. 3 +. 96 0 98 ) = 0. 95 400 400 x t = µ ~ t (. ) S 43 µ [ x t a S, ] x + t a S x x t 0. 05 5 S 009. x t a =. 705 3. =. 690 6 S 009. x + t a =. 705 + 3. =. 70 6 p
E( ) p = E( x ) = p D p D x ( ) ( ) D ( x = = ) = p ( p ) p ~ N( p, p( p)) p p p p Z = N p ( p ) ~ ( 0 ) ( 44. ) p ( p ) p ( p ) [ p Z a, p + Za ] ( 45. ) x 4 p = = = 00 Za = 96. 00 ( 44. ) θ = p Z 004. 096. = 004. 96. 00 θ = p + Z a a p ( p ) p ( p ) = 000. 004. 096. = 004. + 96. = 0078. 00 x x σ σ N( µ ) N( µ ) x x E( x x ) = µ µ σ σ D( x x ) = +
( x x ) ( µ µ ) Z = ( 4. 6) σ σ + σ σ S S σσ ( x x ) ( µ µ ) Z = ( 47. ) S S + µ µ S S S S [ x x Z a + x x + Z a + ] ( 48. ) x x [ 650 480 96. 0 06 650 480 96. 0 06 + + ] 50 50 50 50 σ σ σ = σ ( x x ) ( µ µ ) t = t + S + S + ( ( ) ( ) ( ) ~ (. ) 4 9 ) + 4. 0 560 590 560 570 580 570 600 550 570 550 60 570 650 600 630 580 570 600 600 580
x = 570 ( ) S = ( x x ) = 400 = x = 600( ) S = ( x x ) = 6400 = t a 8 009 ( ) =. µ µ ( ) S + ( ) S θ = x x t a ( + ) + 8800 0 = 600 570. 009 8 00 = 30 0. 8 = 9. µ µ ( ) S + ( ) S θ = x x + t a ( + ) + 8800 0 = 600 570 +. 009 8 00 = 30 + 08. = 508. + + σ σ ( ) S x = ~ x ( ) x σ a
a a a { ( ) } P { x x } ( ) P x x a = = a P x ( ) ( ) S σ x a ( ) a = P S ( ) ( ) S σ = a ( 4. 0) x a ( ) x a ( ) x ( ) = x ( 39) = 580. a x ( ) = x ( 39) = 3. 654 a 0. 05 0. 975 σ [ ( ) ( ), ( ) S S ( ) ] [ 39300 39300 =, x x 580. 3. 654 a a = [ 6039. 9, 3. 654] µ σ µ σ µ µ σ σ S S σ σ ( ) S ( ) S σ σ ] ( ) S S ( ) S σ F = ( ) S / ( ) σ / ( ) S / σ σ / σ = = ( 4. ) S / σ S / S a
a P F Fa ( =, ) a P F F a ( =, ) P F a ( F Fa a =, ) (, ) ( 4. ) S σ S P F a (, ) Fa (, ) S S σ = a µ σ µ σ σ σ a a a = 0. 90= 0. 05 = 095. F0. 05 ( 4, 4) =. 35 F0. 95 ( 4, 4) = = F ( 4, 4) 3. 0. 05 S 6. 38 = = 4. S 55. σ / σ 4 [.,( 4. )( 3. )] = [ 058.,. 64]. 35
4. ( ) σ x µ Z = N σ ~ ( 0, ) [ x Z σ, x Z a + µ x µ Z = ~ N( 0, ) [ x Z, σ S x Z a + σ t x µ = ~ t ( ) [ x t a ( ) S ( x x ) ( µ µ ) Z = ~ N ( 0, ) σ σ σ σ + [x x Z µ -µ ( x x ) ( µ µ ) Z = ~ N ( 0, ) S S [x x Z + a a σ S
µ σ σ σ P( x Za µ x + Za ) = a σ [ x Z, ] x Z σ a + a µ µ µ µ µ µ µ σ [ x Z, ] x Z σ a + a x µ 0 Z = σ Z Z Z Z Z a a a
θθ θ θ µ µ
x = 50 S = 650. t ( 0 ) = t ( 9) =. 6 a 0. 05 x 500 50 500 t = = = 0. 97 S / 650. / 0 t a µ µ µ µ x = 375. x = 8. 67 ( ) S =. 5 ( ) S = 66. 64 = = t a x x t = ( ) S + ( ) S + + 3. 75 8. 67 =. 5 + 66. 64 4 + 44 =. 646 t a σ σ 0 µ σ
σσ 0 σ σ 0 x = ( -) S σ x ( ) x ( ) a x ( ) x x ( ) a a σ σ S (. ) x = ( ) = 5 = 4594. σ (. ) x ( 5) = 6. 6, x ( 5) = 7. 488 0. 975 0. 05 0 x = 4594. > x0. 05 = 7. 488 σ = σ µ σ µ σ σ σ σ σ S / S S F = = ~ F(, ) S / σ S F (, ) F (, ) a F (, ) F F (, ) a a a a
= 8, x = 9. 93, S = 0. 6 = 7, x = 0. 00, S = 0397. S 06. F = = = 0544. S 0397. 4.3 ( ) H H µ=µ H µ µ Z Z H µ µ x µ 0 Z -Z σ Z = ~ N( 0 ) H µ<µ σ / H µ µ Z Z H µ>µ H µ=µ H µ µ Z Z ( ) H µ µ x Z = µ 0 Z -Z ~ N( 0 ) H µ<µ σ / H µ µ Z Z H µ>µ
( ) H H µ=µ H µ µ t t H µ µ x µ σ t = 0 t -ta ~ t( ) H µ<µ S / H µ µ t ta H µ>µ H µ =µ H µ µ Z Z H µ µ ( x x ) ( µ µ ) Z = ~ N ( 0, ) H µ <µ σ σ + H µ µ H µ >µ Z -Z Z Z ( ) H H µ =µ H µ µ Z Z ( ) H µ µ ( x x) ( µ µ ) Z -Z Z = N H µ <µ ~ ( 0, ) S S + H µ µ Z Z H µ >µ H µ =µ H µ µ t t H µ µ t = H µ <µ H µ µ H µ >µ ( x x ) ( µ µ ) S + S + ( ( ) ( ) ) ( ) + ~ t( + ) t -ta t ta
( ) H H σ = σ 0 H σ σ 0 H σ σ 0 H σ < σ 0 H σ σ 0 H σ > σ 0 H σ = σ H σ σ H σ σ H σ < σ H σ σ H σ > σ x F ( ) S = σ 0 ~ x ( ) S = ~ F (, ) S x ( ) x x a x x ( a x x ( F (, ) a F ( a a F F (, a F F ( a = = = 0. 95 F. ( 6, 7) 5. 0 05
θx θ, 0 < x < f ( x) = 0, x f ( x) = e σ < x < σ σ ( ) µ = x + x 3 3 3 ( ) µ = x + x 4 4 ( 3) µ 3 = x + x σ σ σ x S x x x x µ σ x x x
x µ σ µ σ σ σ µ µ
5. A A A 63 84 06 76 98 9 70 79 8 85 90 4
µ σ µ σ H µ = µ = = µ 0 r = = x = xj ( 5. ) r x = xj = j= r = j= = r x ( 5. ) x x r ( xj x )( x j x) = 0 = j= Q = ( x x) = ( x x ) + ( x x) = Q + Q ( 53. ) r Q = ( x x ) = r j= j r = r j= j j = j= = Q = ( x x) ( 54. ) = r
µ x Q / r F = ~ F( r, r) ( 55. ) Q / r µ µ µ µ µ
µ µ µ 5. F r Q x x r- S = ( ) =Q /r- S / S = r Q x x = ( j ) = j= -r S =Q /-r r Q = ( x j x ) = j= - S =Q/- 5.3 F 668.7 334.09 0.93 098.50 9.06 3766.67
5.4 ζ j A A A x x x x x x 3 x x x 4 x x x µ ε µ ε µ ε ε σ µ r µ = µ = µ µ µ ε µ r a = 0 = µ µ µ
x µ r E( x) = E ( x ) r = µ = µ = x µ a = x x ( =,,, r) = E( a ) = E( x x) = µ µ = a ( =,,, r) a a = x x ( 58. ) µ Se Se [ x Fa (, r), x + Fa (, r)] ( 59. ) S = S = Q / r e a = x x = 735. 90. 33 = 6. 83 a = x x = 87. 75 90. 33 =. 58 a 3 = x3 x =. 9. 75 90. 33 = 9. 4 a 3
x = 09. 75 3 0985. Se = =. 06 9 F (, 9) = 5. 0. 05 Se x F 3 ± 0. 05( 9, ) = 09. 75±. 5 5.5 00kg A A A 3 4 5 03 73 6 07 89 98 8 85 83 6 97 5.6 F 304 65 4.9 9 9 3.4 496 x = 03x = x 3 = 86 x S e = 3. 4
Se x ± F0. 05 ( 9, ) = ± 3. 4 5. 4 = ± 3. 0
5.7 B B B B A A x x x x A x x x x Μ Μ Μ Μ Μ A x x x x x. x. x. x. x x
x x j S = xj =,,, r S j= r = xj j = s r,,, = r x = rs = S j= x = x + a + β + e ( 50. ) = r j = s a β j j j j r a = 0 β = 0 = j= S a = x. x = r β j = x. x j = s j j x j σ β β β r S Q = ( x x) = r j= S j = [( x x) + ( x x ) + ( x x x + x )] = j=.. j j.. j r S r S r S.. j j.. j = j= = j= = j= = ( x x) + ( x x) + ( x x x + x ) r S = S ( x x ) + r ( x x) + ( x x x + x).. j j.. j = j= = j= r S = Q + Q + Q (. ) 3 5
Q = S ( x x) = Q = r ( x x) r r S j= S Q = ( x x x + x) 3 = j=.. j j.. j F = S Q / r A = ( 5. ) S Q / ( r )( s ) 3 3 S Q / r FB = = ( 53. ) S3 Q3 / ( r )( s ) α α α α α β β β β β
r r- Q = S ( x. x ) S Q r x j x = (. ) r j= S = Q3 = ( xj x. x. j + x) = j= r S Q = ( xj x) = j= s- (r-)(s-) rs- S = Q / r F S / S = A = B S = Q / s F S / S S3 = Q3 / ( r )( s ) 3 3 5.9 ( ) x. B B B B B A 6.5.8 3.6 3.7 7.6 4.64 A 4. 7. 0.8 8.9.6 0.7 A 3.4 9.4 7. 8.6 7.5 9. A.4.5.7.3.8.4 A 6. 4.8 4.9 4.6 5. 5.4 x. j 8.54 4.9 5.64 5.6 7.4 6.37 SS = ( x x) = x CT ( 54. ) T r s j = j= = j= r s j r r S SS A = S ( x. x) = ( xj) CT ( 55. ) = S = j= S S r SSB = r ( x. j x) = ( xj ) CT ( 56. ) j= r j= = SS = ( x x. x. + x) = j= = SS SS SS r s CT = ( xj ) rs = j= e r s j j T A B ( 57. )
CT = ( 59. 3) = 0506. 5 SS = x CT T r S = j= j = 344. 5 05. 06 = 39. 9 S S SS A = ( xj ) CT 5 = j= = 6. 8 05. 06 = 47. S S SSB = ( xj ) CT 5 j= = = 057. 56 05. 06 = 4. 50 SS = SS SS SS e T A B = 39. 6 47. 4. 50 = 39. 47 S S =0.63 S 3 =.47
5. ( %) B ( ) B ( 5%) B ( 8%) A 59 70 66 A 63 74 70 A 6 66 7 β α α α β β β CT = ( 600) = 40000 9 SS = 4000 40000 = 00 T SS A = ( 3805 + 4849 + 3904) 40000 = 6 3 SSB = ( 33489 + 4400 + 4849) 40000 = 46 3 S S S 3 =.86 S =Q /=73 S / S 3 =0.43 S 3 =Q /4=7 α
δ = S ' F f e a (, ' e ) (. ) f ' 58 e e ' S e f ' e e = + α ' S = SS + SS = 54 e e A ' f = 4 + = 6 9 e = = 3 + F0. 05 ( 6, ) = 599. e x. j ±δ 54 599. δ = = 4. 4 3 6 ±
5.3 B B B B A x,,x x,,x x,,x A x,x x,,x x,,x A Μ Μ Μ Μ A x,x x,x x,,x x j x = x + e ( 5. 0) = r j = s k = l xj = l l k = x jk jk j jk x j σ σ e x j r s r s l x = xj = xjk rs = j= rsl = j= k= s x. = xj( = r) s j= r x. j = xj ( j = s) r = α x x β β β x x
α = 0 β = 0 x = x + ( x. x) + ( x. x) + ( x x. x. + x) = x + α + β + ( αβ) ( αβ) = x x. x. + x j j j = j= ( 5. 0) x = x + α + β + ( αβ) + e ( 5. ) (5. ) r j j j j j j jk j j jk ( αβ) = ( x x) ( x. x) ( x. x) s j j j = ( x x) α β j j j x x s ( αβ) j = ( αβ) j = 0 j= r = α α α β β β αβ Q = ( x x ) = [( x. x ) + ( x. x) + ( x x. x. + x ) + ( x x )] = Q + Q + Q + Q ( 5. ) Q = sl ( x. x) = Q = rl ( x. x) r s j= j r s = j= k = r s = j= k = l l jk 3 4 j j j jk j
Q = l ( x x. x. + x) 3 = j= Q = ( x x ) 4 r r s s = j= j= l j j jk j S Q / r FA = = ( 53. ) S Q / rs( l ) 4 4 S Q / s FB = = ( 53. ) S Q / rs( l ) 4 4 / ( )( ) F = S (. ) S = Q r s 3 3 AB 53 4 Q4 / rs( l ) r Q = sl ( x. x) r- = s Q = rl ( x. x) s- r s j= j Q = l ( x x. x. + x) (r-)(s-) 3 = j= r s j j Q = ( x x ) rs(l-) 4 = j= j= r s l jk j Q = ( x x ) rsl- = j= k = l jk 4 S = Q / r F S / S = A = B = AB 3 S = Q / s F S / S S3 = Q3 / ( r )( s ) F S / S S = Q / rs( l ) 4 4 4 4
5.5 ( ) B I II III 3.0 5.00 6.0 7.30 8.00 7.00 4.40 5.60 3.70 4.30 4.50 5.70 A 4.00 3.60 6.30 7.0 7.0 6.0 α α α β β β αβ SS = ( x x) T r = j= k= r = x CT ( 56. ) SS = sl ( x. x) A r s l = ( x jk ) CT ( 57. ) sl = j= k = SS = rl ( x. x) B s s = j= k = r = s j= l l j jk jk s r l = ( x jk ) CT ( 58. ) sl j= = k = e r s SS = ( x x ) = j= k= l jk j r s l r s l = xjk [ ( xjk ) ] ( 59. ) = j= k = = j= l k = SS = l ( x x. x. + x) A B r s = j= j j r s l r s l s r l = [ ( xjk ) ] ( xjk ) ( xjk ) + CT = j= l k = sl = j= k = rl j= = k= = SSl SS A SS B SSe ( 530. ) r s l CT = ( xjk) rsl = j= k=
5.6 A Q =SS =6.4 3-= B Q =SS =4.04 3-= A B Q =SS =0.9 (3-)(3-)=4 Q =SS =5.36 3 3 (-)=9 Q=SS =36.56 3 3 -=7 F A S =3. F =5.4 B S F =7.0 =.79 A B S 3 F =.73 =4.58 S 4 =0.5956
367 3 94 6 66 9 / 37 737 59 44 6 63 503 6 3 48 45 06 0 493 97 08 46 499 33 99 3 980 98 98 983 984 985 90. 46 350.67 43.63 59.48 664.6 775.08 77. 9 97.77 36. 4.69 504.64 564.55 75. 78 04.4 35.73 98.07 345.00 385.3 55. 78 79.53 7.8 75.78 305.50 358.3 8. 3 5.4 73.03 94.0 336. 360.4
Σ( x x)( y y) r = ( 6. ) Σ( x x) Σ ( y y) xy Σxy xy r = (6.) Σx x Σ y y r t = ( 6. 3) r
r 0. 98 4 t = = = 7. 79 r 0. 98
α βε α β ε ε σ σ = j Cov( ε, ε j ) = 0 j =,,,, j =,,, Σe = m Y
Σe Σxy ΣxΣ y b = Σx ( Σx) ( 68. ) a = y bx t = b b S ( 6. 9 ) b S = S / Σ( x x) S b y y S = Σ( y y ) / = Σe / ( ( 65. )) y α α t.
Σ(y - y) / F = (6.0) Σ(y- y) / y ε ε d = (e - e ) (6.) = - Y y y y y y y y y y y y y y
Σ( y y) = Σ( y y) + Σ( y y ) + Σ( y y)( y y ) Σ( y y)( y y ) = 0 Σ( y y) = Σ( y y) + Σ( y y ) ( 63. ) y y y y SSR Σ( y y) r = = ( 64. ) SST Σ( y y) r = ± r Y Σ( y y ) Σe Sy = = Σ(y - y ) Σe S y = = ( 6. 5) S y (6.8) b
6. 97 6.5 55.7 980 46.8 330.0 973 0.8 63.3 98 49.6 340. 974 4.4 75.4 98 53.0 350.7 975 5.5 78.3 983 58. 367.3 976 3.7 96.7 984 63. 38.3 977 36. 309.3 985 70.5 406.5 978 38.7 35.8 986 78. 430.8 979 40. 38.8 987 85.9 45.5 Y Σe 7. 57 Sy = = =. 55 4 Sb = Sy / Σ( x x) = 0. 0055 α SSR = Σ(y - y) = 573. 78 SSE = Σ( y y ) = 7. 57 573. 78 / F = = 4. 53 7. 57 / 4 α α α α
SSR r = 573 78 SST =. 59 35 = 0.. 9966 S y σ Y = a + bx (6.6) Y 0 Y 0 Y 0 α βε Y 0 Y 0 σ ( x0 x) + Σ( x x) ) Y ( x 0 x) ± t a/ σ + + Σ( x x) 0 x Y 0 S y Y 0 ± Y 0 ±
Y 0 ± Y 6. * ( ) ( ) ( ) ( ) 964 698 097 973 765 86 965 87 84 974 76 3 966 988 50 975 960 003 967 807 394 976 90 435 968 738 303 977 03 65 969 05 555 978 446 948 970 36 97 979 736 355 97 539 05 980 85 337 97 56 * 975 S y y
y 6.3 ( ) ( ) ( ) 98 353.7 3006.83 74.33 37.33 98 368.3 36.86 897.36 348.36 983 3848.0 335.9 3060.4 359.4 984 40.7 3496.30 330.80 376.80 985 40.3 3674.37 3408.87 3939.87 Y = ax b b Y = a + X Y a b = + X Y = ae bx Y = ae x Y = a + b l X Y = x a + be b
b Y = a + X X' = X Y = 50. 7848 + 355457. 05 X 6.4 Y =f (Y) X f (X) Y =ax Y =ly X =lx Y =a+bx a=a b=b b Y =a+bx a=a b=b Y =a+ X Y =Y X = X b Y =a+bx a=a b=b Y =a+ X Y = Y X = X Y =ab Y =ly X =X Y =la+bx a=a b=b b Y =+labx a=e b=b X Y = ae Y =ly X = X Y =a+blx Y =Y X =lx Y =+abx a=a b=b Y =+abx a=a b=b a + be X Y = Y X =e Y =
6.5
β β β β ε β β β β β β Y = b 0 + bx + bx + + bkx k + e (6.8) Y β β β Q = Σ( y y ) y y b0 e y b e Y = B = e = Μ Μ Μ y b k e x x xk x x x k X = Μ Μ Μ Μ x x xk e=e'e=(y-xb)'(y-xb)=(y'-b'x')(y-xb)=y'y-b'x'y-y'xb+b'x'xb=y'y-b'x'y+b'xb B X Y Y XB (B X Y) =Y XB, Y XB=B X Y
β β β β Σ(y - y) / k F = (6.3) Σ(y- y) / k Σ( y y) Σ( y y ) R = = ( 64. ) Σ( y y) Σ( y y) X XB=X Y X X X=0.5X
Σ( y y ) / k R = ( 6. 5) Σ( y y) / R R R = ( R ) ( 6. 6) k Y = 7. 3973+ 0. 0503X + 0. 55X 0. 0040X 0. 43X 3 4 (. 400)( 9004. )( 06. )( 9. 5454) t0.05/=
R
( ) ( /) ( /) ( /).8 6.7 8 4.8 9.8.8 6.9 9 4.9 0.6 3 3.0 7. 0 5. 0.7 4.9 7.3 5.4. 5 3.4 8.4 5.5.8 6 3.9 8.8 3 6.. 7 4.0 9. 4 7.0.4 (%) (%) ( ) ( ) 6.6 6 7 6.3 5 0.4 7 6.4 3 8 8.5 8 3 6. 4 3.0 9 3 6.5 5 4 8. 0 7 6.8
3 (%) (%) (%) (%) 3 5 8 48 6 35 5 3 7 9 7 8 4 95 30 8 6 4
a = a + a + + a = a Σ (7.) a
a a + a + + a + a - (7.) - 7. ( ) 4 5 6 7 040 035 045 058 040 + 035+ 045+ 058 a = = 043( ) 4 a + a a + a 3 a + a ( ) f + ( ) f + + ( ) f a = ( 7. 3) f = 7. 3 3 5 3 5. 3.6 3.0 9 30 3 4. 5.6 5 (. + 36. 36 ) (. + 30 3+. ) + 30 (. + 4. 4 ) 4 (. + 56 +. ) 3 a = = 4. 075
a a, a a,, a, a - (7.4) a a 0 0 0 0 a a, a a, a a,, a, a 3 - a a 0 - - (7.5) 7.3 984 985 986 987 988 677 73 757 779 89 (970 ) (%) 08. 8.8 5.07 0.97 (%) 08. 03.4 0.9 05.3 a a a a 3 a = ( 7. 6) a a a a a 0 0
x x = x x = x (7.7) x Π x x = a / a 0 (7.8) x = / a a 4 = 08%. 03. 4% 0. 9% 053%. = 04. 88% ( 78. ) x 4 = a / a = 89 / 677 = 04. 88% 0 0 x x x x a x + x + x 3 + + x = = a 0 ( 7. 9) x
= - = = = =
( Y + Y + Y3) 3 ( Y + Y3 + Y4 ) 3 ( Y3 + Y4 + Y5 ) 3
' Y t Y ' t Y ' Y Y Y 3 Y ' ` = ( + + + 4 ) ( Y + Y ) 4 Y ' = ( Y + Y 3 + Y 4 + Y 5 ) 4 Y ' 3 = ( Y 3 + Y 4 + Y 5 + Y 6 ) 4 Y ' 4 = ( Y 4 + Y 5 + Y 6 + Y 7 ) 4 Y ' 5 = ( Y 5 + Y 6 + Y 7 + Y 8 ) 4 Y ' 6 = ( Y 6 + Y 7 + Y 8 + Y 9 ) 4 ' ` ( Y + Y3) ( Y + Y ) ' ` 3 4 ' ` ( Y4 + Y5 ) ' ` ( Y5 + Y6 ) ( Y + Y ) ' ` 6 7 Y ' 7 = ( Y 7 + Y 8 + Y 9 + Y 0 ) 4
Y t = 950. 3939 + 46. 77t Y t Y t Yt L Yt = f( t) + ae 7.7 ( ) t t ( ) Y t 975.0 0.09074 976 7.80 0.0568 977 3 7.85 0.0359 978 4 4.08 0.0376 =0.0659 979 5 56.07 0.0783 980 6 69.45 0.07440 98 7 80.05 0.049 98 8 89.98 0.0 =0.05583 983 9 94.06 0.0063 984 0 98.3 0.009 985 98.7 0.003 986 0.08 0.00989 =0.04084
L Y t = + bt ae D = S S = 05076. D = S S = 0. 0499 3 b = (l D l D) = 0577. L = = 0. 093 D S D D L D a = = 4. 897 C D D C e b e b ( ) = b = 539. e 0. 093 Yt =. t + 4. 897e 0577 ( ) f t = (7.)
Yt = ft ( 73. ) V t f f + f+ T + + f ( m ) T+ = =,,, T ( 74. ) m f f = ( T f + f + + f r ) f ' ' f = f =,,, T ( 7. 5) f
7.0 (%) (%) 95.37 7 96.84 83.74 8 97.03 3 0.3 9 0.9 4 0.99 0 99.68 5 04.38 0. 6 08.3 05.33 MA T C = = C T T Tl T 7.9
k ( Yt Yt )( Yt + k Yt ) t= rk = ( Y Y) t= t ( 76. ) ρ ρ / ± t φ φ φ
δ = E( Y φ Y ) t k k j= kj t j = r Z φ γ + φ φ γ 0 k kj j j= j= kj k j δ δ φ φ kj ρ ρk φ k ρ ρ ρ k φ k ρ = Μ Μ φ kk ρ k ρk ρ k φ ρ φ r k = k Tk φ k ; T j k j φkk = j= k =, 3, ( 77. ) k φ k ; r j j j= φ φ φ φ φ 7. k 3 4 5 6 7 8 r 0.84 0.683 0.584 0.55 0.457 0.47 0.405 0.386 7 (k (k=e(yt,yt-k)
φ = r = 0. 84 r φr 0. 683 ( 0. 84) φ = = φ r ( 0. 84) = 0. 083 φ = φ φ φ = 0. 84 ( 0. 083)( 0. 84) = 0. 9 r3 φr φr φ33 = φ r φ r 0. 584 ( 0. 9)( 0. 683) + ( 0. 083)( 0. 84) = ( 0. 9)( 0. 84) ( 0. 083)( 0. 683) φ φ φ φ µ γ µ µ τ µ τ µ (k k (k Yt Yt+k
Y = ( Y ) t = ( Y Y ) t t = Y t t = Yt Yt + Yt 4 D W = Y t > Ds s s B B Y = Y D s D W = Y = ( B ) Y t t t s s t t s t t Y t
φ φ φ φ φ φ φ θ θ θ φ φ φ θ θ θ φ θ φ θ φ φ φ θ θ θ φ φ φ φ θ θ θ θ φ θ φ θ φ( B) d Y = θ( B) e t t φ θ s φ p( B) ΦP ( B )( B) Yt = ( θb) e t
s s s ps s s s Φ ( B ) = Φ B Φ B Φ B, Θ ( B ) = Θ ( B ) Θ ( B ) p Θ QS Q ( B ) p Q 4 4 ( φ B)( Φ B )( B)( B ) Y 4 = ( θ B)( Θ B ) e t t ϕ
m k k= Q = r ( e) ( 7. 4) x a x a x a φ φ φ ϕ φ φ ϕ θ θ ϕ θ θ θ Φ θ θ
Θ Φ Φ Θ Θ φ θ φ
p I = Σ Σp 7.3 0 / 977 978 0.0 0.3 0.0 0.4 0.5 0.6 0.60 0.68 p I = Σ 87 Σp = 0. 68 0 60 = 05%. 77 0. 3 + 0. 4 + 0. 3 I = =. 053 0. 0 + 0. 5 + 0. 30 p Σ 0 p I =
p Σ 87 0. 3 0. 4 06. p + + 77 I = = 0. 0 05. 05. 3 3 5. + 096. + 07. = = 06. 3 p I p Π 3 p87 I = Π = 3 5. 096. 07. = 057. = p 77 7.4 977 978 (/) 0.0 0.5 0.5 977 987 ( ) (/) 500 00 50 0.3 0.4 0.6 ( ) 550 50 60 p q I = Σ Σp q 0 p q I = Σ 0 Σp q 0 0
Σpq 0 I = = Σp q 0 0 03. 500+ 0. 4 00+ 06. 50 00. 500 + 0. 5 00 + 05. 50 5+ 48 + 8 7 = = = 08. 57% 0 + 50 + 75. 575. p q I = Σ Σp q 0 Σp q 03. 550 + 0. 4 50 + 06. 50 I = = Σp q 0. 0 550 + 0. 5 50 + 05. 50 0 65. + 36 + 8 705. = = = 0% 0 + 375. + 75. 55 p Σ p0q 0 p0 I = Σp q 0 0 p Σ p0q 0 p0 Σpq 0 I = = Σp q Σp q 0 0 0 0 p p 0
Σp q Σp q Σp 0q = Σp q Σp q Σp q 0 0 0 ( ) ( ). Σp q Σp q 0 Σp q = Σp q Σp q Σp q 0 0 0 0 0 ( ) ( )
c χ c χ X µ Z = σ X µ Z = ( ) χ σ X µ X µ Z = Z = σ σ Z = Z χ Z + Z + Z χ χ χ χ χ χ χ (f - f 0 e) x = (8.) f e χ χ χ ( f f 0 e ) ( 46 50) ( 54 50) x = = + = 0. 64 f 50 50 e χ χ χ χ χ χ χ c
8. c Μ r ( Oj E j ) x = E χ j j P( j ) = ( )( ) E j j j = ( )( ) = χ x x a a
8. 500 86 38 35 59 500-000 7 54 45 36 000-500 9 78 78 375 500-3000 355 40 607 3000 653 85 59 97 640 567 557 764 χ χ ( 59)( 640) E = = 5368. 764 ( 59)( 567) E = = 533. 8. 3 764 ( 86 53. 68) ( 7 9343. ) ( 59 4. ) χ = + + + = 47. 9 5368. 9343. 4. x 0. 99 x 0. 99 8.3 500 86(53.68) 38(53.3) 35(5.9) 59 500-000 7(93.43) 54(66.87) 45(65.70) 36 000-500 9(.50) 78(76.93) 78(75.57) 375 500-3000 355(360.6) (4.5) 40(.3) 607 3000 653(70.3) 85(45.55) 59(4.) 97 640 567 557 746
8.4 a b a+b c d c+d a+c b+d χ ( ad bc) χ = ( 8. 3) ( a + c)( b + d)( c + d)( a + b) 8.5 0 6 36 6 4 0 6 30 56 56[( 0)( 4) ( 6)( 6)] χ = = 3376. ( 6)( 30)( 0)( 36) x 0. 95 x 0. 9 χ ( ad - bc -0.5) χ c = (8.4) (a + c)(b + d)(c + d)(a + d) 56[ ( 0)( 4) ( 6)( 6) 05. ( 56)] χ c = =. 47 ( 6)( 30)( 0)( 36) c χ χ χ
χ 00( 80 30 0 70) χ = =. 667 ( 50)( 50)( 00)( 00) χ 0. 95 8.6 80 0 00 40 70 30 00 50 50 00 P P 08. 07. Z = = = 633. P( P) P( P) ( 075. )( 0. 5) ( 075. )( 0. 5) + + 00 00 Z =.96.633.96 Z =.633 -a-0.95 =. 667 = χ, = χ = 384. χ Z a a
7 0 6 0 8.7 3 5 40 0 4 5 40 0 7 40 7 6 3 9 0 χ ( 3 4) ( 5 8. 6667) = = 4 8. 6667 = 0. 39 ( 3) + 3 χ χ χ χ χ
0 0 Pj = ( j )( ) 0 3 4 5 O 0 4 3 4 E 0.03 0.9.3 3.56 6.53 7.380 6 7 8 9 0 O 5 0 0 E 6.53 3.56.3 0.9 0.03 ( 6 557. ) ( 3 653. ) ( 4 7. 380) χ = + + 557. 653. 7. 380 ( 5 653. ) ( 557. ) + + = 9. 84 653. 557. χ 0. 95 χ
8.8 x x-0 9.8 0. 9.7 9.9 0 0 9.8 9.7 9.8 9.9-0. 0. -0.3-0. 0 0-0. -0.3-0. -0. - + - - - - - -
P ( X ) ( 0 = X ) 0. 5 0 = 0. 0547 x= 0 S+ - 0.5-0.5 S - 0.5-0.5 Z + = Z- = (8.5) 0.5 0.5 05. Z Z az 8.9 + 7 3 0 5 6 9 ( 7 6 5) χ = = 9., a = 005., χ0 95 384χ χ. ( ) =. < a 0 9
( + ) T = 4 ( + )( + ) T = 4 ( + ) T+ ZT = 4 ( 86. ) ( + )( + ) 4 + 3 5 + 6 + 7 3 3 ( + )( + ) Σt Σt ( 8. 7) 4 48 T = 5. + 4. 5 + 7 + 4. 5 = 7. 5 6( 7) T+ = 7. 5 = 8. 5 ( + ) E( T) = = 68 4
3 ( + )( + ) Σt Σt 4 4 3 3 3 6( 7)( 33) ( + 4 + ) ( + 4 + ) = 4 48 = 374 5. = 375. T+ E( T) 85. 68 Z+ = = =. 63 σ( T) 37. 5 8 3 4 P ( T 8) = = 0. 074, P( T 7) = = 0. 0357, 56 56 ( + ) ( + ) U l = T -, U = T - (8.8)
8. 500 600 670 800 00 800 30 50 600 3 4 4.5 7 4.5 0 8 400 00 780 350 890 9 3 6 ( + ) 9( 0) U = T = 64 = 9 ( + ) U = T = 4 5 ( 6 ) = 6
U U U ( + + ) U Z = ( 89. ) ( + + ) U 3 ( + + ) ( Σt Σt) ( + )( + + ) U Z = ( 80. ) 3 ( + + ) ( Σt Σt) ( + )( + + )
k ( + ) H = R a [ ] ( 8.. ) ( + ) = ( + ) k R H = + b + 3( ) ( 8.. ) ( ) = χ χ 8.3 A B C 78 95 85 87 75 90 80 0 6 7 0 8 3 68 77 84 6 6 7 6 5 3 4 8 8 65 50 93 70 60 73 4 5 9 7 9
= 0 k = 06 47 57 H = + + 3 0 + = 664 0( 0 + ) ( 7 6 7 ) ( ). χ 0. 95 H H c = 3 (8.) Σ(t - t ) -[ ( - ) ] 3 k χ r = T j 3( k + ) ( 83. ) k( k + ) j= χ r χ χ 8.4 k X X X X X X Μ X X X
8.5 3 4 5 6 7 8 9 0 4 3 4 0 5 8 9 8 30 (4) () () (3) () () (4) (3) (4) (3) 6 8 7 0 7 6 7 () (3) (4) () () () (3) (4) () (4) 9 9 8 30 0 0 6 9 9 () (4) () (4) (4) (3) () () (3) () 5 0 6 5 6 0 8 (3) () (3) () (3) (4) () () () () 3 4 3 4 0 6 0 4 (3) () () () 8 () (3) () () 4 7 3 () () (4) (3) 4 0 7 (4) (4) (3) (4) χ r = ΣT k k [ 3( k + )] ( + ) = 34 + 33 + 36 + 37 4( 4)( 5) [ ] [ 3( 4)( 4 + )] = 0. 43 χ 0. 05
8.6 3 4 5 6 6 50 60 70 80 90 95 500 50 530 580 560 000 6 5 4 3 6 5 4 3 6Σd ρ = 3 ( 84. ) ρ
8.7 0 T 3 4 5 6 7 8 9 0 4 6 8 0 9 3 5 7 5 8 6 3 7 4 9 0 7 9 5 4 6 3 8 0 6 5 0 8 3 4 7 9 5 7 9 8 0 4 6 3 4 9 7 5 3 8 0 6 8 5 3 3 33 3 38 3 45 45 k T = 3( + ) W = ( 85. ) K ( ) ( 8 + 5 + + 45 ) 3( 0 + ) W = = 073. 6 ( 0)( 0 ) 0 54 970
µ V = + (8.6) + ( - - ) σv = (8.7) ( + ) ( + ) µ V Z = V - (8.8) σ V
Y, y Y = y 9. S N Y = Y N y = y Y = p = N Y = A = p N N Σ( Y Y) s σ = = Σ( Y Y) N = y a = y y ( ) =
Y = y = y (. ) 9 = σ N S N V( y) = ( 9. ) N N σ σ N N N y Y = y0.3 s. 5 s y f 50 50 ( ) = ( ) = ( ) = 0. 04 750 y y ± s( y) = 0. 3± 04. Y = y = Σ. y = 368 = 40 86 9 s = Σ( y y) = [ 533. 9 9( 40. 89) ] 8 = 35. 67
s 35. 67 9 s( y) = ( f ) = ( ) 9 484 = 97. N Y = Ny = y (. ) 9 3 = ( N S V Y) = N V( y) = ( f) ( 9. 4) Y Y Y = Ny = 750 ( 0. 3 ) = 773. 5 s(y) = N S (y) = (750) ( 0. 04) = 365 365 y y = = P = Σ ( ) (. ) y y 0 95 ( PQ N V P) = ( ) ( Q = P) ( 9. 6) N pq f ( )
N = 300 = 00Σ y = 35 ( 9. 5) p y 35 = Σ = = 035. ( 35%) 00 pq s ( p) = ( f ) ( 035. )( 065. ) = ( ) = 0. 0053 99 3 p ± s( p) = 035. ± ( 0. 039), 7. % 48%. σ Nt s = ( 9. 7. a) N + t s Nt pq = ( 9. 7. b) N + t pq ± Nt s 000( ) ( 00) = = N + t s 000( 0) + ( ) ( 00) = 90. 9 = 9
Nt pq 000( ) ( 05. ) = = N + t pq 000( 005. ) + ( 05. ) 000 = = 334 6
M L = L = N
Y = y N N y st = Σ W y W N = Σ = ( 9. 8) N V( Y ) ( ) (. ) N N N S = Σ 9 9 W S = Σ = ( f) f = N Y Y 9. N N N=ΣN =Σ S N ( Yj Y j= = N S ( yj y ) j= = Y j y j Y = Y N L N j= Y = N Y N = j y y = j= y j = Σ N y st E( yst ) = E( ΣN y ) = Σ N N N Y = Y 30 40 f = = = 0. 5f = = = 0. 7 N 60 N 40
9.3 N y S 60 40 300 30 40 40 0 8 6 4 0.5 f 3 3 40 = = = 0. 3 N 300 3 Y = y N N y st = Σ = [( 60)( 0) + ( 40)( 8) + ( 300)( )] = 57. 600 S ( Y ) ( ). N N N S = Σ = 0087 S( Y ) = 0367. Y = Ny = ΣN y ( 90. ) st V( Y ) N ( N ) S = Σ = ( 9.. a) S ( Y ) N ( N ) S = Σ ( 9.. b) Y = Ny = 600( 57. ) = 340 st S ( Y ) N ( N ) S = Σ S( Y = 6735 ) = 8
N = ( 9. ) N f V( Y ) = ΣWS (.. a) 9 3 V( Y ) = Σ W S b ( 9. 3. ) N S WS = = ( 9. 4) ΣN S ΣW S 9.4 () (W ) S S W S 0.5 S S 0.5S 0. 6S 6 S 0.( 6 S ) 0.3 S S 0.3( S )
3 W S = ΣW S 05. S = 00 05. S + 0. ( 6S ) + 0. 3( S ) = 00( 0. 3536) = 7 W S 0. ( 6S) = = 00 = 00( 0. 3464) = 69 ΣW S 44. S W S 3 3 03. ( S) = = 00 = 00( 0. 3) = 60 ΣWS 44. S p (. ) N N p st = Σ 95 V( p ) (.. ) N N N PQ st = Σ 96 a N S ( p ) ( ) (.. ) N N N p q st = Σ 96 b p N N P st = Σ = [( 55)( 08. ) + ( 6)( 0. 5) + ( 93)( 05. )] = 06. 30 40 30
S p N N N p q ( st ) = ( ) 08 0 = [ 55( 55 0) (. )(. ) 30 0 05 075 + 60( 6 8) (. )(. ) 8 + 93( 93 ) ( 05. ) ] = 00045. S ( pst ) = 0067. ± ± ΣN S ω = ( 97. ) N V( y ) + ΣN S st p q S N = 55S = 5 N = 6S = 5 N 93 S = 00 3 3 V( y st ) = V( y st ) =
55 6 93 ω = ω = ω 3 = 30 30 30 55 5 6 5 93 00 Σ N S ( ) ( ) ( ) ( ) ( ) ( ) = + + ω 55 6 93 30 30 30 = 050 + 434500 + 883000 = 8408750 ( 9. 7) 8408750 = = 69 90600 + 75 55 6 = 69 = 34 = 69 = 4 30 30 93 3 = 69 = 30 NS 775 NS 930 N3S3 930 ω = = ω = = ω 3 = = ΣN S 635 ΣN S 635 ΣN S 635 N S ( 55) ( 5) ( 6) ( 5) ( 93) ( 00) Σ = + + ω 775 930 930 635 635 635 = 69435 ( 9. 7) 69435 = = 57 35 775 = = = = = 635 57 7 930 ( ) ( 57) 0 635 930 3 = ( 57) = 0 635
9.5 N M M I M N M M M Y y Y y Y Y y Y S b N ( Y Y) N = jy I j s ( y y) b = y Y = = ( 98. ) M = y Y = = = M M y = Σ = = M N y ( 9. 9) S (Y) = N - NM N = (y M y) = - 5 Σy - yσm y + y ΣM (9.0) M N
Y = Σy. M = 3900 Σ 5 = 880 3 Σy = 80390000, ΣM y = 840300 = ( y M y ) = 80390000 ( 880. 3)( 840300) + ( 88. 03) ( 047) = 579893. 3 9.6 M y M Y 8 9600 4 0 4900 00 5 9 5300 3 4 400 6 3 5000 4 5 6500 7 6 300 5 6 500 8 5 00 6 6 4000 9 5 4500 7 7 7500 0 4 3700 8 5 6500 6 500 9 8 4500 8 3000 0 3 5000 3 7 3900 8500 4 3 4700 6 4300 5 8 400 3 5 5400 5 3900 ΣM M N M = = 6. 04 45 5 579893. 3 S ( y) = ( ) = 6537. 8 ( 45)( 5)( 6. 04) 4 y Σ Y M y = 0 ( 9. ) ΣM ( f Σ( y M y) S Y) = M 0 M N ( f) Σ( y M y) = ( 9. )
yt = y = N Y = Ny = y ( 9. 3) = ( ) ( ( ) S Y) N N y y = = ( 9. 4) N M N M N 9.7 4 y y 3 4 3 3 3 3 3 3 5 4 4 3 3 9 0 6 0.9.6 Σy 9 + 0 + 6 + 0 y = = = 875. ΣM 4( 0) S ( y) = N NM N 400 4 = 400( 4)( 0) Σ( y M y) 0. 75 = 0. 0089 3 ± 00089. Y = M y = 4000 ( 875. ) = 7500 0 ( S Y) = M V( y) = 4900 6760 854 0
y t yt = y = 8. 75y = = 875. = M Y = Ny = 400 8. 75 = 7500 S ( Y ) = t N ( N ) Σ( y y t ) N = 4900 M π = M 0 Ypps = y ( 9. 5) = ( S Y ) = ( ) pps pps = ( y y ) ( 9. 6) 430 460 5790 y = =. 06y = = 8. y 3 = = 8. 00 90 300 ( 9. 5) Y pps = y =. 0 ( 9. 6) = S ( Y ) = ( ) pps ( y pps = Y ) = 0. 09 M < r < M j= = =
9.8 M 3 3 3 4 4 3 5 5 5 4 6 6 5 4 5 5 6 7 6 7 7 3 30 8 30 M Σa P = ( 9. 7) ΣM N Σ( a M P) S ( P) = ( )( ) ( 9. 8 ) NM
9.9 M a M (a ) 8 4 4 0 5 7 5 9 4 3 4 6 3 4 5 3 7 6 4 5 6 3 8 5 6 6 4 9 3 3 7 7 4 0 4 8 5 6 3 9 8 3 8 3 0 3 3 7 4 4 3 0 6 3 5 8 3 3 5 5 7 a p = Σ M = 7 Σ 5 = 0. 477 M M ΣM M = = 6. 04 N a M p ( ) S ( p) = Σ = 0. 00055 NM
k N =
300 k = = 0 5 k + k + k = = [ + jk, ( j + ) k + ] j = 0,,, ( 9. 9) Μ ( )
[ j + jk ( N = jk) + ] j = 0,,, ( 9. 30) Μ j = 3 j + jk = 6( N jk) + = 75 3 k = = 4. 6 5 Y = y (. ) 9 3 =
σ V( ysy ) = [ + ( ) ρ] ( 9. 3) y y = = Y = ysy = y = ( 7066) = 80. 5( ) = 486800 ( 80. 5) s = Σ( y y) / = = 535. 48 f s y s 7 sy = ( / ) ( ) = ( 535. 48 ) =. 6 y ± y ± psy = y y = 9 33 = 0 (. ) p( p) s ( psy ) = ( f ) ( 9. 34 ) Σ
p. y 65 sy = Σ = = 0678 96 p ( p ) S ( psy ) = ( f ) ( 0678. )( 0. 3) = ( ) = 00009. 96 6 0. 678± 00009. N k = s Y = y ( 9. 35) s = ( ( ) y Y s b = s Y) = ( f), sb = ( 9. 36) s s s 40 k = = 0 4 y y y y Y = Σ y (.. ). = 9 7 + 87 3 = 8 4 4 s = Σ( y Y) b s = [( 9. 7 8. 4) + 3( 8. 7 8. 4 )] = 0. 5 4 s b 0 5 S ( Y. ) = ( f) = ( 0. ) = 0. 0565 4 s 0. 0565
σ σ σ 3 y 08 39 599 66 400 48 50 538 3 440 47 3 88 888 4 59 76 4 473 50 5 35 363 5 94 998 6 880 94 6 0 7 7 73 94 7 89 889 8 487 54 8 57 65.9 83 95 9 388 49 0 863 897 0 44 57
3 4 0 8 9 40 4 3 5 4 3 5 3 4 0 5 3 8 9 4 4 6 8
0. A B C A =80 B =35 C = A =85 B =48 C = 3 A =90 B =55 C =
0. L (3 ) 3 4 3 3 3 3 4 3 5 3 6 3 7 3 3 8 3 3 9 3 3 0.3 A B C 80 35 80 48 3 80 355 3 4 85 35 5 85 48 3 6 85 355 7 390 35 3 8 390 48 9 390 355
0.4 A B C ( ) 80 35 5 48 7 3 355 3 58 4 85 8 5 3 69 6 3 59 7 390 3 77 8 3 85 9 3 3 84 A B C K 80 0 95 K 0 5 37 K 46 0 04 K 60 70 65 K 70 75 79 K 8 67 68 R 8 4 K K K
0.5 L ( ) 3 3 4
0.6 A B C D E () A B C D E 30 3A B D 50 3 A E 90 4 4A 60 5 C 55 6 3 0 7 70 8 4 85 K 85 70 30 35 35 =450 K 60 80 0 5 5 K 60 K 45 R 00 0 0 0 0
0.7 A B C D E PH CaCI 78 Na CO 390 3 89 4 40 5 NaOH 6 3 7 8 4 ( ) X X X X + X = ( /) ( /) 0.7.36 80.04 8 0.5 0.90 540 0.7 5 3 0.80 0.96 55 0.88 7 4 0.60.00 630 0.80 6 5 0.53 0.4 465 0.48 4 6 0. 0.4 90 0.3 7 0.30 0.5 375 0.40 3 8 0.3 0.40 00 0.7
L A S = ( 0. )
0 ( x µ ) = S = 0 ( 03. ) + ( 0. 6) + + ( 3. ) = 0 = 04795. ( mm) 0. 4795 3 SS T 0 = ( x ) = µ = ( 0. 3) + ( 0. 6) + + ( 3. ) = 9. 59 x 0 = 0µ SSA = ( x µ ) = 0( x µ ) = 0( ) 0 0 = 0 x 0µ = = 0(( ) 0 x + x + + x = ( ( ) ( ) ( ) 0 µ µ 0 µ 0 ) 0 + + + = (... 0 0 3 0 6 3 ) =. 66 0 0
0.8 F SS SS SS.66 6.93 9.59 9 0.66 0.365 0.4795 7.9 x x 0. 365 L = 50 = 6. 08( ) 3
x x µ σ µ σ µ± σ
σ T CP = = 6σ 6σ C C.67.67C.33.33C.00.00C 0.67 A B C 0.67C D
x x x x 0.0 x R 9886 630 x R 6. 9. 9.7 96.8 93.57 5. 96.5 98.4 96.8 97.3.9 3 3 99.5 9.4 99. 97.00 7. 4 4 93.5 98.7 90. 97.3 8.5 5 5 9. 95.7 95. 94.33 3.5 6 6 96. 90.9 94.3 93.77 5. 7 7 99.5 90.6 95.8 95.30 8.9 X
9. + 97. + 96. 8 x = = 9357. 3 X 9357. + 97. 3 + + 95. 70 + 94. 93 x = 30 84 = = 94. 70 30 5. +. 9 + + 7. 6 + 4. 5 R = 30 55. 6 = = 587. 30 x (CL) = x = 94. 70 ( UCL) = x + 3σ = x + A R = 94. 70 + 03. 587. = 00. 046 ( LCL) = x3 σ = x A R = 94. 70. 03 587. = 89. 434 R ( CL) = R = 587. ( UCL) = R + 3σ = D R. 575 587. = 3357. ( LCL) = R 3σ = D R 4 3 x x R R =
0. A D D.880 3.67 3.03.75 4 0.79.8 5 0.577.5 6 0.483.004 7 0.49 0.076.94 8 0.373 0.36.864 x x x X X X X X
48 p = = 0. 066 74 38 p = = 007. 8533 8533 = = 74 5 p ( UCL) = p + 3p ( p) / = 0. 07 + 3 ( 0. 0094) = 0. 099 ( LCL) = p 3p ( p) / = 0. 07 3( 0. 0094) = 0. 043 UCL = p + 3 p( p) / LCL = P 3 P( P) / λ c c = Σ k = 40 0 = 4
(UCL) = c + 3 c = 4 + 3 4 = 0 (LCL) = c - 3 c = 4 3 4 = 0 x x x C 3 ( 0048. ) ( 0. 9545) = 0. 005 = 05%.
0.4. 4 47. 8 3 3. 7 8 4. 4 4 5. 6. 6 7 89 00
0.5. 8=56 56 48. 4=4 98 84 3. 4=8 06 9 4. 7=7 3 97 5. 0.8=.6 4.6 98 6. 0.46=.4 7 00 7
c d C P d c d D CN D ( ) = ( 03. ) C d= 0 0 5 0 C5C 00 P( d 0) = 5 5 = 0. 77 C 500 0 5 0 C5C 500 P( d 0) = 5 5 = 0. 9 C N 500 N
P( d ) = d= 0 C C 30 C d 30 d 40 000 40 C40 C960 C = 30 + C = 0. 6603 0 000 30 000 40 9 960 C 30 C 000 N d d P( d ) = C P ( P) d= 0 d 0 0 30 = C ( 004. ) ( 096. ) + C ( 0. 04) ( 0. 96) 30 9 30 = 066. d ( P) p P( d ) = e d d= 0 0 (. ) (. ) = e + 0.. e = 0666. 0.6 P P LP 0.0 0.6 0.879 0.0. 0.66 0.06.8 0.455 0.08.4 0.96 0.0 3.0 0.84 0. 3.6 0.0 0.4 4. 0.064 0.6 4.8 0.036 0.8 5.4 0.00 0.0 6.0 0.0 Μ Μ Μ
α = L( AQL) d c ( P0 ) P0 = e ( 0. 4) d= 0 d c d β = = ( P ) p L( LTPD) e ( 05. ) d= 0 d c d ( P0 ) p α = L( AQL) = e d= 0 d c d ( P) P = = β L( LTPD) e d= 0 d P
c d c d ( P) P ( P) I = e + N( e d d d= 0 d= 0 = N ( N ) d= 0 d ( P) e d = + ( N ) ( N ) c P c d= 0 d ( P) e d P P c d ( P) P = + ( N )( e ) d= d ( 0. 6) 0 P P P P P NP IP AOQ = N P N = I N c d ( P) P ( N ) ( N )( e ) d= 0 d = P N = P N c d ( P) P e ( 0. 7) N d= 0 d N AOQ = P( L P) N P P P P )
L( P) = P( d c ) + P( d + d c, c < d c ) c s ( P) d ( P) d P = e + e d d d= 0 3 d ( P) d [ e d d = 0 P d = c + P ] ( 08. ) 0 0 3 d ( 036. ) 0 36 ( 036. ) L( P) = e + e 0 d d = 0 3 d ( 059. ) d [ e d d = 0. 0. 36 d = 0. 59 ] I = P(d c ) + ( + ) P ( c < d c, d + d c ) + N( L( P)) ( 0. 9) AOQ P N = ( 00. ) N
000 65. 3 AOQ = 0. 0 000. = 0 0093 A = β B = β ( 0. ) α α d = 0 d P ( P ) d L = d ( 0. ) P0 ( P0 ) d P L = P P L = P 0 0
d+ d P ( P ) d d L = d+ d P ( P ) d d 0 0 P d ( P ) d = = = P d ( P ) d 0 0 = = ( 03. ) L P b ( P ) d = = = P ( P ) d 0 0 = = ( 04. ) ( ) P ( P0 ) PlΣd ( P ) Σd A ( 05. ) P Σd ( P ) Σd P P Σd log + ( Σd ) log loga P P P P P Σd (log log ) loga log P P P 0 0 loga Σd P P log log P P α log β h = P P log log P P 0 0 0 0 0 0 0 0 P log P0 P P log log P P 0 P0 log P s = P P log log P P 0 0 0 0 ( 06. )
Σ β log α h = P P log log P0 P0 Σ β 0. A = = = B = β 0. 9 0053. = = 8 α 0. 95 α 005. log A = 0. 9776 log B = 553. P P 080 log = log = log. = 0. 088 P P 0. 98 0 0 α P0 098 log = log = 09777. log = log. = 0088. A β P 080. 0. 9777 553. h = = 08985. h = = ( 536. 0. 088) 088. 0. 088 s = = 0080. ( 0. 088)
A B C D () ( ) (mm) 000 0 0.3 00 3 0.35
θ. θ θ θ θ θ θ θ θ θ θ
θ θ θ θ. ( ) ( θ) θ =0.0 θ =0.0 θ =0.03 θ =0.04 a -6000-000 000 6000 a 0 0 0 0 θ θ θ θ θ θ
E( a ) = X P( θ ) (. ) m j= j j θ.3 θ =0.0 θ =0.0 θ =0.03 θ =0.04 p(θ )=0. p(θ )=0.4 p(θ )=0.3 p(θ )=0. a ( 6000 000 000 6000 a 0 0 0 0 = (. )
= 00 0 = 00( ).4 ( ) P(θ) a a 0.3 00 50 0.7 50 0 5
.5 ( ) 80 40-30 -70 55 37-5 -40 3 3 9 - = α + ( α) ( 3. )
.6 ( ) 0 0 39 69 69 5 3 4 39 39 49 9 0 0 49
k θ θ, θ,, θ, P(θ ) k k k
µ = Wx + W µ 0 ( 4. ) x xµ.7 B 0000 5000 30000 A P θ θ 0.4 0.5 0.6 0.3 0.5 0. 900 500 00 00 500 800 P( θ ) P( X θ) P( θ X) = 3 ( 5. ) P( θ ) P( Xθ ) j= θ θ θ θ
4 4 P( X θ = 0. 4) = C ( 0. 4) ( 0. 6) = 0. 0434 5 4 4 P( X θ = 0. 5) = C ( 0. 5) ( 0. 5) = 0. 38 5 4 4 P( X θ = 0. 6) = C ( 0. 6) ( 0. 4) = 0. 465 3 5 P( θ ) P( X θ ) P( θ X) = 3 P( θ ) P( Xθ ) j= P( θ X) = 0. 608 P( θ X) = 0. 659 ( 0. 3) ( 0. 0434) = ( 0. 3)( 0. 0434) + ( 05. )( 038. ) + ( 0. )( 0. 465) = 097. 3 4 5 = 0. 56 θ θ θ θ θ
A B C 60 90 0 300 00 50
= = = = = + +
= + = + = + + + = = = = + = +
( a) = ( ) = ( b) = + = =
a. + = + = b. + = + + + + + = = = + = +
. A B 0 30 A B C 0 0 45 30 C 0 80 0 40 50 4 5 5 6 0 5 5 0 6 3 5 4 03 05 54 0 95 0 0 0 0 0 0 8 3 0 0 5 0 6 03 05 54. A 70 B 00 C 75 45
.3 3 5 56 40 36 48 3 45 45.4 A B C A 0 0 45 35 00 B 30 0 30 40 00 C 0 80 0 70 50 70 00 75 45 00 00 50 450
.5 w w w e q w w w e q Μ Μ w w w e q z z z q q q w + w + + W + e = q w + w + + W + e = q (. ) w + w + + W + e = q w 30 a = = = 0. 3 q 00 aa a 3 0 0. 0. 3 aa a 3 = 0. 3 0 0. a a a 00. 40 3 3 33 w j a j = q j a q + a q + + a q + e = q a q + a q + + a q + e = q a q + a q + + a q + e = q (. )
a a a l e q a a a e q A = e = q = a a a Μ Μ e q (. 3) q Aq = e ( I A) q = e I A ( ) e = q (.4) 077. 057. 0375. ( I A) = 035. 7. 0. 340 04. 0. 468 36. 35 e = 40 0% 385 54 70 =. 77 077. 057. 0. 375 385 099 q = I A e = 035 7 0340 54 0 04 0 468 36. 77 =. ( )...... 65
( ) = ( ) + ( ) +
.9 75 % 87 96 4 30 457 3 5 435 44 8 44 6 57 43 4 564 479 37 3 59 66 8 4 73 693 7 44 764 90 86 07 90 86 0 7
.0 ( ). 9 55 3. 6 0. 8 54 4. 47 5 5. 6 309 309. ( ) 6. 3 0 9. 55 7.5 7 0. 3 9 8. 9 4. 7 5 4 4
. ( ). 4 47 5.7 7 3. 0 9 4. 0 7 7.3 ( ) 6. 5 5 8. 54 7. 5 9. 8 4 0. 4 57 57
.4 3 4. 0 47 5 309. 55 0 5 4 3. 7 7 4. 54 4 57 309 4 7 57.5 3 4 5 6 7. 693. 300 0 47 5 3 55 9 5 4. 693 7 44 764 5. 54 4 6. 44 7. 764
.6 3 4 5 6 7 3 4 5 6 7
500 300 3900 400 3000 60 3900
A B A B 30 5 40 35 0 5 90 85 35 0 45 90 85 75