1 [ ]H L E B ( ) statistics state G (150l--1576) G (1564 1642) 16 17 ( ) C B (1623 1662) P (1601--16S5) O W (1646 1716) (1654 1705) (1667--1748) (1687--H59) (1700 1782) J (1620 1674) W (1623 1687) E (1656 1742) A (1667 1754) 1733
M (1749 1827) K F (1777 1855) A M (1752 1833) 1815 (probable error) F W (1784 1846) J (1692 1770) n! M (1743 1794) T (1702 176 1) L (1707 1783) T (1710 1761) L R (1717 1783) L (1736 1813) Po B (1678 1719) C (1707 1788) S D (1781 1840) 1835 1870 L A J. (1796 1874) O F (1842 1926) W (1837 1914) 19 25 F (1822 1911) K (1857 1936) ( ) C B (1863 1945) 2 χ! (mean de Viatlon) (standard de V1ation) W S (1876 1937) R A (1890 1962) (null hypothesis) 2
, 3
( ) E 4 4 4 4 ( ). 4
5
6
7
8
9
10
A ( ) ( ) ( ) ( ) 1 2 11
1. : (1) (2) (3) ( 0 5) L A i i ( i = 1,2, L,6) A 2 + A 4 + A 6 Ω φ 12
ω Ω Ω Ω Ω. ω 1 ω 2 Ω { ω 1 ω 2 } ; 0= 1= Ω { 0 1 } 1 2 10 ω i i ( i = 1, 2, L,10) Ω { ω 1 ω 2 L, ω10 } (1,1), (1, 2), L (1, 6), (2,1), (2,2), (2,6), L Ω = L L L L (6,1), (6.2), L (6.6) 7 ω t Ω { ωt 19 ωt 20 } 1 B A, A φ A Ω B U 13
n A1, A2, L, An A1, A2, L, An A + A + L + A 1 2 n n U A i= 1 i A1, A2, L, An A1, A2, L, An A + A + L + A + L 1 2 n U A ( ) A B A B I n. : 4 B A B A B i= 1 i A A A= φ A φ = A Ω Ω= φ Ω. ( ) : A B A B, A I B=φ AB=φ n A1, A2, L, An i j A I A = φ (, i j = 1,2, L, n) i j n n A A A 14
( A) = A A A A A A A A + A =Ω A I A = φ A = Ω A 3 4 3 2 5 l 6 7 B1, B2, L, Bn B1 + B2 + L + Bn =Ω B 1, B 2, L, Bn 8 9 15
5 A= B= 5 C= 5 Ω A B C Ω= { 1, 2,3, 4,5,6} A = { 1, 3, 5} B = { 1, 2, 3, 4} C { 2, 4} = 6 A B C? 7 A B C A B C 16
1. 2 3 A B? Ω B AB 17
2, 1 2 n µ n A µ n p n p A P( A) = p (1) A1, A2, L, An 18
(2) A ( i = 1,2, L, n) i (3) A ( i = 1,2, L, n) i n m A, A m PA ( ) = = n (Laplace) 1812 1 2 3 n 5 m 2 2 a, b I,, I a, b I,, 2 n = 3 = 9 I A 2 m = 2 = 4 4 PA= ( ) 9 3 a b,. 2 2 : a+b 2 n = C + 2 a b 2 2 m = C 1 a 19
2 m1 Ca 2 P = = 2 n C + 1 1 m = C C = ab a b 2 a b m2 ab P = = 2 n C a + b 3 4 20
1 2 21
5 4 6,. A = B = 3 n = A 10 3 m = A 1 6 m A 6 5 4 1 3 1 6 ( ) = = = = 0.167 3 n A10 10 9 8 6 PA B m = C 2 A 2 A 1 2 4 4 6 2 2 1 m2 C4 A4 A6 PB ( ) = = = 0.3 3 n A 10 3 n = 10 3 m = 1 6 3 m1 6 PA ( ) = = = 0.216 3 n 10 B m = C 2 4 2 C 1 2 4 6 2 2 1 m2 C4 4 C6 PB ( ) = = = 0.288 3 n 10 k N (N k) (1) A= k 22
(1) B= k (3) C= k. : N n N n = N k (1) k k n! 2 n N n n C N n n! P 2 n CN n! N! = = n n N N ( N n)! 0 PA ( ) 1 P( Ω ) = 1 P( φ ) = 0 A B P A+B =P A +P B PA ( + A) = PA ( ) + PA ( ) = 1 PA ( ) = 1 PA ( ) 23
1 A B 2 (3) B A P AB = P A P B 2 7 10 I 10 t 10 1 + 2 + + 10 1 24
1 8 9 1 2 3 4 25
(n 4) 10 φ AB = φ 1. 26
2 P 16 ----- 1 4 5 6 7 3 S A P(A) S B A 1 100 70 (50 20 ) 30 (25 5 ) (1) (2) (3) 1 2 3 70 (50 20 ) 70 ( ) { 1} 27
A,B S P(A) 0 4 B, 1 1 2 3 4 5 6 A 6 B 28
φ AB = φ A B ( ) 2 10 8 2 2 29
9 7 3 10 4 3 ( ) A B C 4 30
5 A B 31
PBA ( ) = PB ( ) PAB ( ) = PAPB ( ) ( ) 1 A B 2 A B A B A B A B 6 100 2 5 32
= 3 5 a b c 3 3 3? 33
0 4 100 l01 0 33 o 33 o 67 t01 100 34 too o 6 o 5 34
6 n A = i ( i = 1,2, L, n) i A = A = A + A + L + A 1 2 n A 1, A 2, L, An A A = AA 1 2 L An A 1, A 2, L, An n n PA ( ) = PA ( ) PA ( ) L PA ( n ) = 1 0.6 = 0.4 1 2 n PA ( ) = 1 PA ( ) = 1 0.4 0.99 n 5.026 n A,, 35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
5 n n n n n n ( ) 17 Chevalike Demere 25 Pasca1? 25 25? B 25 (6 6) 25 (6 6) (6 6) 25 (6 6) 25 (6 6) B B B P( B) > P( B) PB ( ) + PB ( ) = 1 1 PB ( ) > 2 1 36 6 1 36 A i i 6 50
1 25 25 25 25? 25 n n 25 25 25 A p (0 < p < 1) n A k 51
q 1 = p 1 100 60 40 5 1 1) 3 2 2) 3 2 1000 0.2 1000 : A 1000 p o 2 q o 8 1000 1000 Pk ( 2) 3 o 7 o 6 (1) (2) A i = i (i =0 1 2 3) B i = i (i =0 1 2 3) 52
A p n A k P ( k) n n λ k λ Pn ( k) e λ = np k! P 39 ----- 1 3 4 1 53
Ω 2 3 3 X X 1 10 =0 1 6 10 =0 6 3 10 =0 3 X ( ) X X [0, + ) 54
: : 3 2 X X x1 x2 x n,, L,, L X X { = } { = } { = } P X x1 P X x2 P X x k p P{ X x } ( k 1,2, ) k k,, L,, L = = = L X X x x x L x 1 2 3 p p p p L p 1 2 3 k k L L X X X k { } ( 1,2, ) p = P X = x k = L ( ) ( ) X 1 X X 0 1 p 0.5 0.5 X k k { } 0.5 ( 0, 1) p = P X = k = k = 2 X X 0 1 2 p 0.1 0.6 0.3 55
X p 0 p p 1 2 { } { } { } = P X = 0 = 0.1, = P X = 1 = 0.6, = P X = 2 = 0.3 1 p (0 < p < 1) X X X X X = k ( k = 1,2, L ) k 1 PX ( = k) = pq ( k= 1,2, L ) q = 1 p X X 1 2 3 L k p p pq pq L pq 2 k 1 L L 2 2 5 1 2 5 3 3 X 3, X 3 4 5 1 1 PX ( = 3) = C = 10 =0 1 2 3 3 5 3 5 C 3 PX ( = 4) = = =0 3 C 10 X =0 6 X 3 4 5 56
p 0.1 0.3 0.6 1. X PX ( = a) = p (0< p< 1) PX ( = b) = q= 1 p X p a = 1, b = 0 X 0, PX ( = 1) = p (0< p< 1) PX ( = 0) = q= 1 p 0. : 1 X 0 3 100 95 5 0 95 0 05 X PX ( = 1) = 0.95 PX ( = 0) = 0.05, X 0 2. : X 0 1 2 n, k k n k P( X = k) = C p q ( k = 0,1,2, L, n) n (0 < p < 1, q = 1 p) X n, p 57
n 3 1000 o 005 X 10 1000 1000 X : B(1000, 0.005) ( 10 k k 1000 k 10) = C1000 (0.005) (1 0.005) 0.986 k = 0 PX * ( 5) 58
Poisson X 0 1 2 k λ λ PX ( = k) = e ( k= 0,1,2, L ; λ > 0) k! X λ 59
60
3. 4 61
3 X f( x) ( < x < + ) ab, ( a< b) b { } ( ) P a X b f x dx < < = a X f ( x) X f ( x) : ( f x) 0 ( < x< + ) + f( x) dx = P( < X < + ) = 1 x x 1 (1) (2) X a a ( PX= a) = 0 X X ( ) ab, ( a< b) { < < } = { < } = { < } P a X b P a X b P a X b b = P{ a X b} = f( x) dx a 62
1 X X λ A 1. X X : U[ a, b] 1 λ λ = b a 2. : 63
λ X : E( λ) X 0 a < b X λ 3. : X =1 64
µ 0 σ 2 = 1 X : N(0,1) X φ( x) φ( x) = 1 e 2π 1 2 x 2 (a) f ( x) ; (b) x = µ (c) x = µ x = µ ± σ (d) σ µ f ( x) x f ( x) σ µ x ± x ; σ, σ N(0,1) X ( a, b) 2 1 x x 2 φ( x) = e ( x) φ( tdt ) 2 π 1 2 t 2 1 b P( a < X < b) = e dt a 2π 1 Φ = 0 x 1 2 1 2 t a t 2 2 1 b 1 = e dt e dt = Φ( b) Φ( a) 2π 2π 65
1 Φ (0) = PX ( 0) = Φ ( + ) = 1 ; Φ( ) = 0 2 ab>, 0 ( P a < X < b) =Φ( b) Φ ( a) 0 a > ( P X a) =Φ( a) X : N(0,1) a a ( Φ a) = P( X < a) = ϕ( t) dt = 1 φ( t) dt = 1 Φ ( a) ( P X > a) = 1 P( X a) = 1 Φ ( a) ( P a < X b) =Φ( b) Φ( a) =Φ( b) (1 Φ ( a)) = Φ ( b) +Φ( a) 1 ( P X a) = P( a X a) = 2 Φ( a) 1 P(1 < X < 2) =Φ(2) Φ (1) = 0.9773 0.8413 = 0.1360 P( X < 1) = P( 1 < X < 1) = 2 Φ(1) 1 = 2 0.8413 1 = 0.6826 PX ( 1.96) = 1 Φ (1.96) = 1 0.975 = 0.025 P( 1 < X 2) =Φ (2) +Φ(1) 1 = 0.9773 + 0.8413 1 = 0.8190 2 (, ) X ( a, b) N µ σ 2 (, ) X ( a, b) N µ σ X 2 : (, ) N µ σ 2 1 ( x µ ) 2 2 b 1 σ P( a < X < b) = e dx a 2πσ x µ t =, σ b µ 1 2 t 2 1 b µ a µ σ Pa ( < X< b) = a µ e dt=φ( ) Φ( ) 2π σ σ σ 66
P( µ σ < X < µ + σ) =Φ(1) Φ( 1) = 2 Φ(1) 1 = 0.6826 P( µ 2σ < X < µ + 2 σ) =Φ(2) Φ( 2) = 2 Φ(2) 1 = 0.954 P( µ 3σ < X < µ + 3 σ) =Φ(3) Φ( 3) = 2 Φ(3) 1 = 0.9974 2 (, ) X N µ σ [ µ 2 σ, µ + 2 σ] [ µ 3 σ, µ + 3 σ] 2 X : N(2, 0.3 ) ( PX> 2.4) µ = 2, σ = 0.3, 2.4 2 PX ( > 2.4) = 1 PX ( 2.4) = 1 Φ ( ) = 1 Φ (1.33) = 0.0918 0.3 4 a. 67
5 6 X 68
X 7 P 68 69
70
71
72
73
. 3 4 74
5 75
76
77
78
79
80
81
82
83
84
85
86
87
88
1. 1 89
90
3 91
2 4 92
3 X, 93
94
95
40 ( ) 5 p(0 p l p ) 5 1 p 5 a (a ) 5 b (b a) b m 96
97
98
99
100
101
102
103
104
105
106
107
108
109
2 110
111
112
+ ( x EX) 2 q( x) dx λ = µ λ 2 2 + 2 t t ( x )/ t e dt + 2 2 t 2 2 = λ te dt= λ Γ (3) = 2λ 0 q = 1 p, DX. 113
114
n 1 n. 115
4 EX EX X EX EX = ( DX + ( EX ) ) + 4EX + 4= 30 ( 2 + 2) = ( 2 + 4 + 4) = 2 + 4 + 4 2 116
5 6 ( ) X X P p q E( X) = p, D( X) = pq 117
. q = 1 p 118
3 7 119
120
EX 1, λ 1 λ = DX = 2 121
(8) X : N ( µ, σ 2 ) EX 2 = µ, DX = σ 122
123
8 124
P 93 --------- 1 2 1 3 5 1 125
1. 2 126
127
128
129
130
1 131
132
133
1. : 2. : 134
135
136
137
138
139
8 P 109 ---- 1 7 140
141
( ρ 0) f( x, y) f ( x) f ( y) X Y 142
f ( xy, ) f ( x) f( y) ( ρ 0) X Y 143
Q p = p p (, i j = 1,2,3) ij ig gj X, Y 144
145
146
147
1 P.115 --- 1, 2, 4, 8 2 P.116 ---3, 5, 7. P(1 X 2, 3 Y 4) 148
149
2 150
3 2 ρ XY ρ( X, Y) ρ 151
152
153
154
X Y ρ XY = 0 155
156
157
158
+ 2Y, X Z X Z EXZ ( ) EXEZ ρxz = DX DZ EX = 0, DX = 1, EZ = EX + 2EY = 2, DZ = DX + 4DY = 9, EXZ EXX Y EX XY EX EXY 2 2 ( ) = ( ( + 2 )) = ( + 2 ) = + 2 ( ) ρ xz 2 = EX + 2EX EY = 1 X Y 1 0 1 = = 1 9 3 159
. p.136 ----. 3 2 2 1 X = 1 Y = 0 0 cov( X, Y ) 2 160
161
3 2 162
DX 0, DY 0, 163
164
165
166
1. P.116 ------ 7 2. p.136 ----4,6 3. 3 2 2 1 X = 0 cov( X, Y) 1 Y = 0 167
3. 168
1. 2. 169
3 170
1 2 171
2 172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
2 187
2 1 188
1. : 2. 2. : 189
190
191
1 192
χ 2 ( n) 1 2 2 χ 2 ( n 1) 1 193
2 3 3 4 4 5 194
1 2 6 195
3 7 196
197
198
2 199
4 200
201
1 202
203
2 204
1 205
3 X 1 X = x + x + L + x 1 2 n 2 n 1 S x x n 2 2 = ( i ) n 1 i= 1 206
P : 1 X ~ p( x) = e 0 x λ x > 0 x 0 x, x2,, x λ 1 Λ n λ 4 207
208
209
1 (1) (2) 4 1000 10 4 p 0 04 10 4 ( α 0 05 H 0 H0 ( ) α o 05 210
1 2 211
2 H : µ = µ 2 σ, o H : µ = µ 1 o o ( µ o ) U 2 = X µ o 2 σ n o 3 H o U : N(0,1) 4 α 1 u α 1 2 X µ o P( > u α ) = α 2 1 σ 2 n 5 u o H u > u α 1 2 o H u u α 1 2 o H 1 212
α = 0.05 X 200 P( > 1.96) = 0.05 5/ 10 200. P.191 2.1 α = 0.05 0.01 P.193 2 2 H : µ = µ 2 σ, o H : µ = µ o 1 o o ( µ o ) 2 2 T = X µ S n o 3 H o T : t( n 1) 4 α 1 P( X µ o > λ) = α 2 S n n t 2 λ 5 t o H > λ t o H λ t o H 213
2 µ o 100 9 99.3 98.7, 100.5 101.2 98.3 99.7 99.5 102.1 100.5?( α = 5 ) S = 1.21 H : µ = 100 1 2 2 o T X 100 = S 9 3 H o T : t(8) 4 α =0.05 t 2 λ = 2.36 P( X 100 > 2.36) = 0.05 2 S 9 5 t o = t o = 0.055 < 2.36 100 214
3 5 1250 1265 1245 1260 1275( ) 1277 ( ) ( ) ( P.187 -- 1.2) T t(4) :, n 1= 5 1= 4 P. 200 2.3 10620 10 ( ) 10512 10623 10668 10554 10776 10707 10557 10581 10666 10670 α = 0.05 H : µ 10620 o 215
H : σ = σ µ, 2 2 o o H : σ = σ 2 2 2 o o ( σ o 1 2 χ ( n 1) S = σ 2 2 o 2 ) 3 H o n 2 χ : χ 2 ( n 1), 1 4 α n 1 2 λ = χ, λ = χ 2 2 1 α 2 α 1 2 2 χ 3 2 α 2 α P( χ < λ1) =, P( χ > λ2) = 2 2 2 χ o 5 H χ λ χ λ 2 o 1 2 o 2 H λ < χ < λ 2 1 2 o H P. 202--- 2.4 52 8 2 1 6 2 9 ( 2 ) 216
: 51 9 53 0 52 7 54 7 53 2 52 3 52 5 51 1 54 1 H : σ = 1.6 1 o 2 2 2 χ = 9 S 1.6 2 2 2 3 H o χ 2 : χ 2 (8), 4 α = 0.05 λ = 2.18, λ = 17.54, 1 2 2 χ 3 2 χ o 5 2 2 2 8S 9.54 8S = 9.54, χo = = = 3.72 2 2 1.6 1.6 2 2 σ = 1.6 217
H : σ σ µ, H : σ σ (1) 2 2 o o 2 2 2 o o ( σ o 2 χ (2) ( n 1) S = σ 2 o 2 ) (3) H o 2 χ χ 2 ( n 1), : 1 n, 2 2 ( n 1) S 2 ( n 1) S 2 P{ > χ ( n 1) ) } P{ > χ α( n 1) } = α σ 2 α 2 o σ 4 α n 1 2 λ = χ 2 ( n 1) α 2 ( n 1) S P > λ = α σ { } 2 o 2 χ o 5 χ > λ 2 o H χ λ 2 o H χ 3 218
6 χ 2 o 2 (9 1) 0.007 = = 15.68 > 15.5 2 0.005. : P. 213 1, 2, 3, 4, 5 219
, --- (1) ( ) (2) (3) (4) 1 Y x x Y ( x y ), ( x y ), L, ( x y ), 1, 1 2, 2 n, n Y x 220
y = a+ bx+ ε a b? Y x.. : 1 24 y x ( x y ) ( 1 i 24) i, i 24 ( ) a b b 221
a b 24 y a b 24 24 n ( x 1, y 1 ), ( x 2, y 2 ), L, ( xn, yn), l : y = a+ bx [ y ( a+ bx )] ( x, y ) i i i i 2 l, n Qa (, b) = [ y ( a+ bx)] i= 1 i i l n, a b,, n : 2 a b, Qa (, b) a = aˆ, b = bˆ, Qa ( ˆ, bˆ ) = min( Qa (, b)) ( Qa, b) n Qa (, b) a b aˆ, bˆ 222
: n 1 ( x, y 1 ), ( x 2, y 2 ), L, ( xn, yn) :, ˆb â 223
2 P 236 1.2 Y X. Y X Y X. : n ( x, y ), ( x, y ), L, ( x, y ) 1 1 2 2 n n, : n n 2 2 ( y ) ( ˆ i y = yi yi) i= 1 i= 1 + y ˆi = aˆ + bx ˆ, ( i = 1,2, L, n) l yy = n i= 1 i ( y y ) i 2 n 2 ( yˆ i y) (1) i= 1 n U = ( yˆ y) i= 1 i 2 n Q = ( y yˆ ) i= 1 i i l = U + Q (1) yy 2 224
â = y bˆ x, bˆ = n i= 1 ( x x)( y y) i n i= 1 ( x x) i i 2 0 lyy = U + Q n n 2 2 ( y ) ( ˆ i y = yi yi) i= 1 i= 1 + n i= 1 ( yˆ y) i 2 y ˆi = aˆ bx ˆ + i xi 225
ˆ 1, ˆ, y y2 L, yˆ n y l yy, U, Q 226
lyy, U, Q (1) y ( i = 1,2, L, n) i U Q, Q b (2)U 0, X Y U Q Y ) lxy b =, aˆ = y bx ˆ ; U = l 2 bl ˆ xx = ˆ xy, yy xx ( P.244+3, : ) : H : b = 0 1 o U F = Q /( n 2) 2 bl Q = l U. 3 H o F : F(1, n 2), 4 α 1 n 2., F 4 λ PF ( > λ ) = α, 5 F o H F o > λ H Fo < λ, H 227
F X Y X Y F X Y, R = l l xx xy l yy R 0, Y X R 1 Y X R Y X. H o F R 228
P. 243 --- P.244 229
3 P.244 1.4 4 12 ( ) (kg mm 2 ) ( α = 0.05) Y X 1, x y, lxx, lxy, lyy x i y i 2 x x i i yi yi yi 1 1.3 41 1.69 53.3 1681 2 1.4 44 1.96 61.6 1936 3 1.4 45 1.96 63 2025 4 1.5 43 2.25 64.5 1849 5 1.6 46 2.56 73.6 2116 6 1.6 47 2.56 75.2 2209 7 1.7 47 2.89 79.9 2209 8 1.8 46 3.24 82.8 2116 9 1.9 46 3.61 87.4 2116 10 2.0 49 4.00 98 2401 11 2.1 49 4.41 102.9 2401 12 2.2 51 4.84 112.2 2601 20.5 554 35.97 954.4 25660 16 i= 1 x 2 i = 35.97 16 i= 1 y 2 i = 25660 16 i= 1 xy i i = 954.4 230
l xx 1 = ( x ) = 0.942 12 12 2 2 xi i i= 1 12 i=1 l xy 12 12 12 1 = x y ( x )( y ) = 7.983 i i i i, i=1 12 i=1 i= 1 1 l = y ( y ) = 83.67 12 12 2 2 yy i i i= 1 12 i= 1 ˆ lxy b = = 8.4 l xx aˆ = y bx ˆ = 31.81 Y X yˆ = 31.81+ 8.4x 2 X Y Ho : b = 0 U F =, n 12 Q/( n 2) = H o F : F(1, 10), α = 0.05 F 0.05 (1,10) = 4, 96 ˆ U = b l xy = 67.15 Q = lyy U = 16.52 U F = = 40.64> 4.96 Q /10 H 5 A 7 A 231
232
ˆb = â = P 254 ---- 1 2 233
3 234
235
. 1. : m n n m n m m n1 n 2 n m 1 2 236
2. : m n n2 m n m n 1 + n 2 + + n m m 1. : n r n r n Z ( ) n r < n r n n n n r r r dl n r 237
r n 3 4? 1) 2) 1) 2) r n r n r n r (2) 238
r n 1 r 1 r n r r 4?? 1 2 3 4 5 6 1 n r n n2 r nr 1 239
5 15 15 3 1)15?2)?3)3? 1)15 2) 3 3! 12 3) 3 3 ( 3 ) 12 2 3 5 3 3 4 4 240
2 r n1 n2 r n r n 6 4? 8 3 a 2 m 2 4 (1 + x + x + x )(1 + x+ x )(1 + x) = 1+ 8x+ 31x + 78x + 143x + L + x 2 3 2 5 2 3 4 12 5 3 10 7 241
lo 5 5 5 r Rt n2 r n r 5 8 5 9 5 14 A B C D (a) (b) (a) A B C D ABC ABD ACD BCD 4 4 4 (b) A B C D ABC ACB BAC BCA CAB CBA ABD ADB BAD BDA DAB DBA ACD ADC CAD CDA DAC DCA BCD BDC CBD CDB DBC DCB 24 4 24 5 15 4 (a) (b)a B C D 24 4 4 24 n ( ) n n 5 3 n 4 ( A) (n 1) n(n 1) 5 3 n 2 n(n 1)(n 2) n n n(n 1) (n 2) 2 1 ni( n ) n 242
n n(n 1)(n 2) 2 1 (5 9) Pn n n n Pa n n1 (5 10) 1 P184 1 100 100 342 340 348 346 343 342 346 341 344 348 346 346 340 344 342 344 345 340 344 344 343 344 342 343 345 339 350 337 345 349 336 348 344 345 332 342 342 340 350 343 347 340 344 353 340 340 356 346 345 346 340 339 342 352 342 350 348 344 350 335 340 338 345 345 349 336 342 338 343 343 341 347 341 347 344 339 347 348 343 347 346 344 345 350 341 338 343 339 343 346 342 339 343 350 341 346 341 345 344 342 243
1 1 332 356 2 a=332 b=356 13 2 3 332~334 1 334~336 1 336~338 3 338~340 8 340~342 15 342~344 20 344~346 21 346~348 15 348~350 7 350~352 6 352~354 2 354~356 0 356~358 1 4 0.25 0.2 0.2 0.21 = *1/2 0.15 0.1 0.05 0 0.15 0.15 0.08 0.07 0.06 0.01 0.01 0.03 0.02 0 0.01 332 334 336 338 340 342 344 346 348 350 352 354 356 2 (1) m=332 M=356 (2) a=331.5 b=357.5 13 = 2. (3) ν i ν y i = 1 i f i = 200 244
1 331.5~333.5 1 0.005 2 333.5~335.5 1 0.005 3 335.5~337.5 3 0.015 4 337.5~339.5 8 0.04 5 339.5~341.5 15 0.075 6 341.5~343.5 21 0.105 7 343.5~345.5 21 0.105 8 345.5~347.5 14 0.07 9 347.5~349.5 7 0.035 10 349.5~351.5 6 0.03 11 351.5~353.5 2 0.01 12 353.5~355.5 0 0 13 355.5~357.5 1 0.005 (4) 0.12 y 0.1 0.08 0.06 0.04 0.02 0 331.5 335.5 339.5 343.5 347.5 351.5 355.5 245