10:30 12:00 P.G. vs vs vs 2

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1 1

2 10:30 12:00 P.G. vs vs vs 2

3 LOGIT PROBIT TOBIT mean median mode CV 3

4 4

5 5

6

7 45 7

8 P(A B) = P(A) + P(B) - P(A B) P(B A)=P(A B)/P(A) P(A B)=P(B A) P(A) P(A B) P(A) P(B A) P(B) P(A B) P(A) P(B) P(B A)P(A) P(A B) P(B A)P(A) P(B A c )P(A c ) 8

9 9

10 10

11 P( ) P( ) 1- X P( X=x ) C x p x q n-x B(n,p) 11

12 X n x λ p(x) C x λs n x λs n n-x p(x) λ x exp λ x! X 0,1, 12

13 x a<x<b a b 1/ ba E(x)= 1/ b-a ab xdx =(a+b)/2 V(x)=(b-a) 2 /12 13

14 normal distribution N µ 0 1 N 0, 1 µ 14

15 N 0 1 µ=0 σ 2 =1 - s + s µ 68.2% 95.4% 15

16 µ=0 σ 2 =0.5 N (0, 1) N (0, 2) N (0, 0.5) σ 2 =1 σ 2 =2 16

17 µ = -2 µ = 0 µ = 2 N (-2, 1) N (0, 1) N (2, 1) σ 2 =1 17

18 µ µ X,Y 18

19 19

20 X µ σ 2 X n {X 1 X 2 X n } µ /n 20

21 2 i 1, 2,., m i µ 21

22 3 Z 22

23 4 X n {X1 X2,, Xn} X µ c 23

24 5 X n {X1 X2,, Xn} c 24

25 6 n {X1 X2,, Xn} i 1, 2, n µ n 25

26 7 n {X1 X2,, Xn} n

27 χ 2 t χ 2 χ 2 27

28 2 Z1 Zk k k 28

29 χ 2 W W Z1 Z1 1 W k W Z Z 2 k 2 E(z 4 =3 V W 2k 2 Xi µ k 29

30 χ

31 t Z W k Z W k t k t t t

32 t 0 k/(k 2) 1 1 t 32

33 Z P c P Z c 33

34 F V m W k V W V W m k F F F F k/(k 2) k 3 k 1 34

35 F

36 estimator vs estimate vs vs 36

37 µ 12 76, 63, 83, 86, 53, 71 95% Z= = µ σ 2 /n= 144/6 24 Z 95% P( 1.96 Z 1.96 ) µ 64.2 µ

38 (unbiasness) consistency efficiency sufficiency 38

39 moment method (maximum likelyhood method) 39

40 (alternative) hypothesis (null hypothesis) p p 0 test statistics) 10%

41 critical value) α β 41

42 1%,5%,10% 42

43 25 P: P 0 : H 0 : P P 0 Ha: P P 0 H 0 : P P 0 H 0 : P P 0 43

44 3.1kg 0.2kg kg 3.1kg 0.2/

45 α 0.05 β=0.198 H a :µ=3.1 H 0 :µ=3.1 α β Z=-2.5( =3) Z=0 ( =3.1) Z=-1.65( =3.034) 45

46 46

47 cm 158.5cm cm 152.2cm µ cm 5.07cm 37 µ µ µ µ

48 C 48

49 n-1 49

50 µ=1200 µ n 100 1% z 0 =2.33 X 1200+(120/10)2.33=1228 1% P 0.01 α 0 ξ 100α µ 100α ξ α µ 100(1- α)% µ 0 µ 0 50

51 51

52 1) 2) n 1 +n 2-2 t 3) σ 12 σ S 22 52

53 3)

54 100 α/2 Z α/2 Z 0 b=1.65, p=1/6-1.65{1/6(1-1/6)/25} 0.5 =0.044,

55 55

56 2 X,Y ρ n-2 T r= T 3.0 n=12 5%

57 f(x,θ) L 0 L a La 0 λ 6.1 X X 1 X n θ θ 1 θ k H 0 θ 1 =c 1 θ c n -2log(λ) χ 2 χ2 57

58 χ χ E = n x x TSS = 58

59 59

60 60

61 61

62 62

63 63

64 64

65 65

66 correlation coefficient 2 66

67 20 ( ) = α + β ( ) + 67

68 ( ) (kg) 68

69 69

70 y y j y k µ k µ j x 70

71 y y j µ j y k µ k U i (0,σ 2 ) (i=j,k) x 71

72 72

73 73

74 74

75 75

76 76

77 (1),(2) a b n 77

78 78

79 79

80 80

81 81

82 82

83 83

84

85

86 86

87

88 88

89 DW DW 2(1 r) DW

90 DW dl du dw<dl du<dw<4-du 4-dL<dw DL<dw<dU 4-dU<dw<4-dL 90

91 DW 10 h< <h< <h 1-nv 0 e j e j-1 e j-1 91

92 1% % DW

93 93

94 94

95 95

96

97 1% P DW 97

98 98

99 99

100 100

101 FI* FI* FI* β 1 β 2 X i ei FI FI* FI

102 FI* FI FI Pi Pr FI= Pr FI* Pr ε i β 1 β 2 X i Pr ε i β 1 β 2 X i (1) ε i (1) P i Pr ε i β 1 β 2 X i Φ β 1 β 2 X i

103 β 1 β 2 Δ β 1 β 2 X i

104 2 Censored odel Truncated model FI* FI i * β 1 β 2 X i i FI FI*

105 FI* FI* 0

106

107 FDIB z SB ET APCC NAFTA EU _ AIC= NAFTA EU 1980

108 FDIB z- - C SB ET APCC AIC=

109 FDIB z- - C SB ET APCC _89 ) AIC=

110 4 FDIB z- - C SB ET APCC _89(80 ) AIC=

111 RDSA FDI [FDI] [RDSA]=17.44 [RDSA] LSALE FDI [FDI] ( ) [LSALE]=6.214 [LSALE]

112 33 4 p

113 < > < >

114 Rxy(τ τ

115 Dxy(θj Px (θj X Y X(t) Y(t) πθj τ θj X(t) Y(t) τ θj X(t) Y(t)

116 MBP kg AOP kg STN

117

118 χα22(v) α% α α χ2 P(θj V V

119

120

121 ii iii

122 50ha X 1 ha X 2 ha ha 1ha 100 ha 50 ha ha 80 ha 100 ha X 1 + X 2 50 X 1 + X X X X X 2 Z 122

123 XX2 2 X 2 =0.8X Z 123

124 (i) x 1,x 2,x 3,x 4 S y 1,y 2,y 3 y 1 50 y 2 =100 y 3 =3000 (ii) y 1,y 2,y 3 0 (iii)z j -C j S 0 (i) Z j -C j (ii)s R 2 (iii) (iv) (iii) 2 (v) Z j -C j Zj Cj Z j C j 2 Z j -C j 3 Z j -C j R Z j -C j S y2=20 20 =40 40 x2=10 10ha Z 124 j - C j =

125 y2 125

126 X1 + X X X X X2 360 Z X1 + X2 126

127 127

128 128

n Y 1 (x),..., Y n (x) 1 W (Y 1 (x),..., Y n (x)) 0 W (Y 1 (x),..., Y n (x)) = Y 1 (x)... Y n (x) Y 1(x)... Y n(x) (x)... Y n (n 1) (x) Y (n 1)

n Y 1 (x),..., Y n (x) 1 W (Y 1 (x),..., Y n (x)) 0 W (Y 1 (x),..., Y n (x)) = Y 1 (x)... Y n (x) Y 1(x)... Y n(x) (x)... Y n (n 1) (x) Y (n 1) D d dx 1 1.1 n d n y a 0 dx n + a d n 1 y 1 dx n 1 +... + a dy n 1 dx + a ny = f(x)...(1) dk y dx k = y (k) a 0 y (n) + a 1 y (n 1) +... + a n 1 y + a n y = f(x)...(2) (2) (2) f(x) 0 a 0 y (n) + a 1 y

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