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6 θ 3
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P 2 P P =
P +
%
.
.
∗ Φ = 1 ' , = ' ( 2 P P =
% A P ' (
A P − + ' ( P = =
P +
%
.
.
% A P
A P − +
∗ 6 ,C& < R < (C- =
2 P P =
P +
P = %
.
.
1 R =
5
*
R
*
8 = ) R ⇒ R V 87) $3
7) (
= 2 7) =
)
, < < &
= A (
. ) )
(
& ≤ < +
= A − + (
.
)
)
=,
=
= 2 7) '2
!)
*
* = " 5 $ D $ ; 4 = 4 = ' D 2 D $ ; ;3
∗ = 4 = 3
= γ 4 = 4 = γ 4 = 4
∗ 1 I =
∂# 7∂5 ∂# 7∂
,
( (
=
=
(
7
7
−
5
∂# 7∂5 ∂# 7∂
∗ 1 0 = ∈ℜ * < < * < < 3
022 = # 5 ∈ℜ * < 5 < * < # < 5
# = $ # = 57
,
# = 5
&
;
, < # < &
,<<&
⇒
, < # < &
, < 57 < & ⇒ , < 5 < & .
D
∗ G
5 $ D $ ; 3
5 $ = γ 5 $ $ γ 5 $ I = ( $ 5 $ ∈%UU
. ∗ 0
"
& # D2
D $ ; 3
! = +∞
! =
( = ( 4 . , < 5 < .
5 =
5 $ =
! = −∞
! = % . 5
.
%UU > ,$ 3 ( = (
. . !)
*
#
, ( )
6 = # ,CB ,C) ,C&
1
**
" * " / =51
/
*
25
8&3
'
;3
*
3 3
#
, ( )
#
, ( )
$
6 = # ,CB ,C) ,C& 6 = # ,CB ,C) ,C&
0 *
* $3
6 = # $ = # = 6 = # 6 = # ⇒
(
)
7 ,
,
,C)B ,C(, ,C(B
⇒
(
,C(, ,C,A ,C,+
)
,C(B ,C,+ ,C,.
"
= + 7) 3
= + 7)
,
,CB
(
,CB
(
(B
C
(
(B
C
)
# $ # 6 = # $ = # , $ ,
,C)B
, $ (
,C(,
, $ )
,C(B
( $ , ,C(,
( $ (
,C,A
( $ ) ,C,+
) $ ,
,C(B
) $ (
,C,+
) $ )
,C,.
= + 7) 2
** 3
6 = , = 6, $ ,
= ,C)B
66 == (,CB= =6 6,$,)$(+
+66($(($ ,+
=6 ,)C),$ , = ,C&A ⇒
6 = (B
C = 6( $ )
+ 6) $(
= ,C()
6 = ) = 6) $ )
= ,C,.
⇒
,
,CB
(
(B
)
#
C
6 = # ,C)B ,C), ,C&A ,C() ,C,.
0 " 5 *
5
!*
3
∗ 1 = , ,C)B + ,CB ,C), + ( ,C&A + (B
C ,C() + ) ,C,. = ∗ ; = 1 − 1 = 1 = , ,C)B + ,CB ,C), + ( ,C&A + (B
C ,C() + ) ,C,.
∗ Φ = 1 ' ) =
= ' ,C)B + ' ,C), + ' ,C&A + ' ,C() + ' ,C,. = ( ≤ ) = 6 − ,C- ≥ ( = 6 ≥ (C) = ,() + ,C,.
∗6
)
− ,C-
)/
&
0
9
1
9
6 '
*Q
Q = − 3
# $ # , $ , , $ ( , $ ) ( $ , ( $ ( ( $ ) ) $ , ) $ ( ) $ ) 6 # $ # ,C)B ,C(, ,C(B ,C(, ,C,A ,C,+ ,C(B ,C,+ , C,.
Q = − ,
(
)
(
,
(
)
(
,
,C(, + ,C(, +,C,++,C,+
,C(B+,C(B
,C)B+,C,A +,C,.
Q
,()
+ + 1
∗ 1 Q = , ,C&@ + ( ,C&) + ) ,C&, = ∗ ; Q = 1 Q − 1 Q = 1 Q = , ,C&@ + ( ,C&) + ) ,C&,
∗ Φ = 1 '- = ' ,C&@ + ' ,C&) + ' ,C&, = ∗ 6 (7 Q − ,C- ≤ ) = 6 Q − ,C- ≥ (7) = 6 Q ≥ (C) = ,C&,
!"#$%&6(
( -, W "
(,, 5*
"
',C+B,C@
) %*
,C.B
"
)*+,-."
( "
'# T
,C-
-,W
"
* #
! (,, * = + + 7(,,
# "
$ ! 2 # 5 3
1 = 1 = ,C-
≈ T ⇒ 1 = ; = ( − ; ,C- ,C&
=
= ,C,,)(
(,,
(,,
; =
63
6 ,C+B < < ,C@ ≅ 6 ,C+B < K ,C- $ ,C,,)( < ,C@ =
= 6 K , $ ( < ,C@ − ,C- − 6 K , $ ( < ,C+B − ,C- = ,C,,)(
,C,,)(
)1
K ,C- $ ,C,,)( "
,C.B
K K ,C- $ ,C,,)( '
,C-2'
"
'
6
6 > * 6 − ,C- < = ,C.B 3
= ,C.B ⇒
,C,,)(
− ( = ,C.B ⇒ 6 K , $ ( <
= ,C.-B ⇒
⇒ ) 6 K , $ ( <
,C,,)(
,C,,)(
⇒
= (C.+ ⇒ = (C.+ ,C,,)( = ,C,@.@
,C,,)(
=
!(,, ≈ T ,C- .BW
6 − ,C- < = ,C.B ⇒ 6 K , $( <
* ≈ K ,C- $ ,C,,)( ,C- − ,C,@.@ $ ,C- + ,C,@.@ !"#$%&6&
(66B
)6 T A $ ,C& &6 1# ,C,) A6 Q −( $ (
B6 # = ) # , ≤ # ≤ (
+62',C(
-6 S ), $ ) )*+,-."
%
!@(1
2
*
,C.B
*
0
! ≥ * µ 5 σ 424#
* 5 $ K µ $ σ7 1 K µ $ σ7 " ,C.B
K K µ $ σ7 ' µ 2 ' "
'
6 6 > * 6 − µ < = ,C.B 3
6 − µ < = ,C.B ⇒ 6 K , $( <
− ( = ,C.B ⇒ 6 K , $( < = ,C.-B ⇒
σ7 σ7 ⇒ = (C.+ ⇒ = ,C)(- σ
σ7 = @(
⇒ ) 6 K , $ ( <
= ,C.B ⇒
σ7 ( ≈ 6B 1 = µ = B; = σ = B * 6 − B < = ,C.. = ,C)(- B = ,CA@ $ !@( ≈ 6B .BW
B − ,CA@ $ B + ,CA@ ) ≈ T A $ ,C& 1 = µ = A ,C& = (C) ; = σ = A ,C& ,C- = ,C@A * 6 − (C) < = ,C.. = ,C)(- ,C@A = ,C(. $ !@( ≈ T A $ ,C& .BW
≈ K(C) $ ,C@A 7. 2/
(C) − ,C(. $ (C) + ,C(.
& ≈ 1# ,C,) 1 = µ = (7,C,) = B, ; = σ = (7,C,) = )B,, * 6 − B, < = ,C.. = ,C)(- )B,, = (,C.B $ !@( ≈ 1# ,C,) .BW
≈ Q −( $ ( A ≈ KB, $ )B,, 7. B, − (,C.B $ B, + (,C.B
1 = µ = −(+(7) = , ; = σ = (− −( 7() = (7& * 6 − , < = ,C.. = ,C)(- (7& = ,C() $
! @( ≈ Q −( $ ( .B W ≈ 7 * −,C() $ ,C() B # = ) # , ≤ # ≤ ( 3
1 =
1 =
# # # =
) # # = )7&
; = σ = 1 − 1 = (7(@
# # # =
) # # = (7)
* 6 − )7& < = ,C.. = ,C)(- (7(@ = ,C,B $
!@( .B W ≈ 7 8 2/
)7& − ,C,B $ )7& + ,C,B
+ ≈ S ,C( 1 = µ = ( − ,C(7,C( = .; = σ = ( − ,C(7,C( = ., * 6 − . < = ,C.. = ,C)(- ., = )C,B $
! @( ≈ S ,C( .B W . − )C,B $ . + )C,B
- ≈ S ), $ ) 1 = µ = ),7) = (, ; = σ = ),7) = B * 6 − (, < = ,C.. = ,C)(- B = ,CA@ $
! @( ≈ S ), $ ) .B W ≈ K(, $ B7. (, − ,CA@ $ (, + ,CA@ !"#$%&6'
4
+,,,(,,,,<2
%*
&),*
@,,,<2
)*+,-."
#
Q +,,, $ (,,,, #
! &), *
= + + 7&), 0!
2#
5 3
63
1 = 1 = +,,, + (,,,, = @,,,
)
− ≈ Q $ ⇒ 1 = + ; =
)
()
; A,,, ; =
=
&),
()
> 8*** ≅ 78*** *** > 8*** = 7 * > * = *9
)*
+,
*5
!
µ 5 σ 3
−
=
+
µ
−
µ
−
=
∑ ∑ ∑ − µ − − µ =
=
=
=
= ∑ − µ − ) − µ − µ + − µ =
=
= ∑ − µ − ) − µ ∑ − µ + − µ =
=
=
∑ − µ = ∑ − µ = − µ
=
=
1 = 1 ( ∑ − = ( 1 ∑ − µ − − µ
=
=
=
=
∑ = ∑ − µ − ) − µ − µ + − µ =
=
= ∑ − µ − − µ =
(
= 1 ∑ − µ − 1 − µ = ( σ − σ = − ( σ =
∗ 1 ∑ − µ = ∑ 1 − µ = ∑ ; = σ =
=
=
1 = µ ⇒ 1 − µ = ; ∀ = ( ) ∗ 1 − µ = 1 − 1 = ; = σ 7
=
µ = 1 = 7 − ( *
5
3
1 = 1 = 1 = − ( σ = σ −(
−(
−( 1 8 & # * 5
5 σ 5 σ 0
1 = − ( σ 7 ≠ σ *5
2 σ $ σ #
1 = − ( σ 7 = σ → ∞
→ ∞
!"#$%&7(
%*
5
!)
D ≈ 1#(
)*+,-."
D ≈ 1#( 5 = − 5 > , 4
2
$ ? #
! ) D ≈ 1#( ?
'3
2 # $ = # = − + # > , > ,
≈ 1#(? ≈ 1#(
Q = + ? 7) *5
83
+? =
+
?
−
) = ( − ? + ? − = ( − ? ) )
)
A
8 = ( − Q + ? − Q = ( − + ?
)
)
)
•G
83
G+ = 6 8 ≤ = 6 ( − ? ≤ = 6 − ? ≤ A =
A
= 6 −) ≤ − ? ≤ ) =
2 # $ # =
.
2 $ ? % = X # $ ∈ℜ 7 −) ≤ # − ≤ ) # > , > ,Y
?
# − = −) =
= '
=
=
= + '
=
) ,
# − = ) #
− + # +
#
) = +∞
= '
= + ' − + = − '
# =
= ' − = + '
= +∞ − = + '
− − # +
− − # =
=
=
= '
= − '
= ' − = +∞ − − + '
( − − − ' # +
− − − ' # =
=
= '
= ' − = ' − − '
=
# −
#
=
=
= +∞ − + '
= +∞ − − '
+
# −
# =
= '
= '
' ( − − ' '
= − − + −
)
+∞
+∞
+ ( − − '
=
− ( − + '
)
' )
'
− ' − − '
−∞
− '
−∞
− '
= ( − − ' + − −
+ −
=
)
)
= ( − − ' > ,
=
)
•G
83 + = G+ 7 = ( − ' > ,
!"#$%&7&
%*
5
!)
D ≈ Q , $ (
)*+,-."
D ≈ Q , $ ( 5 = ( 5 ∈ , $ ( 4
2
$ ? #
! ) D ≈ Q , $ ( ?
'3
2 # $ = # = ( # ∈ , $ ( ∈ , $ (
≈ Q , $ (? ≈ Q , $ (
Q = + ? 7) *5
83
+? =
+
?
−
) = ( − ? + ? − = ( − ? ) )
)
A
8 = ( − Q + ? − Q = ( − + ?
)
)
)
•G
83
G+ = 6 8 ≤ = 6 ( − ? ≤ = 6 − ? ≤ A =
A
= 6 −) ≤ − ? ≤ ) =
2 # $ # =
.
2 $ ? % = X # $ ∈ℜ 7 −) ≤ # − ≤ ) , < # < ( , < < (Y
"2/
"*
2# $ 2
= ( − ) O%U = ( − )
( − ) = A − A )
(
?
# − = −) ) # − = ) ,
•G
83
G+ )
=
− A , < < (7A
+ =
(
) !
"!#$
-
./++
≈ K µ $ σ # !
σ
σ
µ' + σ '
Φ = = + + 7 5
$ K µ $ σ7 62 1
≈ K µ $ σ *
5
12 +(
$ − $ $ − 3
= 1 # + ∑ − =
=
= 1 # ( ∑ + ∑ − =
=
=
= 1 # ∑ + − ( ∑ =
= = + + + − = 1 # ∑ −
=
= Φ $ $ $ = 1 # + − + + − =
"δ = ( ∑ =
− δ − = 1 # − δ − =
∑= ∏= 1#6 V Φ 6Φ 2 = ∏ 1# − δ − = ∏ Φ − δ − =
=
=
2 ≈ K µ $ σ Φ λ = #µ λ + ( λ σ )
= 1 #
δ
δ
−
−
(
= # −
=
µ + σ ∑ −
)
=
= # ∑ − δ + µ + ( σ ∑ − δ − =
) =
= = ∏ # − δ − µ + ( − δ − σ =
)
=
δ = ( ∑ ⇒ ∑ = δ =
=
= # µ + σ ∑ + − δ =
) =
= # µ + σ ∑ + − δ + ) − δ
) =
=
=
σ
+ ∑ − δ + ) ∑ − δ =
= # µ +
=
= ) δ = ( ∑ ⇒ ∑ − δ = ,
=
= = # µ + σ + ∑ − δ =
=
) σ
σ
(
= # µ + # ∑ − δ = Φ Φ $ $ ) ) =
Φ = # µ + ( σ $ Φ $ $ = # σ ∑ − δ ) ) =
= # µ + σ + ∑ − δ + ) ∑ − δ ) =
=
0 Φ 2 ≈ K µ $ σ7 Φ 2 − $ $ − 02 $ − $ $ − 2 − $ $ − '
$' 3
= ( ∑ − =
!
"#####$
%&%
'
#(σ
σ
1 ! ≈ K µ $ σ *
7σ χ − 1
5
* 3
∑ − µ − − µ = =
6 ∑ − µ = ∑ − + − µ $ *3
=
=
−µ − µ
(
∑ σ = σ ∑ − + σ7 ⇒
=
=
∑ − =
(
= ∑ − ⇒ ∑ − = =
=
−µ −µ
⇒∑
=
+
⇒ ≈ χ −
σ
σ
σ
σ7 =
− µ
− µ ≈ χ ⇒
∗ ≈ K µ $ σ ⇒
≈ K , $ ( ⇒
σ
σ
− µ ⇒∑
≈ χ σ
=
−µ
−µ
∗ ≈ K µ $ σ7 ⇒
≈ K , $ ( ⇒
σ7 σ7 ≈ χ −µ
∗ 0 σ
σ7 ≈ χ
χ " ≈ χ −
σ
)
σ
σ
7σ −(
=
−µ
≈ −
7 − (
D=
−µ
σ7 ≈ K µ $ σ7 ' −µ
≈ K , $( ≈ χ − $ σ
σ7 <2
6 ≈ K , $ ( *5
I
≈ χ 26I
3
= 7 − ( 7 − ( = 7 $'3
−µ
≈ −
7 D=
*
+
%
0
7 µ σ 7 µ σ ! 5
,-%
≈ K µ $ σ 7 ≈ K µ $ σ 7 3
− ≈ K µ − µ $
σ σ +
,-%
%&
≈ K µ $ σ7 ≈ K µ $ σ7 3
− ≈ K µ − µ $ σ ( + (
7σ ≈ χ − 7σ ≈ χ − ' 3
+ +
=
≈ χ / − σ
σ
σ
> < 2 6 ≈ K , $ ( *5 I
≈ χ 2 6
I
− − µ − µ ≈ K , $(
(
(
+
σ
+ I
=
≈ χ / − σ
6 =
3
− − µ − µ σ ( + (
− − µ − µ D=
=
≈ + −
+ ( (
+ 7σ +
+−)
+−)
,-%
&
− − µ − µ D=
2! ≥ &, 5
5$
σ = σ = 3
≈ K , $(
+
,-%
%.
6
!3
D=
− − µ − µ +
≈ 0
U 3
( = + ( − U − ( − (
=
7 − (
+ −( −(
/
-
%
≈ 7 µ σ ' ≈ 7 µ σ ! 5
>
G % & 2
6 ≈ χ I
≈ χ 2 6 I
6 = 7σ ≈ χ − $ I
= 7σ ≈ χ −
3
7σ
− ( σ −
(
=
≈ G − − ⇒
D=
7σ − ( σ −(
$ =
=
−(
−(
σ ⇒ D = ≈ G − −
σ !"#$%&8(
Q
2
))CB*(CB
%* &+ )A
)*+,-."
≈ K ))CB $(B
C #
# !&+*
= + + 7&+ 3
1 = 1 = ))CB $ ; = ; 7&+ = (B
C 7&+
63
6 > )A = 6 K ))CB $(C+7+ > )A = 6 K , $ ( > )A − ))CB = (C+7+
!"#$%&8&
%
5(,,, !(,, %
*
,C)
)*+,-."
≈ K µ $ (, # !
(,,*
= + + 7(,, 4
1 = 1 = µ ; = ; 7(,, = ( *3
6 − µ ≥ ,C) = 6 K , $ ( ≥ ,C) = (
!"#$%&8'
≈ K(,, $ () *!
*
25,C.B
)
)*+,-."
≈ K(,, $ () # !
*
= + + 7 4
1 = 1 = (,, ; = ; 7 = (AA7 % 6 − (,, ≤ ) ≥ ,C.B3
6 − (,, ≤ ) ≥ ,C.B ⇒ 6 K , $ ( ≤
)
− ( ≥ ,C.B ⇒ 6 K , $ ( ≤ )
≥ ,C.-B ⇒
()7 ()7 ⇒ ) ≥ (C.+ ⇒ ≥ (&@C). ⇒ ≥ (&.
()7 ⇒ ) 6 K , $ ( ≤
)
≥ ,C.B ⇒
()7 !"#$%&86
≈ K µ $ ( *!
* 25,C.B
,CB
)*+,-."
≈ K µ $ ( #
!
*
= + + 7 4
1 = 1 = µ ; = ; 7 = (7
%
6 − µ ≤ ,CB ≥ ,C.B3
⇒ ) 6 K , $ ( ≤ ,CB − ( ≥ ,C.B ⇒ 6 K , $ ( ≤ ,CB ≥ ,C.-B ⇒
(7 (7 6 − µ ≤ ,CB ≥ ,C.B ⇒ 6 K , $ ( ≤ ,CB ≥ ,C.B ⇒
(7 ⇒ ,CB ≥ (C.+ ⇒ ≥ (BC)( ⇒ ≥ (+
(7 !"#$%&87
1"
K(,,, $ (,, B,",C.B
( %*!
) %*!
(,,,*(,,
)*+,-."
( ≈ K(,,, $ (,, #
! * = + + 7 4 1 = 1 = (,,, ; = ; 7 = (,, 7 H 6 − (,,, ≤ B, ≥ ,C.B3
6 − (,,, ≤ B, ≥ ,C.B ⇒ 6 K , $( ≤
6 K , $ ( ≤ = ) 6 K , $ ( ≤ − (
B,
≥ ,C.B ⇒
(,,7 B,
− ( ≥ ,C.B ⇒ 6 K , $ ( ≤ B,
≥ ,C.-B ⇒
(,,7 (,,7 ⇒ B, ≥ (C.+ ⇒ ≥ (BC&+ ⇒ ≥ (+
(,,7 ⇒ ) 6 K , $ ( ≤
) 1 = 1 = (,,, ; = ; 7 = (,, 7 8""3
; 6 − (,,, ≤ B, = 6 − 1 ≤ B, ≥ ( −
=
B, (,, 7
=(−
≥ ,C.B ⇒ ≥ @,
B, !"#$%&88
%
≈ K(& $ + !.
)*+,-."
( %* ,C..
) >( = (,, = (,,,,
& 9Z
'*
!(,,,,
(B:
( 1
!
≈ K µ $ σ * = :
≈ K(& $ + K µ $ σ7 6
≈ K(& $ +7 . ≡ K(& $ ) 1
≈ K(& $ ) "
,C..
K
K(& $ ) '
(&2'
" ' 6 6 > * 6 − (& < = ,C..
6 − (& < = ,C.. ⇒ 6 K , $ ( < = ,C.. ⇒
)
⇒ ) 6 K , $ ( < − ( = ,C.. ⇒ 6 K , $( < = ,C..B ⇒
)
)
C
⇒ = )CB- ⇒ = B(A
)
*
!. ≈ K(& $ + ..W
* (& − B(A
C $ (& + B(A
C ≡ -C@+ $(@C(A ) = ** ≈ K(& $ +7 (,, ≡ K(& $ ,C+$ 3
6 − (& < = ,C.. ⇒ 6 K , $( < = ,C.. ⇒
,C+
⇒
= )CB- ⇒ = (BA
C
, C+
*
!(,, ≈ K(& $ + ..W
*
(& − (BA
C $ (& + (BA
C ≡ ((CA+ $(A CBA • = **** ≈ K(& $ +7 (,,,, ≡ K(& $ ,C,+$ 3
6 − (& < = ,C.. ⇒ 6 K , $ ( < = ,C.. ⇒ = )CB- ⇒ = ,C(BA
,C,+
,C,+
*
!(,,,, ≈ K(& $ + ..
W * (& − ,C(BA $ (& + ,C(BA ≡ ()C@A+ $ (&(BA
C &9
'*
!(,,,, = 9
':
2 "
2
2
0 12!!&&
! (,,,,
2
,C..
C L
2/ ()C@A+ $ (&(BA
(&C&B = (B ∉()C@A+ $(&(BA
C 3"
2 " 2
= **** ' ()C@A+ $ (&(BA
C (W
"12
2!(,,,,"
"
"!
"
C 2
"
= (B ∉()C@A+ $(&(BA
2
5
• ! " " / •! 2[5
""
≈ K(& $ + ≈ K(& $ + • )
" ≈ K(& $ + "2
%
2
3
2
'"2
"
""
≈ K(& $ + ""
'
!"#$%&8>
!(,,,,
= ()C@& ∉()C@A+ $ (&(BA
C *
= (B ∉()C@A+ $(&(BA
C = 98 '
K
()C@&
∉((CA+ $ (A CBA = ** (B
2
= **
%
≈ KB $ ,C( !(+
%*
< < 9 ≤ ,C,(.()B > *9 < < 9 ≤ *9*: )*+,-."
1
!
K µ $ σ = ( ∑ $ = ( ∑ − =
=
≈ K µ $ σ7 7σ ≈ χ − * = (+ µ = Bσ = ,C( 3
≈ KB $ ,C(7A $ (+ 7,C( ≈ χ
≤ &,C+ = ,C..
• 6 ≤ ,C,(.()B = 6(+ 7,C( ≤ (+ ,C,(.()B7,C( = 6 χ
• < < 9 = < 7 *9 < 9 = • < < 9 ≤ *9*: = < < 9
> (+ = • 6 > ,C( = 6 > ,C( = 6 (+ 7,C( > (+ ,C( 7,C( = 6 χ
*
5
!"#$%&8?
≈ K(C- $ A ! (, * *
,C..
)*+,-."
1!
≈ K µ $ σ *
5
7σ ≈ χ − 6 = * σ = (, 7A ≈ χ & > , 6 > = ,C.. 3
6 > = ,C.. ⇒ 6 > = ,C.. ⇒ 6 (, 7A > (, 7A = ,C.. ⇒
⇒ 6 χ & > (, 7A = ,C.. ⇒ (, 7A = )C,. ⇒ = (@)
C
!"#$%&8@
1
!
*
*5
)*+,-."
D*5
!
K µ $ σ R = D7σ ≈ χ − ≡ S − (7) $ (7) •G
5
D3
G 5 = 6 D ≤ 5 = 6 σ R 7 ≤ 5 = 6 R ≤ 57σ = G, 57σ R = D7σ ⇒ D = σ R 7
G, R ≈ χ −
•G
5
D3
5 =
G 5 G, 57σ G, 57σ 57σ =
=
=
5
5
5
57σ , R ≈ χ − 3
G, 57σ = , 57σ 57σ (7) −%
= , 57σ = 57σ − % − % σ =
σ
σ Γ − (7) (7) −% − % − ( %
R ≈ χ − ≡ S − ( $ ( ⇒ , P =
P
P>,
) )
Γ − (7) (7) σ −% −% − %σ 5>,
= 5
σ Γ − (7) S − (7) $ 7) σ !"#$%&8(A
1
K µ $ σ 5
+ ≈ 7 µ σ *
83
− −(
8 = +
+(
)*+,-."
1!
K µ $ σ 3
≈ K µ $ σ7 $ 7σ ≈ χ −
0 + + + − 3
1 + − = 1 + − 1 = µ − µ = ,
; + − = ; + + ; = σ + σ = + ( σ 6 + − ≈ 7 * σ + 3
+ − ≈ K , $ (
σ + (7
> ? ≈ K , $ (Q ≈ χ K , $ ( + − σ + (7
7σ ≈ χ − 3
+ − σ + (7 + − − (
8=
=
≈
+ ( −
7σ −(
? ≈ Q7<
!"#$%&8((
%
≈ K µ $ ) !.%*
,C.B
5
> = *
)*+,-."
1!
K µ $ σ 7σ ≈ χ − • = . σ = ) . 7A ≈ χ1 1
. 7A ≈ χ1 "
,C.B
0
χ1
'2/
2
− *9: = *9* 2
5
"" χ1 '
'$
. 7A ≈ χ1 3
98 ≤ : ≈ χ1 ≤ ;9 = *9:
6
6 ,C.+ ≤ ≤ -C-. = ,C.B
)C(@ A ≤ ≤ (-CB& A = ,C.B $
.
. 6
3
1 ! . ≈ K µ $ ) .BW
*5
2/
,C.+ $ -C-.
6 • = (,( σ = ) (,( 7A ≈ χ
3
(,( 7A ≈ χ
6
≤ ().C+ = ,C.B
6 -A C) ≤ (,( 7A ≈ χ
6
-AC) A ≤ ≤ ().C+ A = ,C.B $
(,( (,(
3 9: ≤ ≤ 9 = *9: 1 ! (,( ≈ K µ $ ) .BW
*5
2/
)C.& $ B(&
C !"#$%&8(&
%
5ACB
!%*
,C.B
)
)*+,-."
≈ K µ $ A CB ' # !3
= ( ∑ ≈ K µ $ A CB7 $ ? = ( ∑ ? ≈ K µ $ A CB7 =
=
6*
' 3
− ? ≈ K , $ .7 1 − ? = 1 − 1 ? = µ − µ = ,
; − ? = ; + ; ? = .7
%
6 − ? ≤ ) ≥ ,C.B 3
6 − ? ≤ ) = ,C.B ⇒ 6 K , $ ( ≤
⇒ ) 6 K , $ ( ≤
)
≥ ,C.B ⇒
.7
)
− ( ≥ ,C.B ⇒ 6 K , $ ( ≤ )
≥ ,C.-B ⇒
.7
.7
⇒ ) ≥ (C.+ ⇒ ≥ .
.7
!"#$%&8('
% 7 µ σ 7 µ σ ! 5 %* * <
)*+,-."
8 = − ( + − ( σ
σ − ? − µ − µ + − )
8 =
8
+
σ
σ
7 7 6
! 7 µ σ 5
− ( 7σ ≈ χ − 7σ ≈ χ − = − ( 7 6
! 7 µ σ 5 − ( 7σ ≈ χ − 7σ ≈ χ − = − ( 7
1
3
8 = − ( + − ( ≈ χ + − σ
σ ≈ K µ $ σ 7 ? ≈ K µ $ σ 7 − ? ≈ K µ − µ $ σ 7 + σ 7 $3
− ? − µ − µ σ 7 + σ 7 ≈ K , $ (
1
<2
6 ≈ K , $ ( *5
I
≈ χ 26
I
6 =
3
− ? − µ − µ σ 7 + σ 7 ≈ K , $ ( $ I
= 8 ≈ χ / − − ? − µ − µ 8 =
σ 7 + σ 7 8
+−)
=
− ? − µ − µ + − ) ≈ + −
8
σ 7 + σ 7 !"#$%&8(6
%5 σ ! - ' 5
'
; R − = σ 7 + )*+,-."
' #
3
= ( ∑ $ ? = ( ∑ ?2
2= =
- '53
2 =
=
63
( ; R − = ; + 2∑= ?2 − ∑= =
R − = ( ∑ + ∑ ?2 − ( ∑ =
+ = 2= =
= ( − ( ∑ + ( ∑ ?2 = ( ∑ ?2 − ∑ + +
+ 2= = =
2= (
∑ ; ?2 +
∑ ; =
=
+ ( + ?
+ ∑ ∑ 2
R=
2=
=
? ? (
σ + σ = σ
+ + =
? ? 5σ !"#$%&8(7
4
)B,,"*
+,,"
T)&,,"
*@,,"&,, ),,T
( 0/
(,,"
T
) 0/
),,"
T
& %* ,C.B
)*+,-."
?
T
3
1 = )B,, $ ; = +,, $ 1 ? = )&,, $ ; ? = @,, ' 2!
&,,),,
# 424 5 5 3
1 = 1 = )B,, $ ; = ; 7&,, = +,, 7&,,
1 ? = 1 ? = )&,, $ ; ? = ; ? 7),, = @,, 7),,
6 * ' − 3
(13
1 − ? = 1 − 1 ? = )B,, − )&,, = ),,
; − ? = ; + ; ? = +,, 7&,, + @,, 7),, = AA,,
)13
6 − ? ≤ (,, = 6 K ),, $ AA,, ≤ (,, = 6 K , $ ( ≤ (,, − ),, = AA,,
6 − ? > ),, = 6 K ),, $ AA,, > ),, = 6 K , $ ( > ),, − ),, = ,CB
AA,,
&1
* − ? ≈ K ),, $ AA,, "
,C.B
K K ),, $ AA,, '
),,2
'"
*
6 > * 6 − ? − ),, < = ,C.B 3
6 − ? − ),, < = ,C.B ⇒ 6 K , $ ( <
⇒
= (C.+ ⇒ (&,
AA,,
= ,C.B ⇒
AA,,
6
!&,,
!),,T
),, − (&, $ ),, + (&, .BW
!"#$%&8(8
5
!BA2
5
(%*
7 \ BC)
)0!
K & $ ) K-$@ * ,C.B 5
)*+,-."
1
!
K µ $ σ *
7σ χ − 6 5
!B
A ≈ 7 µ σ ' ≈ 7 µ σ 3
B 7σ ≈ χ− = χ $ A 7σ ≈ χ − = χ A 7σ (+ &
=
≈ G 1
σ = σ 3
B 7σ (B A
(+ (+
( 6 7 \ BC) = 6
> BC) = 6 G > (+ BC) =
(B
(B
(B = ( − 6G ≤ (+ BC) = ( − ,C.)@
(B
6G ≤ A C(. = ,C.6G ≤ +CB. = ,C.B
) ≈ K & $ ) ? ≈ K-$@ !
BA3
B 7) ≈ χ− = χ $ A 7@ ≈ χ − = χ B 7) (B A
=
≈ G 63
A 7@ &
1
(B 7 ≈ G "
,C.B
0
G '2/
2 − *9: = *9* 2
5
"
" G '
'2/ G ! ≤ 9 = *9:; $3
6 G ≤ = ,C,)B ⇒ 6 (7G ≥ (7 = ,C,)B ⇒ 6 G ≥ (7 = ,C,)B ⇒
⇒ ( − 6 G ≤ (7 = ,C,)B ⇒ 6 G ≤ (7 = ,C.-B ⇒ (7 = .C.@ ⇒ = ,C(
* 6 ,C( ≤ (B 7 ≈ G ≤ (B(
C = ,C.B 3
C 7(B = ,C.B
6 ,C(7(B ≤ 7 ≤ (B(
6
!BA
K & $ ) K-$@ .BW
* 7 ,C(7(B $ (B(
C 7(B