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21 X X X + X + = + X N (. ) N X = 3 N = N = N N X X = = ( ) X X f X f X f k = f + f + + f (. ) X f. 5 k k = X = = = ( ) 30 k = k = X f f

22 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 =

23 Σf L + Sm Me = (. 6) f m Σf 30 0 M e = = ( ) 3 M0 = L + (. 7) M 0 = = 04. 9( ) ( 3 7) + ( 3 5) N Mg = X X X N (. 8)

24 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]

25 X + X + + X ([ ] + ) ([ ] + ) ( [ ]) = [ ] X( ) + X( 3) + + X( 0) = = 9 = 9. 6 X ( ) + X( ) + X( ) X0 = = X 0 = X a = X( 6) 5 X = = X ( 6) = 95.

26 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 =

27 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

28 .8 Xf X f X f X f Xf = = σ = k ( k ) f f = = = ( ) = 04. ( ) k k

29 N = = 55.

30

31

32

33

34 φ φ Ω Ω 6

35 P A A m ( ) = = ( 3. ) m 3. m m f(a)= K K

36 5 5 5 P( A ) = P( A ) ( 3. ) = =

37 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 = + = φ A A A A 0

38 A φ B P( A) = P( B) = P( B) = = C3 C7 C3 C7 3 P( A) = = + = C C A φ P( AB) P( AB) = ( 36. ) P( B)

39 3 P( A ) =, P( A A ) = 0 9 P( A A ) = 3 P( A ) P ( A A ) = P ( AB ) P( B) P ( AB ) P( A) P( AA ) = P( A ) P( A ) = = P(B) = P(A B) + + P(A B) k k = P(A )P(BA ) (3.0) =

40

41 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 ) = = = = k k k

42 ξ C8 8 P( X = 0) = = C 45 0 CC8 P( X = ) = = C C P( X = ) = = C P( X = ) = C p ( p), = 0,,, 5 5 X = 0

43 p =,, k f( x) = ( 3. ) 0 ( ) f( x ) = p = ( ) = = 8 pl = P( X = 0) = 45 6 p = P( X = ) = 45 p3 = P( X = ) = X X=x x =0 x = x = P(X=x )=p

44 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 =

45 () 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 )

46 X = 0 P( X x) p x = = = p x = ( ) 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.

47 ( 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

48 7 0 ( ) P ( X < 7) = F( 7) = φ( ) 3 = φ( ) = ( ) P ( X 5) = F( 5) = φ( ) 3 φ( 67. ) = x 0 ( 3) P ( X < x) = F( x) = φ( ) = Z = x 0 =. 8 x = 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 + =

49 f x b a a < x < b ( ) = ( 3. 4) < r < 500 f( r) = P( 00 < R < 300) = 00 dr =

50 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 X,Y X=x Y=y P(x) P(y)

51 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

52 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

53 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 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)

54

55 (/) ()

56

57 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

58 ()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) = ( > )

59 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

60 θ σ σ σ θ θ θ θ θ θ µ σ µ σ µσ x x σ µ x = µ x = µ + σ = =

61 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

62 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 = = 0 90 = p ( p) p L( p x x ) = 0p ( p) 90p ( p) = 0 0 p = = µ σ µ σ ( x µ ) σ L( µ, σ x x) = ( e ) = σ π ( x µ ) σ = = ( ) e σ π

63 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

64 θ θ θ θ x ~ N(, ) P x θ ( ) = σ P( x ( 4. ) θ 3) = σ σ x θ 3 θ σ

65 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, 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

66 x S P( x Z x Z S a µ + a ) = P( µ ) = x t = µ ~ t (. ) S 43 µ [ x t a S, ] x + t a S x x t S 009. x t a = = S 009. x + t a = = p

67 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 = ( 44. ) θ = p Z = θ = p + Z a a p ( p ) p ( p ) = = = x x σ σ N( µ ) N( µ ) x x E( x x ) = µ µ σ σ D( x x ) = +

68 ( 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 [ ] σ σ σ = σ ( x x ) ( µ µ ) t = t + S + S + ( ( ) ( ) ( ) ~ (. ) 4 9 )

69 x = 570 ( ) S = ( x x ) = 400 = x = 600( ) S = ( x x ) = 6400 = t a ( ) =. µ µ ( ) S + ( ) S θ = x x t a ( + ) = = = 9. µ µ ( ) S + ( ) S θ = x x + t a ( + ) = = = σ σ ( ) S x = ~ x ( ) x σ a

70 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) = a σ [ ( ) ( ), ( ) S S ( ) ] [ =, x x a a = [ , ] 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

71 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= = 095. F0. 05 ( 4, 4) =. 35 F0. 95 ( 4, 4) = = F ( 4, 4) S = = 4. S 55. σ / σ 4 [.,( 4. )( 3. )] = [ 058.,. 64]. 35

72 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

73 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

74 θθ θ θ µ µ

75 x = 50 S = 650. t ( 0 ) = t ( 9) =. 6 a x t = = = S / 650. / 0 t a µ µ µ µ x = 375. x = ( ) S =. 5 ( ) S = = = t a x x t = ( ) S + ( ) S = =. 646 t a σ σ 0 µ σ

76 σσ 0 σ σ 0 x = ( -) S σ x ( ) x ( ) a x ( ) x x ( ) a a σ σ S (. ) x = ( ) = 5 = σ (. ) x ( 5) = 6. 6, x ( 5) = x = > x0. 05 = 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

77 = 8, x = 9. 93, S = 0. 6 = 7, x = 0. 00, S = S 06. F = = = S ( ) 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

78 ( ) 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

79 ( ) 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 = = = F. ( 6, 7)

80 θx θ, 0 < x < f ( x) = 0, x f ( x) = e σ < x < σ σ ( ) µ = x + x ( ) µ = x + x 4 4 ( 3) µ 3 = x + x σ σ σ x S x x x x µ σ x x x

81 x µ σ µ σ σ σ µ µ

82 5. A A A

83 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

84 µ x Q / r F = ~ F( r, r) ( 55. ) Q / r µ µ µ µ µ

85 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

86 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

87 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 = = a = x x = =. 58 a 3 = x3 x = = 9. 4 a 3

88 x = Se = = F (, 9) = Se x F 3 ± 0. 05( 9, ) = ± kg A A A F x = 03x = x 3 = 86 x S e = 3. 4

89 Se x ± F0. 05 ( 9, ) = ± = ± 3. 0

90 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

91 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

92 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

93 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 ) ( ) x. B B B B B A A A A A x. j 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. )

94 CT = ( 59. 3) = SS = x CT T r S = j= j = = S S SS A = ( xj ) CT 5 = j= = = 47. S S SSB = ( xj ) CT 5 j= = = = SS = SS SS SS e T A B = = S S =0.63 S 3 =.47

95 5. ( %) B ( ) B ( 5%) B ( 8%) A A A β α α α β β β CT = ( 600) = SS = = 00 T SS A = ( ) = 6 3 SSB = ( ) = 46 3 S S S 3 =.86 S =Q /=73 S / S 3 =0.43 S 3 =Q /4=7 α

96 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 δ = = ±

97 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

98 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

99 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 )

100 5.5 ( ) B I II III A 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=

101 5.6 A Q =SS =6.4 3-= B Q =SS = = A B Q =SS =0.9 (3-)(3-)=4 Q =SS = (-)=9 Q=SS = =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

102 /

103

104 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

105 r t = = = r 0. 98

106 α βε α β ε ε σ σ = j Cov( ε, ε j ) = 0 j =,,,, j =,,, Σe = m Y

107 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.

108 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

109 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

110 Y Σe Sy = = = Sb = Sy / Σ( x x) = α SSR = Σ(y - y) = SSE = Σ( y y ) = / F = = / 4 α α α α

111 SSR r = SST = = 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 ±

112 Y 0 ± Y 6. * ( ) ( ) ( ) ( ) * 975 S y y

113 y 6.3 ( ) ( ) ( ) 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

114 b Y = a + X X' = X Y = 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 =

115 6.5

116 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

117 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

118 Σ( y y ) / k R = ( 6. 5) Σ( y y) / R R R = ( R ) ( 6. 6) k Y = X X X 0. 43X 3 4 (. 400)( )( 06. )( ) t0.05/=

119 R

120 ( ) ( /) ( /) ( /) (%) (%) ( ) ( )

121 3 (%) (%) (%) (%)

122 a = a + a + + a = a Σ (7.) a

123 a a + a + + a + a - (7.) - 7. ( ) a = = 043( ) 4 a + a a + a 3 a + a ( ) f + ( ) f + + ( ) f a = ( 7. 3) f = ( ) ( ) + 30 ( ) 4 ( ) 3 a = =

124 a a, a a,, a, a - (7.4) a a a a, a a, a a,, a, a 3 - a a (7.5) (970 ) (%) (%) a a a a 3 a = ( 7. 6) a a a a a 0 0

125 x x = x x = x (7.7) x Π x x = a / a 0 (7.8) x = / a a 4 = 08% % 0. 9% 053%. = % ( 78. ) x 4 = a / a = 89 / 677 = % 0 0 x x x x a x + x + x x = = a 0 ( 7. 9) x

126 = - = = = =

127

128 ( Y + Y + Y3) 3 ( Y + Y3 + Y4 ) 3 ( Y3 + Y4 + Y5 ) 3

129 ' Y t Y ' t Y ' Y Y Y 3 Y ' ` = ( ) ( 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

130 Y t = t Y t Y t Yt L Yt = f( t) + ae 7.7 ( ) t t ( ) Y t = = =

131 L Y t = + bt ae D = S S = D = S S = b = (l D l D) = L = = D S D D L D a = = C D D C e b e b ( ) = b = 539. e Yt =. t e 0577 ( ) f t = (7.)

132 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

133 7.0 (%) (%) MA T C = = C T T Tl T 7.9

134 k ( Yt Yt )( Yt + k Yt ) t= rk = ( Y Y) t= t ( 76. ) ρ ρ / ± t φ φ φ

135 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 r (k (k=e(yt,yt-k)

136 φ = r = r φr ( 0. 84) φ = = φ r ( 0. 84) = φ = φ φ φ = ( )( 0. 84) = 0. 9 r3 φr φr φ33 = φ r φ r ( 0. 9)( ) + ( )( 0. 84) = ( 0. 9)( 0. 84) ( )( ) φ φ φ φ µ γ µ µ τ µ τ µ (k k (k Yt Yt+k

137 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

138 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

139 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

140 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

141 Θ Φ Φ Θ Θ φ θ φ

142 p I = Σ Σp / p I = Σ 87 Σp = = 05% I = = p Σ 0 p I =

143 p Σ p I = = = = p I p Π 3 p87 I = Π = = 057. = p (/) ( ) (/) ( ) p q I = Σ Σp q 0 p q I = Σ 0 Σp q 0 0

144 Σpq 0 I = = Σp q = = = % p q I = Σ Σp q 0 Σp q I = = Σp q = = = 0% p Σ p0q 0 p0 I = Σp q 0 0 p Σ p0q 0 p0 Σpq 0 I = = Σp q Σp q p p 0

145 Σp q Σp q Σp 0q = Σp q Σp q Σp q ( ) ( ). Σp q Σp q 0 Σp q = Σp q Σp q Σp q ( ) ( )

146

147

148 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 = = + = f e χ χ χ χ χ χ χ c

149 8. c Μ r ( Oj E j ) x = E χ j j P( j ) = ( )( ) E j j j = ( )( ) = χ x x a a

150 χ χ ( 59)( 640) E = = ( 59)( 567) E = = ( ) ( ) ( ) χ = = x x (53.68) 38(53.3) 35(5.9) (93.43) 54(66.87) 45(65.70) (.50) 78(76.93) 78(75.57) (360.6) (4.5) 40(.3) (70.3) 85(45.55) 59(4.)

151 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) [( 0)( 4) ( 6)( 6)] χ = = ( 6)( 30)( 0)( 36) x 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

152 χ 00( ) χ = =. 667 ( 50)( 50)( 00)( 00) χ P P Z = = = 633. P( P) P( P) ( 075. )( 0. 5) ( 075. )( 0. 5) Z = Z =.633 -a-0.95 =. 667 = χ, = χ = 384. χ Z a a

153 χ ( 3 4) ( ) = = = ( 3) + 3 χ χ χ χ χ

154 0 0 Pj = ( j )( ) O E O E ( ) ( ) ( ) χ = ( ) ( 557. ) + + = χ χ

155 8.8 x x

156 P ( X ) ( 0 = X ) = x= 0 S S Z + = Z- = (8.5) Z Z az ( 7 6 5) χ = = 9., a = 005., χ χ χ. ( ) =. < a 0 9

157

158

159 ( + ) T = 4 ( + )( + ) T = 4 ( + ) T+ ZT = 4 ( 86. ) ( + )( + ) ( + )( + ) Σt Σt ( 8. 7) 4 48 T = = ( 7) T+ = 7. 5 = 8. 5 ( + ) E( T) = = 68 4

160 3 ( + )( + ) Σt Σt ( 7)( 33) ( ) ( ) = 4 48 = = 375. T+ E( T) Z+ = = =. 63 σ( T) P ( T 8) = = , P( T 7) = = , ( + ) ( + ) U l = T -, U = T - (8.8)

161 ( + ) 9( 0) U = T = 64 = 9 ( + ) U = T = 4 5 ( 6 ) = 6

162 U U U ( + + ) U Z = ( 89. ) ( + + ) U 3 ( + + ) ( Σt Σt) ( + )( + + ) U Z = ( 80. ) 3 ( + + ) ( Σt Σt) ( + )( + + )

163 k ( + ) H = R a [ ] ( 8.. ) ( + ) = ( + ) k R H = + b + 3( ) ( 8.. ) ( ) = χ χ 8.3 A B C

164 = 0 k = H = = 664 0( 0 + ) ( ) ( ). χ 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

165 (4) () () (3) () () (4) (3) (4) (3) () (3) (4) () () () (3) (4) () (4) () (4) () (4) (4) (3) () () (3) () (3) () (3) () (3) (4) () () () () (3) () () () 8 () (3) () () () () (4) (3) (4) (4) (3) (4) χ r = ΣT k k [ 3( k + )] ( + ) = ( 4)( 5) [ ] [ 3( 4)( 4 + )] = χ 0. 05

166 Σd ρ = 3 ( 84. ) ρ

167 8.7 0 T k T = 3( + ) W = ( 85. ) K ( ) ( ) 3( 0 + ) W = = ( 0)( 0 )

168 µ V = + (8.6) + ( - - ) σv = (8.7) ( + ) ( + ) µ V Z = V - (8.8) σ V

169

170

171

172

173

174 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 ( ) =

175 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 ( ) = ( ) = ( ) = y y ± s( y) = 0. 3± 04. Y = y = Σ. y = 368 = s = Σ( y y) = [ ( ) ] 8 =

176 s s( y) = ( f ) = ( ) = 97. N Y = Ny = y (. ) 9 3 = ( N S V Y) = N V( y) = ( f) ( 9. 4) Y Y Y = Ny = 750 ( 0. 3 ) = s(y) = N S (y) = (750) ( 0. 04) = y y = = P = Σ ( ) (. ) y y 0 95 ( PQ N V P) = ( ) ( Q = P) ( 9. 6) N pq f ( )

177 N = 300 = 00Σ y = 35 ( 9. 5) p y 35 = Σ = = 035. ( 35%) 00 pq s ( p) = ( f ) ( 035. )( 065. ) = ( ) = p ± s( p) = 035. ± ( ), 7. % 48%. σ Nt s = ( a) N + t s Nt pq = ( b) N + t pq ± Nt s 000( ) ( 00) = = N + t s 000( 0) + ( ) ( 00) = = 9

178 Nt pq 000( ) ( 05. ) = = N + t pq 000( 005. ) + ( 05. ) 000 = = 334 6

179 M L = L = N

180 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 f = = = 0. 5f = = = 0. 7 N 60 N 40

181 9.3 N y S f = = = 0. 3 N Y = y N N y st = Σ = [( 60)( 0) + ( 40)( 8) + ( 300)( )] = S ( Y ) ( ). N N N S = Σ = 0087 S( Y ) = 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

182 N = ( 9. ) N f V( Y ) = ΣWS (.. a) 9 3 V( Y ) = Σ W S b ( ) 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 )

183 3 W S = ΣW S 05. S = S + 0. ( 6S ) ( S ) = 00( ) = 7 W S 0. ( 6S) = = 00 = 00( ) = 69 ΣW S 44. S W S ( 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. )] =

184 S p N N N p q ( st ) = ( ) 08 0 = [ 55( 55 0) (. )(. ) ( 6 8) (. )(. ) ( 93 ) ( 05. ) ] = S ( pst ) = ± ± ΣN S ω = ( 97. ) N V( y ) + ΣN S st p q S N = 55S = 5 N = 6S = 5 N 93 S = V( y st ) = V( y st ) =

185 ω = ω = ω 3 = Σ N S ( ) ( ) ( ) ( ) ( ) ( ) = + + ω = = ( 9. 7) = = = 69 = 34 = 69 = = 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 = ( 9. 7) = = = = = = = ( ) ( 57) = ( 57) = 0 635

186

187 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

188 Y = Σy. M = 3900 Σ 5 = Σy = , ΣM y = = ( y M y ) = ( )( ) + ( ) ( 047) = M y M Y ΣM M N M = = S ( y) = ( ) = ( 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. )

189 yt = y = N Y = Ny = y ( 9. 3) = ( ) ( ( ) S Y) N N y y = = ( 9. 4) N M N M N y y Σy y = = = 875. ΣM 4( 0) S ( y) = N NM N = 400( 4)( 0) Σ( y M y) = ± Y = M y = 4000 ( 875. ) = ( S Y) = M V( y) =

190 y t yt = y = 8. 75y = = 875. = M Y = Ny = = 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) y = =. 06y = = 8. y 3 = = ( 9. 5) Y pps = y =. 0 ( 9. 6) = S ( Y ) = ( ) pps ( y pps = Y ) = M < r < M j= = =

191 9.8 M M Σa P = ( 9. 7) ΣM N Σ( a M P) S ( P) = ( )( ) ( 9. 8 ) NM

192 9.9 M a M (a ) a p = Σ M = 7 Σ 5 = M M ΣM M = = N a M p ( ) S ( p) = Σ = NM

193 k N =

194 300 k = = 0 5 k + k + k = = [ + jk, ( j + ) k + ] j = 0,,, ( 9. 9) Μ ( )

195 [ j + jk ( N = jk) + ] j = 0,,, ( 9. 30) Μ j = 3 j + jk = 6( N jk) + = 75 3 k = = Y = y (. ) 9 3 =

196 σ V( ysy ) = [ + ( ) ρ] ( 9. 3) y y = = Y = ysy = y = ( 7066) = 80. 5( ) = ( 80. 5) s = Σ( y y) / = = f s y s 7 sy = ( / ) ( ) = ( ) =. 6 y ± y ± psy = y y = 9 33 = 0 (. ) p( p) s ( psy ) = ( f ) ( ) Σ

197 p. y 65 sy = Σ = = p ( p ) S ( psy ) = ( f ) ( )( 0. 3) = ( ) = ± 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 (.. ). = = s = Σ( y Y) b s = [( ) + 3( )] = s b 0 5 S ( Y. ) = ( f) = ( 0. ) = s

198 σ σ σ 3 y

199

200

201 0. A B C A =80 B =35 C = A =85 B =48 C = 3 A =90 B =55 C =

202 0. L (3 ) A B C

203 0.4 A B C ( ) A B C K K K K K K R 8 4 K K K

204 0.5 L ( ) 3 3 4

205

206 0.6 A B C D E () A B C D E 30 3A B D 50 3 A E A 60 5 C K =450 K K 60 K 45 R

207 0.7 A B C D E PH CaCI 78 Na CO NaOH ( ) X X X X + X = ( /) ( /)

208 L A S = ( 0. )

209 0 ( x µ ) = S = 0 ( 03. ) + ( 0. 6) + + ( 3. ) = 0 = ( mm) SS T 0 = ( x ) = µ = ( 0. 3) + ( 0. 6) + + ( 3. ) = 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 ) = ( ) =

210 0.8 F SS SS SS x x L = 50 = 6. 08( ) 3

211 x x µ σ µ σ µ± σ

212 σ T CP = = 6σ 6σ C C.67.67C.33.33C.00.00C 0.67 A B C 0.67C D

213 x x x x 0.0 x R x R X

214 x = = X x = = = R = = = x (CL) = x = ( UCL) = x + 3σ = x + A R = = ( LCL) = x3 σ = x A R = = R ( CL) = R = 587. ( UCL) = R + 3σ = D R = ( LCL) = R 3σ = D R 4 3 x x R R =

215 0. A D D x x x X X X X X

216 48 p = = p = = = = 74 5 p ( UCL) = p + 3p ( p) / = ( ) = ( LCL) = p 3p ( p) / = ( ) = UCL = p + 3 p( p) / LCL = P 3 P( P) / λ c c = Σ k = 40 0 = 4

217 (UCL) = c + 3 c = = 0 (LCL) = c - 3 c = = 0 x x x C 3 ( ) ( ) = = 05%.

218

219 0.5. 8= = = = = =

220 c d C P d c d D CN D ( ) = ( 03. ) C d= C5C 00 P( d 0) = 5 5 = C C5C 500 P( d 0) = 5 5 = 0. 9 C N 500 N

221 P( d ) = d= 0 C C 30 C d 30 d C40 C960 C = 30 + C = C 30 C 000 N d d P( d ) = C P ( P) d= 0 d = C ( 004. ) ( 096. ) + C ( 0. 04) ( 0. 96) = 066. d ( P) p P( d ) = e d d= 0 0 (. ) (. ) = e e = P P LP Μ Μ Μ

222 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

223 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 )

224 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. ) d ( 036. ) 0 36 ( 036. ) L( P) = e + e 0 d d = 0 3 d ( 059. ) d [ e d d = d = ] I = P(d c ) + ( + ) P ( c < d c, d + d c ) + N( L( P)) ( 0. 9) AOQ P N = ( 00. ) N

225 AOQ = = 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

226 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 P log P0 P P log log P P 0 P0 log P s = P P log log P P ( 06. )

227 Σ β log α h = P P log log P0 P0 Σ β 0. A = = = B = β = = 8 α α 005. log A = log B = 553. P P 080 log = log = log. = P P α P0 098 log = log = log = log. = A β P h = = h = = ( ) s = = ( )

228 A B C D () ( ) (mm)

229 θ. θ θ θ θ θ θ θ θ θ θ

230 θ θ θ θ. ( ) ( θ) θ =0.0 θ =0.0 θ =0.03 θ =0.04 a a θ θ θ θ θ θ

231

232 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 ( a = (. )

233 = 00 0 = 00( ).4 ( ) P(θ) a a

234

235

236

237 .5 ( ) = α + ( α) ( 3. )

238 .6 ( )

239 k θ θ, θ,, θ, P(θ ) k k k

240 µ = Wx + W µ 0 ( 4. ) x xµ.7 B A P θ θ P( θ ) P( X θ) P( θ X) = 3 ( 5. ) P( θ ) P( Xθ ) j= θ θ θ θ

241 4 4 P( X θ = 0. 4) = C ( 0. 4) ( 0. 6) = P( X θ = 0. 5) = C ( 0. 5) ( 0. 5) = P( X θ = 0. 6) = C ( 0. 6) ( 0. 4) = P( θ ) P( X θ ) P( θ X) = 3 P( θ ) P( Xθ ) j= P( θ X) = P( θ X) = ( 0. 3) ( ) = ( 0. 3)( ) + ( 05. )( 038. ) + ( 0. )( ) = = θ θ θ θ θ

242 A B C

243

244

245

246

247 = = = = = + +

248 = + = + = = = = = + = +

249

250 ( a) = ( ) = ( b) = + = =

251

252 a. + = + = b. + = = = = + = +

253 . A B 0 30 A B C C A 70 B 00 C 75 45

254 A B C A B C

255 .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 aa a 3 = a a a 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 (. )

256 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) ( I A) = e = 40 0% = q = I A e = =. ( )

257

258

259

260 ( ) = ( ) + ( ) +

261 .9 75 %

262 .0 ( ) ( )

263 . ( ) ( )

264

265

266

267

268

269 A B A B

270

271

272

., /,, 0!, + & )!. + + (, &, & 1 & ) ) 2 2 ) 1! 2 2

., /,, 0!, + & )!. + + (, &, & 1 & ) ) 2 2 ) 1! 2 2 ! # &!! ) ( +, ., /,, 0!, + & )!. + + (, &, & 1 & ) ) 2 2 ) 1! 2 2 ! 2 2 & & 1 3! 3, 4 45!, 2! # 1 # ( &, 2 &, # 7 + 4 3 ) 8. 9 9 : ; 4 ), 1!! 4 4 &1 &,, 2! & 1 2 1! 1! 1 & 2, & 2 & < )4 )! /! 4 4 &! &,

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