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. 4. (P.51 V(X E(X µ V(X E ( ( (x i µ f(x i, i (x µ f(xdx, σ, ( σx V(X E ( ( E(X µx + µ E(X µe(x + µ E(X µ µ E(X X V(X X ( ( V(X 3. a, b 4.3 (P.5 V(aX + b a V(X E(aX + b aµ + b 1. a, b 4.1 (P.51 E(aX + b ae(x + b X ( ((ax V(aX + b E + b E(aX + b E ((ax aµ E ( a ( a E ( ( a V(X E(aX + b i (ax i + bf(x i a x i f(x i + b f(x i i i ae(x + b f(x i 1 i X E(aX + b a + b (ax + bf(xdx xf(xdx f(xdx ae(x + b f(xdx 1 X x 1 x x 3 x 4 x 5 x 6 1 3 4 5 6 p 1 p p 3 p 4 p 5 p 6 1 1 6 1 6 1 6 1 6 1 6 1 6 E(X 6 x i p i 1 1 6 + 1 6 + 3 1 6 + 4 1 6 + 5 1 6 + 6 1 6 7 10

E(X 6 x i p i 1 1 6 + 1 6 + 3 1 6 + 4 1 6 + 5 1 6 + 6 1 6 91 6 V(X E(X µ 91 ( 7 6 35 1 1. σ V(X. X ( Z σ 3. 4.4 (P.5 E(Z 0, V(Z 1 4.1 (P.51, 4.3 (P.5 a 1 σ, b µ σ E(Z E( σ 1 E( σ 1 ( E( σ 0 V(Z V( σ 1 σ V(X 1 : (p + q x0 C x p x q x E(X p, V(X p(1 p E(X x x x x xf(x x C x p x (1 p x! x x!( x! px (1 p x! (x 1!( x! px (1 p x p ( 1! (x 1!( x! px 1 (1 p x x p! (1 x!( x! px p x x p x C x px (1 p x p 1, x x 1 V(X E(X µ E(X X X(X 1 + X E(X E ( X(X 1 + E(X V(X E ( X(X 1 + µ µ 1 x E ( X(X 1 x(x 1f(x x x(x 1 C x p x (1 p x f(x C x p x (1 p x! x!( x! px (1 p x, x 0, 1,,,, C x p x (1 p x 1 x x x! x(x 1 x!( x! px (1 p x! (x!( x! px (1 p x ( 1p x (! (x!( x! px (1 p x 11

( 1p! (1 x!( x! px p x x ( 1p x C x px (1 p x X \ Y y 1 y y m (X ( 1p, x x V(X E(X µ E ( X(X 1 + µ µ ( 1p + p p p + p p(1 p X Y X i, Y j (i, j 1,, 3, 4, 5, 6 P (X i, Y j P (X ip (Y j 1. p j, j 1,,, m 36 X Y y j X Y Y A, B (P.38: P (A B P (AP (B x 1 p 11 p 1 p 1m p 1 x p 1 p p m p............ x p 1 p p m p p 1 p p m 1 (Y 1. p i, i 1,,, X, Y 3. 1 Y X x i X 4.3 (P.54 m p i p ij f(x i P (X x i X, Y j1 f(x i X p j p ij f(y j P (Y y j f(y j Y P (X x i, Y y j p ij f(x i, y j i 1,,,, j 1,,, m f(x i, y j X \ Y y 1 y y m x 1 p 11 p 1 p 1m x p 1 p p m..... x p 1 p p m j1 m p ij m p i p j 1 j1 (P.55 A, B (P.36: P (A B P (A B P (B 1

Y y j X x i P (X x i Y y j P (X x i, Y y j P (Y y j Y y j X f(x i y j f(x i y j f(x i, y j f(y j A, B (P.38: P (A B P (AP (B X x i Y y j Y Y g(x, Y Y E(Y y j p ij y j f(x i, y j i j i j y j p ij y j p j y j f(y j j i j j µ y X ( x g(x, Y ( x V(X E ( ( x (x i µ x p ij i j (x i µ x f(x i, y j i j i (x i µ x j p ij i (x i µ x p i P (X x i, Y y j P (X x i P (Y y j i σ x (x i µ x f(x i f(x i, y j f(x i f(y j p ij p i p j i, j X Y (P.56 g(x, Y E ( g(x, Y E ( g(x, Y i i g(x i, y j p ij j g(x i, y j f(x i, y j j X X g(x, Y X E(X x i p ij x i f(x i, y j i j i j x i p ij x i p i x i f(x i i j i i µ x Y (Y µ y g(x, Y (Y µ y V(Y E ( (Y µ y (y j µ y p ij i j (y j µ y f(x i, y j i j j j σ y (y j µ y i (y j µ y f(y j p ij j (y j µ y p j X Y (X µ x (Y µ y g(x, Y ( x (Y µ y Cov(X, Y E ( ( x (Y µ y (x i µ x (y j µ y p ij i j (x i µ x (y j µ y f(x i, y j i j 13

1. X, Y 4.5 (P.57 E(X ± Y E(X ± E(Y E(X ± Y (x i ± y j p ij i j x i p ij ± y j p ij i j i j E(X ± E(Y. X Y 4.6 (P.57 E(XY E(XE(Y E(XY x i y j p ij i j x i y j p i p j i j x i p i y j p j i j E(XE(Y p ij p i p j 3. X, Y 4.7 (P.58 Cov(X, Y E(XY E(XE(Y Cov(X, Y (x i µ x (y j µ y p ij i j (x i y j µ x y j µ y x i + µ x µ y p ij i j x i y j p ij i j µ x y j p ij i µ y x i p ij i + µ x µ y i i j j j p ij x i y j p ij µ x µ y µ y µ x + µ x µ y j x i y j p ij µ x µ y i j E(XY E(XE(Y Cov(X, Y E ( ( x (Y µ y E ( XY µ x Y µ y X + µ x µ y E(XY E(µ x Y E(µ y X + µ x µ y E(XY µ x E(Y µ y E(X + µ x µ y E(XY µ x µ y µ y µ x + µ x µ y E(XY µ x µ y E(XY E(XE(Y 4. X Y 4.6 E(XY E(XE(Y Cov(X, Y 0 5. ρ xy (P.58 ρ xy Cov(X, Y V(X V(Y Cov(X, Y σ x σ y 6. X Y Cov(X, Y 0 ρ xy 0 7. X, Y V(X ± Y V(X ± Cov(X, Y + V(Y 14

X Y 8. 1 ρ xy 1 V(X ± Y ( ((X E ± Y E(X ± Y ( ((X E µx ± (Y µ y E ( ( x ± ( x (Y µ y +(Y µ y E ( ( x ± E ( ( x (Y µ y + E ( (Y µ y V(X ± Cov(X, Y + V(Y t f(t V(xt y t f(t 0 t E(X E( i V(xt y V(xt Cov(xt, y + V(y t V(x tcov(x, y + V(y D ( Cov(x, y V(xV(y 0 ( Cov(x, y V(xV(y 1 1 Cov(x, y V(x V(y 1 1 ρ xy 1 ρ xy 1 i ρ xy 1 9. X Y i 4.8 (P.59 V(X + Y V(X + V(Y V(X + Y V(X + Cov(X, Y + V(Y Cov(X, Y 0 V(X + Y V(X + V(Y 10. X 1, X,, X µ σ i 1,,, E(X i µ, V(X i σ X 1 X i 4.9 (P.59 E(X µ, V(X σ i i i µ V(X V( i i σ X i E( X i 1 E(X i 1 µ X i V( X i 1 V(X i 1 σ 4.5 (P.57 4.1 (P.51 4.8 (P.59 4.3 (P.5 15

4.1 (P.59 X, Y X \ Y 0 1 1 c 0.3 0. 0.1 3 P (X, Y 0 P (X Y 0 P (Y 0 0. 0.6 1 3 1. c c + 0.3 + 0. + 0.1 1 c 0.4. X Y X \ Y 0 1 X 1 c 0.3 0.7 0. 0.1 0.3 Y 0.6 0.4 1.0 3. X E(X i x i p ij j x i p i i 1 0.7 + 0.3 1.3 V(X E ( ( x E(X µ x x i p ij µ x i j 5. Z X + Y Z P (Z 1 P (X 1, Y 0 0.4 P (Z P (X 1, Y 1 + P (X, Y 0 0.3 + 0. 0.5 P (Z 3 P (X, Y 1 0.1 Z Z 1 3 P (Z 0.4 0.5 0.1 1 6. Y E(Y i y j p ij j y j p j j 0 0.6 + 1 0.4 0.4 x i p i µ x i 1 0.7 + 0.3 1.3 0.1 4. Y 0 X P (X 1, Y 0 P (X 1 Y 0 P (Y 0 0.4 0.6 16 V(Y E ( (Y µ y E(Y µ y yj p ij µ y i j j y j p j µ y 0 0.6 + 1 0.4 0.4 0.4

7. X Y Cov(X, Y E ( ( x (Y µ y E(XY µ x µ y x i y j p ij µ x µ y i j 1 0 0.4 + 1 1 0.3 + 0 0. + 1 0.1 1.3 0.4 0.0 8. X Y ρ xy Cov(X, Y V(X V(Y 0.0 0.1 0.4 0.089 5 (P.65 (χ t 1. x µ. ( ( µ 3. 1 f(xdx 1 N(0, 1 X N(µ, σ ( Z N(0, 1 (P.5 4.4 σ X 1, X,, X X i µ σ X 1 X i N(µ, σ (P.59 4.9 ( σ/ N(0, 1 5. (P.67 F (x F (x P (X x x f(tdt 5.1 (P.65 f(x ( 1 f(x exp 1 (x µ πσ σ exp(x e x π 3.14159 (, e.7188 ( E(X µ, V(X σ µ σ N(µ, σ X N(µ, σ X N(µ, σ 5.1 f(t (P.68, P.45 (P.68, P.45 N(0, 1 Z N(0, 1 P (Z > 1.96 N(0, 1 Z z P (Z > z P (Z > z α z 100α % P ( Z > z α P ( Z > z α z 100α/ % P (Z > 1.96 0.050 17

5.1 (P.68 P (Z 1.64 P (Z > 1.64 0.0505 5. (P.69 P (Z < 1.96 1 P (Z 1.96 1 0.050 0.9750 5.3 (P.69 P (Z < 1.96 P (Z > 1.96 0.050 5.4 (P.69 P ( 1.96 < Z < 1.64 1 P (Z > 1.64 P (Z > 1.96 1 0.0505 0.050 0.945 5.5 (P.70 P (0.5 < Z < 1.96 P (Z > 0.5 P (Z > 1.96 0.4013 0.050 0.3763 5.6 (P.71 X N(5, P (6 < X < 8 89.4 5.1 (P.7 Z N(0, 1 1. P (Z 1.57 0.058. P (Z < 1.34 1 P (Z > 1.34 1 0.0901 0.9099 3. P ( 0.37 < Z 1.6 1 P (Z > 0.37 P (Z > 1.6 1 0.3557 0.0548 0.5895 4. P (0.55 < Z < 1.67 P (Z > 0.55 P (Z > 1.67 0.91 0.0475 0.437 Z N(0, 1 σ Z X 5 N(0, 1 P (6 < X < 8 P ( 6 5 < X 5 P (0.5 < Z < 1.5 < 8 5 P (Z > 0.5 P (Z > 1.5 0.3085 0.0668 0.417 i.e., X N(, 3, i.e., Z X N(0, 1 5.7 (P.71 3 60 15 1. P (X 5.6.5 % P ( X 5.6 3 3 P (Z < 1. X X N(60, 15 Z X 60 15 Z N(0, 1 P (Z > z 0.050 z 1.96 P (Z > 1.96 0.050 P ( X 60 > 1.96 0.050 15 P (X > 89.4 0.050 5. P (.08 < Z < 0.1 P (0.1 < Z <.08 P (Z > 0.1 P (Z >.08 0.4168 0.0188 0.3980 5. (P.7 X N(, 9,. P (X < 10 P ( X < 10 3 3 P (Z <.67 3. P (1 < X 4.7 P ( 1 < X 4.7 3 3 3 P ( 0.33 < Z < 0.9 18

4. P (3. < X < 7.7 P ( 3. < X 3 3 P (0.4 < Z < 1.9 < 7.7 3 5. P ( 1.3 < X < 1.19 P ( 1.3 < X < 1.19 3 3 3 P ( 1.1 < Z < 0.7 6 (P.75 1 (P.95 T T f(x 1, X,, X X S 6.1 (P.77 (X 1, X,, X X 1, X,, X i 1,,, (1 4.9 (P.59 X (X 1, X,, X (x 1, x,, x X X 1, X,, X X N(µ, σ X µ X 1 (P.66 P.80 6.3 X i (3 E(X µ V(X σ S X ( ( 4.4 P.5 S 1 1 (X i X E(X i µ, V(X i σ X X 1 X i E(X µ, V(X σ ( i X i N(µ, σ σ Z X E(X σ/ V(X/ 19

1: N(0, 1 P.68, 45 Z 1 α Prob(Z > z α exp( 1 z α π x dx z α.00.01.0.03.04.05.06.07.08.09 0.0.5000.4960.490.4880.4841.4801.4761.471.4681.4641 0.1.460.456.45.4483.4443.4404.4364.435.486.447 0..407.4168.419.4091.405.4013.3974.3936.3897.3859 0.3.381.3783.3745.3707.3669.363.3594.3557.350.3483 0.4.3446.3409.337.3336.3300.364.38.319.3156.311 0.5.3085.3050.3015.981.3946.91.877.843.810.776 0.6.743.709.676.644.611.579.546.514.483.451 0.7.40.389.358.37.97.66.36.07.177.148 0.8.119.090.061.033.005.1977.1949.19.1894.1867 0.9.1841.1814.1788.176.1736.1711.1685.1660.1635.1611 1.0.1587.1563.1539.1515.149.1469.1446.143.1401.1379 1.1.1357.1335.1314.19.171.151.130.110.1190.1170 1..1151.1131.111.1094.1075.1057.1038.100.1003.0985 1.3.0968.0951.0934.0918.0901.0885.0869.0853.0838.083 1.4.0808.0793.0778.0764.0749.0735.07.0708.0694.0681 1.5.0668.0655.0643.0630.0618.0606.0594.058.0571.0559 1.6.0548.0537.056.0516.0505.0495.0485.0475.0465.0455 1.7.0446.0436.047.0418.0409.0401.0390.0384.0375.0367 1.8.0359.035.0344.0333.039.03.0314.0307.0301.094 1.9.087.081.074.068.06.056.050.044.039.033.0.08.0.017.01.007.00.0197.019.0188.0183.1.0179.0174.0170.0166.016.0158.0154.0150.0146.0143..0139.0136.013.019.015.01.0119.0116.0113.0110.3.0107.0104.010.0099.0096.0094.0091.0089.0087.0084.4.008.0080.0078.0076.0073.0071.0070.0068.0066.0064.5.006.0060.0059.0057.0055.0054.005.0051.0049.0048.6.0047.0045.0044.0043.004.0040.0039.0038.0037.0036.7.0035.0034.0033.003.0031.0030.009.008.007.006.8.006.005.004.003.003.00.001.001.000.0019.9.0019.0018.0018.0017.0016.0016.0015.0015.0014.0014 3.0.0013.0013.0013.001.001.0011.0011.0011.0010.0010 3.1.0010.0009.0009.0009.0008.0008.0008.0008.0007.0007 3..0007.0007.0006.0006.0006.0006.0006.0005.0005.0005 3.3.0005.0005.0005.0004.0004.0004.0004.0004.0004.0003 3.4.0003.0003.0003.0003.0003.0003.0003.0003.0003.000 α.10.05.05.010.005 z α 1.816 1.6449 1.9600.363.5758 0

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P ( 0 σ/ > z α/ α 0.01 H 0 1 α µ (x z α/ σ, x + z α/ σ µ 0 H 0 604 40 616 56 40 608 56 608 µ H 0 : µ 604 µ (σ 40, 56 H 0 : µ 616 H 1 : µ < 616 P ( X 616 40/ 56 < z α α 0 σ/ x 616 40/ 56 < z α α x µ 0 σ/ < z x µ 0 α/ σ/ > z H 0 α/ α 0.01 H 0 : µ µ 0 x 616 α H 0 (H 1 40/ 56 608 616 α µ µ 0 40/ 56 3. < z α.36 H 1 : µ 604 H 0 : µ 616 H 1 : µ < 616 i X i N(µ, σ (σ 40 X X N(µ, σ σ/ N(0, 1 i X i N(µ, σ (σ 40 X X N(µ, σ σ/ N(0, 1 (σ 40, 56 37

H 0 : µ 604 H 1 : µ 604 α 0.05 z α 1.645 P ( X 616 40/ α 0.10 z α 1.8 56 > z α/ α x 10 0/ 135 10 4 0/ 1.5 < z 0.01.36 4 x 604 40/ 56 < z x 604 α/ 40/ 56 > z α/ 0.01 H 0 α H 0 α 0.05 x 10 x 604 40/ 0/ 135 10 4 0/ 1.5 < z 0.05 1.645 4 56 608 604 40/ 0.05 H 0 56 1.6 < z α/ 1.96 x 10 0.05 H 0 0/ 135 10 4 0/ 1.5 > z 0.10 1.8 4 0.10 H 0 8.1 (P.138 8.4 (P.139 1986 µ 10 σ 0 1 80.9 m (SIS 100 6.5 m 4 135 ( 18 m 1 %, 5 %, 10 % X i X i N(µ, σ, i 1,,, σ 0, 4 X N(µ, σ σ/ N(0, 1 H 0 : µ 10 H 1 : µ > 10 H 0 X 10 0/ N(0, 1 4 P ( X 10 0/ 4 > z α α α 0.01 z α.36 X 1, X,, X X i N(µ, σ σ/ N(0, 1 H 0 : µ µ 0 H 1 : µ < µ 0 H 0 0 σ/ N(0, 1 P ( 0 σ/ < z α α 38

x µ 0 σ/ < z α H 0 : µ µ 0 0 α H 0 S/ (H 1 x µ 0 α µ µ 0 α H 0 (H 1 18 m σ 18 α 0.05 z α 1.645 100, µ 0 80.9, x 80.9 ( x µ 0 σ/ 6.5 80.9 18/ 100 10. < z α 1.645 H 0 : µ µ 0 0.05 H 0 H 1 : µ > µ 0 H 0 8.5 t ( 0 S/, P.16 N(µ, σ X 1, X,, X X X N(µ, σ 0 S/ σ/ x µ 0 N(0, 1 s/ > t α( 1 H 0 : µ µ 0 α H 0 (H 1 σ σ S α µ µ 0 S/ t( 1 ( 6.5, P.86 1 ( H 0 : µ µ 0 H 1 : µ < µ 0 H 0 0 S/ t( 1 P ( 0 S/ < t α( 1 α s/ < t α( 1 H 0 : µ µ 0 α µ µ 0 t( 1 P ( 0 σ/ > t α( 1 α 3 ( H 0 : µ µ 0 H 1 : µ µ 0 H 0 0 S/ t( 1 P ( 0 σ/ > t α/( 1 α 0 S/ 39

x µ 0 s/ < t x µ 0 α/( 1 s/ > t α/( 1 P ( 0 H 0 : µ µ 0 S/ < t α( 1 α α H 0 (H 1 α µ µ 0 x µ 0 s/ < t α( 1 H 0 : µ µ 0 1 α µ (x t α/ ( 1 s, x + t α/ ( 1 s µ 0 H 0 (1 x µ 0 s/ 40.7 41 0.9/ 5 1.68 > t 0.01(4.49 H 0 8.5 (P.18 1986 ( 144 x µ 41 (1 0 s/ 5 40.5 41 40.7 0.8/ 144 0.9 7.50 > t 0.01 (143 z 0.01.36 0.01 ( H 0 144 40.7 0.9 0.01 X 1, X,, X X i N(µ, σ σ/ N(0, 1 σ S S/ t( 1 µ 0 41 α H 0 (H 1 α µ µ 0 8.3 (P.139 740 630 690 3 3 16 655 60 (1 5 % 3 ( µ µ 95 % 3 H 0 : µ µ 0 H 1 : µ < µ 0 H 0 X 1, X,, X X i N(µ, σ σ/ N(0, 1 σ S 0 S/ t( 1 S/ t( 1 40

H 0 : µ µ 0 H 1 : µ µ 0 H 0 0 S/ t( 1 P ( 0 σ/ > t α/( 1 α x µ 0 s/ < t x µ 0 α/( 1 s/ > t α/( 1 H 0 : µ 740 H 0 : µ µ 0 H 0 : µ 630 (H 1 H 0 : µ 690 α H 0 α µ µ 0 (1 α 0.05 t 0.05 (15.131 ( H 0 : µ 740 H 1 : µ 740 x µ 0 s/ 655 740 60/ 16 5.67 < t 0.05(15.131 H 0 H 0 : µ 630 H 1 : µ 630 x µ 0 s/ 655 630 60/ 16 1.67 < t 0.05(15.131 H 0 H 0 : µ 690 H 1 : µ 690 x µ 0 s/ 690 740 60/ 16.33 < t 0.05(15.131 H 0 σ σ/ N(0, 1 ( 1 α µ H 0 : µ µ 0 S/ t( 1 P ( σ/ < t α/( 1 α ( 16 P S/ < t α/( 1 1 α α 0.05 t α/ ( 1.131 1 α µ (x t α/ ( 1 s, x + t α/ ( 1 s 0.95 µ (655.131 60 16, 655 +.131 60 16 (63, 687 0.95 µ (63, 687 0.05 0.05 0.05 X 1, X,, X E(X i µ, V(X i σ ( 6.1, P.81 X E(X V(X σ/ N(0, 1 σ S 0 σ/ S/ N(0, 1 N(0, 1 (µ µ 0 0 σ/ x µ 0 σ/ 1. H 1 : µ < µ 0 ( 41

( 0 P σ/ < z x µ 0 α α σ/ < z 1 α X 1i N(µ 1, σ1, i 1,,, 1 α H 0 : µ µ 0 X 1 1 1 X 1i 1. H 1 : µ > µ 0 ( S1 1 1 (X 1i X 1 ( 0 1 1 P σ/ > z x µ 0 α α σ/ > z α α H 0 : µ µ 0 X i N(µ, σ, i 1,,, 3. H 1 : µ µ 0 ( ( P 0 σ/ X 1 X i > z α/ α x µ 0 σ/ > z α/ α H 0 : µ µ 0 S 1 (X i X 1 X 1 X σ S/ N(0, 1 4.1 (P.51 4.5 (P.57 H 0 : µ µ 0 0 S/ N(0, 1 (µ µ 0 0 S/ x µ 0 s/. H 1 : µ > µ 0 ( ( σ ( 0 (X1 X (µ 1 µ / 1 + σ N(0, 1 P S/ > z x µ 0 α α s/ > z 1 α α H 0 : µ µ 0 3. H 1 : µ µ 0 ( ( P 0 S/ > z α/ α x µ 0 s/ > z α/ α H 0 : µ µ 0 8.6 (P.19 E(X 1 X µ 1 µ 4.3 (P.5 4.8 (P.59 V(X 1 X σ 1 + σ 1 1. H 1 : µ < µ 0 ( ( 0 P S/ < z x µ 0 α α s/ < z α α H 0 : µ µ 0 X 1 X N(µ 1 µ, σ 1 1 + σ 1 ( H 0 : µ 1 µ H 1 : µ 1 < µ H 0 / σ1 (X 1 X + σ N(0, 1 1 8.6.1 ( 1 / σ1 P ((X 1 X + σ < z α α 1 4

(X 1 X (x 1 x / / ( H 0 : µ 1 µ H 1 : µ 1 > µ σ1 + σ (X 1 X 1 σ1 + σ < z α H 0 : 1 (x 1 x H 0 / σ1 (X 1 X + σ N(0, 1 1 / σ1 P ((X 1 X + σ > z α α 1 (X 1 X / σ1 N(µ + σ 1, 30.5 N(µ, 75.6 1 / σ1 (x 1 x + σ > z α H 0 : 1 1 µ 1 µ X 1 X N(µ 1 µ, σ 1 + σ α H 0 (H 1 1 α µ 1 µ ( (X 1 X (µ 1 µ 3 ( H 0 : µ 1 µ H 1 : µ 1 µ H 0 / σ1 (X 1 X + σ N(0, 1 1 + σ < z α/ µ 1 µ 1 α H 0 (H 1 / σ α µ 1 µ 1 (x 1 x + σ > z α/ 1 / σ 1 / σ 1 1 + σ H 0 : µ 1 µ α H 0 (H 1 α µ 1 µ 8.6 (P.131 5 64 9 56 5% H 0 : µ 1 µ H 1 : µ 1 > µ / σ 1 1 + σ N(0, 1 H 0 / σ1 (X 1 X + σ N(0, 1 1 / σ1 P ( X 1 X + σ > z α/ α 1 / σ1 P ((X 1 X + σ > z α α 1 43

/ σ1 (x 1 x + σ > z α H 0 : 1 S1 1 1 (X 1i X 1 1 1 µ 1 µ α H 0 (H 1 S 1 (X i X α µ 1 µ 1 α 0.05 z α 1.645 x 1 64, x 56, σ1 30.5, σ 75.6, 1 5, 9 / 8.6. ( 1,, P.13 1 1 X 1i N(µ 1, σ 1, i 1,,, 1 X 1 X i N(µ, σ, i 1,,, α H 0 (H 1 X α µ 1 µ 1,, X 1 X s 1 1 1 (x 1i x 1 1 1 / σ1 X 1 X + σ N(0, 1 1 t σ1 (x 1 x + σ 1 ( 1 / H 0 : µ 1 µ 30.5 (64 56 5 + 75.6 H 1 : µ 1 < µ 9.10 > z 0.05 1.645 H 0 H 0 / (X 1 X S 1 1 + S N(0, 1 / S1 P ((X 1 X + S < z α α 1 (X 1 X (x 1 x / / σ1, σ S 1, S 1, ( 6.1, P.81 ( / S1 X 1 X + S H 0 : µ 1 µ N(0, 1 1 H 1 : µ 1 > µ S 1 1 + S s 1 + s < z α H 0 : 1 µ 1 µ s 1 1 (x i x 44

H 0 8.7 (P.13 / S 1 (X 1 X + S N(0, 1 1 / S1 P ((X 1 X + S > z α α 1 (X 1 X / S1 + S 1 1 1, / s 1 (x 1 x + s > z α H 0 : 1 X 1 X N(µ 1 µ, S 1 + S 1 µ 1 µ α H 0 (H 1 ( / (X 1 X (µ 1 µ α µ 1 µ 3 ( H 0 : µ 1 µ H 1 : µ 1 µ H 0 / / S1 (X 1 X + S S N(0, 1 1 (X 1 1 X + S N(0, 1 1 / S1 P ( X 1 X + S > z α/ α 1 (X 1 X / S1 + S 1 (X 1 X 154 615 40 10 606 3 / / s s 1 (x 1 x + s 1 (x 1 x + s > z α H 0 : < z α/ 1 1 µ 1 µ / s α H 0 (H 1 1 (x 1 x + s > z α/ α µ 1 1 µ H 0 : µ 1 µ α H 0 (H 1 α 0.05 z α 1.645 α 0.01 z α.36 α µ 1 µ 10 1 %, 5 % H 0 : µ 1 µ H 1 : µ 1 > µ S 1 1 + S N(0, 1 H 0 1, / S1 P ((X 1 X + S > z α α 1 / S 1 1 + S x 1 615, x 606, s 1 40, s 3, 1 154, 45

/ s 1 (x 1 x + s 1 / 40 (615 606 154 + 3 10.07 > z 0.05 1.645 Z X E(X 0.05 H 0 V(X/.07 > z 0.01.36 1 ( 0.01 H 0 H 0 : p p 0 H 1 : p < p 0 X X 1, X,, X ( 6.1, P.81 p(1 p E(X p, V(X X p p(1 p/ N(0, 1 8.7 (P.136 ( i X i 1 X i 0 R X i R 1 p P (X i 1 p X i E(X i 1 P (X i 1 + 0 P (X i 0 p V(X i (1 p P (X i 1 +(0 p P (X i 0 p(1 p H 0 X p 0 N(0, 1 p0 (1 p 0 / X p 0 P ( p0 (1 p 0 / < z α α X p 0 p0 (1 p 0 / x p 0 p0 (1 p 0 / < z α H 0 : p p 0 α H 0 (H 1 α p p 0 p p 0 p0 (1 p 0 / < z α α p p 0 P.50 51 (4.1 ( (4.14 H 0 : p p 0 p X H 1 : p > p 0 X R 1 X i ( p X p E(X 1 E(X E(X p V(X 1 V(X V(X p(1 p H 0 X p 0 N(0, 1 p0 (1 p 0 / X p 0 P ( p0 (1 p 0 / > z α α 46

1350 65 X p 0 p0 (1 p 0 / 170 x p 0 p0 (1 p 0 / > z α H 0 : p p 0 α H 0 (H 1 X p Z N(0, 1 α p p 0 p(1 p/ p p 0 p0 (1 p 0 / > z α α p p 0 3 ( H 0 : p p 0 H 1 : p p 0 H 0 X p P ( 0 X p p0 (1 p 0 / > z α α 0 N(0, 1 p0 (1 p 0 / X p 0 p0 (1 p 0 / X p 0 P ( p0 (1 p 0 / > z α/ α x p 0 p0 (1 p 0 / > z α H 0 : p p 0 α H 0 (H 1 X p 0 p0 (1 p 0 / α p p 0 x p0 p0 (1 p 0 / < z p p 0 α/ p0 (1 p 0 / > z p 0 0.109 α/ α 0.05 z α 1.645 H 0 : p p 0 1350, x 170 1350 1.16 α H 0 (H 1 x p 0 α p p 0 p p 0 p0 (1 p 0 / < z α/ p p 0 p0 (1 p 0 / < z α/ α p p 0 H 0 : p p 0 H 1 : p > p 0 H 0 X p 0 N(0, 1 p0 (1 p 0 / p0 (1 p 0 / 0.16 0.109.00 > z α 0.109(1 0.109/1350 1.645 0.05 H 0 65 1987 10.9 % 47

( µ X 1 X i x 1 x i σ S 1 (X i X s 1 (x i x 1 1 p (? X R 1 X i x 1 x i ( p {X 1, X,, X } {x 1, x,, x } R x X S X µ {X 1, X,, X } i 1,,, X i N(µ, σ σ ( σ/ N(0, 1 P σ/ < z α/ 1 α z α/ 100 α % α (P.45 σ σ P (X z α/ < µ < X + z α/ 1 α σ σ X x 1 α µ (x z α/, x + z α/ σ ( S/ t( 1 P S/ < t α/( 1 1 α t α/ ( 1 100 α % α 1 t (P.47 P (X t α/ ( 1 S < µ < X + t α/ ( 1 S 1 α ( X, S x, s 1 α µ x t α/ ( 1 s, x + t α/ ( 1 s 48

(, {X 1, X,, X } i 1,,, X i (µ, σ ( σ ( 6.1, P.81 ( σ/ N(0, 1 P σ/ < z α/ 1 α σ σ P (X z α/ < µ < X + z α/ 1 α σ σ X x 1 α µ (x z α/, x + z α/ σ σ S σ/ N(0, 1 ( S/ N(0, 1 P S/ < z α/ 1 α S S P (X z α/ < µ < X + z α/ 1 α ( X, S x, s s s 1 α µ x z α/, x + z α/ σ ( p X p p(1 p/ N(0, 1 p X X p ( X p N(0, 1 P X(1 X/ X(1 X/ < z α/ 1 α ( X(1 X X(1 X P X z α/ < p < X + z α/ 1 α ( x(1 x x(1 x X x 1 α p x z α/, x + z α/ 49

( µ {X 1, X,, X } i 1,,, X i N(µ, σ σ X σ/ N(0, 1 H 0 : µ µ 0 0 σ/ N(0, 1 (µ µ 0 0 σ/ x µ 0 σ/ 1. H 1 : µ < µ 0 ( ( 0 P σ/ < z x µ 0 α α σ/ < z α α H 0 : µ µ 0. H 1 : µ > µ 0 ( ( 0 P σ/ > z x µ 0 α α σ/ > z α α H 0 : µ µ 0 3. H 1 : µ µ 0 ( ( P 0 σ/ > z α/ α x µ 0 σ/ > z α/ α H 0 : µ µ 0 σ X S/ t( 1 H 0 : µ µ 0 0 S/ t( 1 (µ µ 0 0 S/ x µ 0 s/ 1. H 1 : µ < µ 0 ( ( 0 P S/ < t x µ 0 α( 1 α s/ < t α( 1 α H 0 : µ µ 0. H 1 : µ > µ 0 ( ( 0 P S/ > t x µ 0 α( 1 α s/ > t α( 1 α H 0 : µ µ 0 3. H 1 : µ µ 0 ( ( P 0 S/ > t α/( 1 α x µ 0 s/ > t α/( 1 α H 0 : µ µ 0 ( {X 1, X,, X } i 1,,, X i (µ, σ ( 50

σ σ/ N(0, 1 H 0 : µ µ 0 0 σ/ N(0, 1 (µ µ 0 0 σ/ x µ 0 σ/ 1. H 1 : µ < µ 0 ( ( 0 P σ/ < z x µ 0 α α σ/ < z α α H 0 : µ µ 0. H 1 : µ > µ 0 ( ( 0 P σ/ > z x µ 0 α α σ/ > z α α H 0 : µ µ 0 3. H 1 : µ µ 0 ( ( P 0 σ/ > z α/ α x µ 0 σ/ > z α/ α H 0 : µ µ 0 σ S/ N(0, 1 H 0 : µ µ 0 0 S/ N(0, 1 (µ µ 0 0 S/ x µ 0 s/ 1. H 1 : µ < µ 0 ( ( 0 P S/ < z x µ 0 α α s/ < z α α H 0 : µ µ 0. H 1 : µ > µ 0 ( ( 0 P S/ > z x µ 0 α α s/ > z α α H 0 : µ µ 0 3. H 1 : µ µ 0 ( ( P 0 S/ > z α/ α x µ 0 s/ > z α/ α H 0 : µ µ 0 (H 0 : µ 1 µ 1 1 i 1,,, X 1i N(µ 1, σ1 i 1,,, X i N(µ, σ σ1 σ X 1 X 4.1 (P.51 4.5 (P.57 E(X 1 X µ 1 µ 4.3 (P.53 4.8 (P.59 V(X 1 X σ 1 + σ X 1 X N(µ 1 µ, σ 1 + σ ( 1 1 51

(X 1 X (µ 1 µ X 1 X N(0, 1 H 0 : µ 1 µ σ1 / 1 + σ / σ 1/ 1 + σ / N(0, 1 X 1 X x 1 x (µ 1 µ 0 σ 1/ 1 + σ / σ 1/ 1 + σ / 1. H 1 : µ 1 < µ ( ( X 1 X P σ 1/ 1 + σ / < z α α x 1 x σ 1/ 1 + σ / < z α α H 0. H 1 : µ 1 > µ ( ( X 1 X P σ 1/ 1 + σ / > z α α x 1 x σ 1/ 1 + σ / > z α α H 0 3. H 1 : µ 1 µ ( ( X 1 X P σ1/ 1 + σ/ > z α/ α x 1 x σ1/ 1 + σ/ > z α/ α H 0 σ1 σ ( t ( 1, 1 1 i 1,,, X 1i (µ 1, σ1 ( i 1,,, X i (µ, σ ( σ1 σ (X 1 X (µ 1 µ σ1 / 1 + σ / N(0, 1 H 0 : µ 1 µ X 1 X X 1 X σ 1/ 1 + σ / N(0, 1 (µ 1 µ 0 σ 1/ 1 + σ / x 1 x σ 1/ 1 + σ / 1. H 1 : µ 1 < µ ( ( X 1 X P σ 1/ 1 + σ / < z α α x 1 x σ 1/ 1 + σ / < z α α H 0. H 1 : µ 1 > µ ( ( X 1 X P σ 1/ 1 + σ / > z α α x 1 x σ 1/ 1 + σ / > z α α H 0 5

3. H 1 : µ 1 µ ( ( X 1 X P σ1/ 1 + σ/ > z α/ α x 1 x σ1/ 1 + σ/ > z α/ α H 0 σ1 σ (X 1 X (µ 1 µ S1 / 1 + S / N(0, 1 H 0 : µ 1 µ X 1 X X 1 X S 1/ 1 + S / N(0, 1 (µ 1 µ 0 S 1/ 1 + S / x 1 x s 1/ 1 + s / 1. H 1 : µ 1 < µ ( ( X 1 X P S 1/ 1 + S / < z α α x 1 x s 1/ 1 + s / < z α α H 0. H 1 : µ 1 > µ ( ( X 1 X P S 1/ 1 + S / > z α α x 1 x s 1/ 1 + s / > z α α H 0 3. H 1 : µ 1 µ ( ( X 1 X P S1/ 1 + S/ > z α/ α x 1 x s 1/ 1 + s / > z α/ α H 0 p X p N(0, 1 H 0 : p p 0 p(1 p/ X p 0 N(0, 1 p0 (1 p 0 / (p p X p 0 0 p0 (1 p 0 / x p 0 p0 (1 p 0 / 1. H 1 : µ < µ 0 ( ( X p 0 P p0 (1 p 0 / < z α α x p 0 p0 (1 p 0 / < z α α H 0 : µ µ 0. H 1 : µ > µ 0 ( ( X p 0 P p0 (1 p 0 / > z α α x p 0 p0 (1 p 0 / > z α α H 0 : µ µ 0 3. H 1 : µ µ 0 ( ( X p 0 P p0 (1 p 0 / > z x p 0 α/ α p0 (1 p 0 / > z α/ α H 0 53

9 α, β (Y i α βx i 0, (1 9.1 (X 1, Y 1, (X, Y,, (X, Y X i Y i Y i α + β X i, (3 Y i α + βx i, X i Y i α X i Y i α, β ( ( Y ( i α β {(X i, Y i, i 1,,, } X X i iy i X i X i (Y i α βx i 0, ( X i + β Xi, X i ( 1 ( a b 1 d b c d ad bc c a 1. ( i α, β ( i ( α β ( α β,. ( i ( i i ( X i X i X i 1 ( Y i X iy i 9. α β S(α, β S(α, β u i mi S(α, β α,β (Y i α βx i α, β ( α, β S(α, β α S(α, β β 0 0 α, β α, β 1 X i ( X i ( X i X i X i β ( Y i X iy i β X iy i ( X i( Y i X i ( X i X iy i XY X i X (X i X(Y i Y (X i X (3 α Y βx X 1 X i, Y 1 Y i, 54

Y i α + βx i i Y i X i X i Y i Xi Ŷ i α β α β 1 6 10 60 100 6.8 i Y i X i 1 6 10 9 1 3 10 14 4 10 16 α β β X iy i XY X i X α Y βx X Y Xi X i Y i i Y i X i X i Y i Xi 1 6 10 60 100 9 1 108 144 3 10 14 140 196 4 10 16 160 56 Y i Xi Xi Y i X i 35 5 468 696 Y X 8.75 13 468 4 13 8.75 β 696 4 13 13 0 0.65 α 8.75 0.65 13 0.3 Y i 9 1 108 144 8.1 3 10 14 140 196 9.4 4 10 16 160 56 10.7 Y i Xi Xi Y i X i Ŷi Y 10 5 0 35 5 468 696 35.0 X 8.75 13 by i Y i X i Ŷi 0 5 10 15 0 X i Ŷ i Y i û i Y i Ŷi, û i Y i Ŷi + û i α + βx i + û i, Y (Y i Y (Ŷi Y + û i, 1. α, β. α, β 9.3 û i α, β Ŷ i α + βx i, Ŷ i 0.3 + 0.65X i û i Y i α βx i (1 û i 0, ( X i û i 0, 55

Ŷ i α + βx i Ŷ i û i 0, Ŷ i û i ( α + βx i û i α 0 û i + β X i û i 1.. 3. (Y i Y y (Ŷi Y Ŷi ( û i Ŷi ( R R (Ŷi Y (Y i Y i Y i X i Yi b bu i X i bu i Yi b bu i 1 6 10 6.8 0.8 8.0 5.44 9 1 8.1 0.9 10.8 7.9 3 10 14 9.4 0.6 8.4 5.64 4 10 16 10.7 0.7 11. 7.49 P P P Y i Xi byi P P P bui Xibu i byibu i 35 5 35.0 0.0 0.0 0.00 9.4 R (Y i Y (Ŷi Y + û i, (Y i Y ((Ŷi Y + û i (Ŷi Y + (Ŷi Y û i + (Ŷi Y + (Y i Y (Ŷi Y + û i 1 (Ŷi Y (Y i Y + û i (Y i Y û i û i R 1 û i (Y i Y, Y i Ŷi + û i (Ŷi Y (Ŷi Y (Y i Y û i (Ŷi Y (Y i Y (Ŷi Y (Y i Y R (Ŷi Y (Y i Y (Ŷi Y û i ( (Ŷi Y (Y i Y (Ŷi Y (Ŷi Y (Y i Y (Y i Y (Ŷi Y R Y i Ŷi Ŷ i α + βx i Y α + βx (Ŷi Y β (X i X 56

β (X i X(Y i Y α β R β (X i X β X iy i XY (Y i Y X i X β α Y βx (X i X(Y i Y (Y i Y X Y X i X i Y i (X i X(Y i Y (Y i Y (X i X ( β R X i X (Y i Y (Ŷi Y + û i Y i Y β X Y X 0 R i Yi 1, R 1 t 9.5 0.9 ( β R X i X Y i Y β X Y Xi Y i i Y i X i Yi Xi 1 6 10 36 100 9 1 81 144 3 10 14 100 196 4 10 16 100 56 Y i Xi Y i X i 35 5 317 696 Y X 8.75 13 β 0.65 X 13 Y 8.75 317 X i 696 Yi R 0.65 (696 4 13 317 4 8.75 8.45 10.75 0.786 57

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