T覲ICOS EM ESTAT蚐TICA
Transcrição
T覲ICOS EM ESTAT蚐TICA
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()2 3 -4 3 %8.&4 &3 .* $#2 3 $# *2 &)(") 3 <8( *2 IBK&)&L &3 ) ) )2 A; MN 9 9+9 :&,&3 ; :&,O3 :O,&3 :O,O3 ! 3 #) 06<8( *.-2 MN 9 PGQR < PGQR ! ; SD S; ; SD D ) )% -06 # &8& .-J'& (2 .-J'&#& .B .-J'& :3 +)%.-#&8))&2 ) ).(8()))&)( :3B ) )#))5()9 :3 :3B :93 :;3 A> 3 #) 06T8.&) 06)2 :$3 ; D ! ; $ #01)&7 ) )#0) 29 <"2∅ +62∪BCI2I∈I∈F )&062∩BCI2I∈I∈F # 2 BCI2I∈9I∉FB9H .02HBCI2I∈I∉FB∩ 2 ( ∪B∪4 ∩B∩ ;2))& ( ∪:∪3B:∪3∪B∪∪4 ∩:∩3B:∩3∩B∩∩ >2) ( AD ∩:∪3B:∩3∪:∩34 ∪:∩3B:∪3∩:∪3 D2)# ) : 3B ∩ B∅ ∪ B9 9 B∅ ∅ B9 E2 ) ∩9B ∪9B9 ∩∅B∅ ∪∅B 2)N% : ∪ 3 B ∩ 4 : ∩ 3 B ∪ A2&7 #))& &2 B:∩3∪:∩ 3 2&7 ∪#))& &2 :∪3B∪: ∩3 29⊂, 62 ∩B∪B AE ; I N99 9 97)#0) ,ξ&))( ) .06 (.ξ 6 &=.06# ,#( ,)))% )$))(.& U ( ,!≤:3≤3 :>3 ;U :93B :D3 >U 9)6( ) $&)(),) ,6# &) #, 62 :+3B:3V:3 :E3 DU 9 , ;, , )-J'& ( ) $&)(), 62 :+;++3B:3V:;3VV:3 :3 $#)2 H =8 >! ) ! (=), E ") E &) & #)5(=" 9062 : < 3 = ! E = 4 : W3 = = >! > >! ) ( ) (= " ) $& #& $>, H)2 : < ∪ 3 = : < 3 + : 3 = + = > ; ;H+ & $ 5 &) = & E; & )&#)2 3 4 &3,)6)4 3 & )4 3,) A 9062 97)( )2BK& L BK& )L 3 :3 = D 4 E; 3 :3 = > 4 E; &3 )7)( )2BK& L BK& )L G)&&2 : − 3 = :3 − : ∩ 3 = 9 >; > D > − = E; E; E; 3 :,)3 : ∩ 3 = : ∪ 3 = > = E; ; : ∪ 3 = − : ∪ 3 = − [:3 + :3 − : ∩ 3] > D + + : ∪ 3 = − E; E; E; : ∪ 3 = − 9 >; > > = E; E; >H') &() , ) 6 & ) (") ) #(8(%=-)("))- 3 G))6)#)( *&,) ,:3, :3:3X 3 G))#)-%=X AA 9062 3 97:3B )("))#(8(%=-, 6:3B; )("))#(8(-, 62 :3 B ;:3 B ;:;3 B D :3 V :3 V :3 B , H)2 V ; V D B A = ∴ = )) H)2 A ; D :3 = 4 : 3 = 4 : 3 = A A A 3 )6 $& ), H)2 : ∪ 3 = : 3 + :3 = ; > + = A A A > N99 9 U 9 ∅ &7 (", 62 : ∅ 3B! :A3 ) 062 E H)-2 :∅ ∪ 9 3 B9 :3 :∅ ∩ 9 3 = ∅ ,% ∅ 9)6 $& )#& $>:3 H)2 : ∅ ∪93B:93∴: ∅ 3V:93B:93∴: ∅ 3B! ;U 9 ( &# ( , 62 : 3BH:3 :3 A ) 062 = 9 − ∴ : 3 = : 9 3 − : 3 : 3 = − : 3 >U 9:Y3.0 , 62 :!3 : − 3 = : 3 − : ∩ 3 ) 062 9 − = − : ∩ 3 ∴ : − 3 = : 3 − : ∩ 3 DU 9.)( )-)-,) , 6 $&)(), 62 : ∪ 3 = : 3 + : 3 − : ∩ 3 :3 ) 062 ( ∪ # ) &#) ) ( ) $&)():Y3,)72 ∪B:H3∪ +) >$> H)2 :∪3B:H3V:3 :∪3B:3H:∩3V:3∴:∪3B:3V:3H:∩3 EU 9 , . ') ( ) -)-, ) , 6 $& ), 62 :∪∪3B:3V:3V:3H:∩3H:∩3H:∩3V:∩∩3 $#)2 H ))% )))6)#5().2 D!Z)& )&## E!Z)& )&## :;3 A D!Z)& )&## Z)& )&#)# ) Z)& )&#)# ) ;Z)& )&#)# ) Z)& )&#)# ), 9 & )&= &), - #  3 # 4 34 3 )# )4 3=)# )4 &3 ) # 4 .3)# ) 9062 %< H)2 9 A ; ; E ! 3&4 : 3 = D! !! 3 : ∪ 3 = : 3 + : 3 − : ∩ 3 = D! E! A; + − = !! !! !! !! & 3 : − − 3 = :3 − : ∩ 3 − : ∩ 3 + : ∩ ∩ 3 = = E! ; A − − + = !! !! !! !! !! ! 3 : ∩ 3 = : ∪ 3 = − : ∪ 3 = − [: 3 + : 3 − : ∩ 3] = D! ; > E! + − : ∩ 3 = − = !! !! !! !! 3 : ∪ ∪ 3 = − : ∪ ∪ 3 = : ∪ ∪ 3 = − [: 3 + :3 + :3 − : ∩ 3 − : ∩ 3 − : ∩ 3 + : ∩ ∩ 3] = E! D! ; D! + + − − − + : ∪ ∪ 3 = − = !! !! !! !! !! !! !! : ∪ ∪ 3 = − . 3 : ∩ 3 = = !! !! !! ;H) # &# ) ) &$ .&=) )!!H)2 3 - # - # .&=, $ 5 &),6& =%)E4 3 )7;EE;4 &3 6)7 " 9062 3 97( 2 BK)&%)E !!L BCE,E,;E,>E,DE,E!,E,E;,E>,ED,EE,E,EA,E,E,E,AE,E,EF : 3 = − = !! !! 3 : ;E ∪ E;3 = : ;E3 + : E;3 = & 3 : 3 = ! !! ; + = = !! !! !! E! > D >H9 : 3 = , : 3 = )6 $&)(),&&2 D 3 : 3 4 3 : 3 4 & 3 : ∩ 3 4 3 : ∪ 3 4 & 3 : ∩ 3 9062 3 : 3 = − : 3 = − 3 :3 = :3 = > = 4 D D 4 D & 3 : ∩ 3 = ! 4 3 : ∪ 3 = : 3 + : 3 = > + = 4 D D > + = D D 3 : ∩ 3 = : ∪ 3 = : 3 + : 3 = ; DH9 : 3 = 4 : 3 = : ∩ 3 = ,& 2 > D 3 : ∪ 3 4 3 : ∪ 3 4 & 3 : ∩ 3 4 3 : 34 9062 3 : ∪ 3 = : 3 + :3 − : ∩ 3 = A 4 ; 3 : ∪ 3 = : ∩ 3 = − : ∩ 3 = & 3 : ∩ 3 = : ∪ 3 = − : ∪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∩ ; 3 = : ∩ > 3 = : ; ∩ > 3 = !,! : ∩ ; ∩ > 3 = !,!! [: ∩ ; 3 − > ] = [: ∩ > 3 − ; ] = [: ; ∩ > 3 − ] )) − )2 [: ∩ ;3 − > ] = : ∩ ; 3 − : ∩ ; ∩ > 3 [ ] : ∩ ; 3 − > = !,!− !,!!= !,!! ) #) # () % < )%2 9 ; !,! !,!! !,! !,!! !,!! !,!! !,! !,A; > 3 97( 2 B K #0 . )L4 - )%.& - #0 # ). ))( #))& &2 B ∪ ; ∪ > 42 : ∪ ; ∪ > 3 = : 3 + : ; 3 + : > 3 − : ∩ ; 3 − :: ∩ > 3 − : ; ∩ > 3 + + : ∩ ; ∩ > 3 = : ∪ ; ∪ > 3 = : 3 = > !, − > !,!+ !,!!= !,;A 3 97( 2 BK#06 . L :3BH:3BH!,;AB!,A; D &3 97( 2 BK. ;L :3B:;3B!, 3 97( 2 BK. ) L % H)-:3B!,!2 BH;H> :3 = : − ; − > 3 = : 3 − : ∩ ; 3 − : ∩ > 3 + : ∩ ; ∩ > 3 :3 = !,− !,!− !,!+ !,!!= !,! 3 97( 2 BK. >)6;L = : ∪ > 3 − ; :3 = : ∪ > 3 − [: ∪ > 3 ∩ ; ] = : ∪ > 3 − [: ∩ ; 3 ∪ : ; ∩ > 3] = :3 = : ∪ > 3 − [: ∩ ; 3 + : ; ∩ > 3 − : ∩ ; ∩ > 3] = :3 = : 3 + : > 3 − : ∩ > 3 − : ∩ ; 3 − : ; ∩ > 3 + : ∩ ; ∩ > 3 = :3 = !+ !,− !,!− !,!− !,!+ !,!!= :3 = !,A .3 97( 2 PBK). );L :P3B:∩;3B!,! %3 97( 2 TBK6 . >L :T3 = : > 3 = − : > 3 = − !,= !, E =3 97( 2 \BK8$). )L [ ] :\3 = : ∩ ; ∩ > 3 ∪ : ∩ ; ∩ > 3 ∪ : ∩ ; ∩ > 3 ∪ : ∩ ; ∩ > 3 = :\3 = > !,!+ !,A; = !,A; 4 2 [ ] :\3 = : ∩ ; ∩ > 3 ∪ : ; ∩ ∩ > 3 ∪ : > ∩ ∩ ; 3 ∪ : ∩ ; ∩ >3 3 = [ ] :\3 = : − ; − > 3 ∪ : ; − − > 3 ∪ : > − − ; 3 ∪ : ∪ ; ∪ > 3 = :\3 = !,!+ !,!+ !,!+ !,A; = !,A; U& .06297) )&:3]! )# :S3#&'&,=#* )78 & &, #)) ) ( )#0 ) )) H) )% .062 : S 3 = : ∩ 3 : 3 :>3 AUN #&06) $#))6:>3 H)2 : ∩ 3 = : 3: S 3 :D3 $#))6:D3)"-#&'& % # &'& (") # &'&=#* )78 &:$ 06)#)063 $#)2 H+ & $ 5 &) = & E; & ) #2 3 & ).%,)H)-& )4 3 & )),)H)-& .% 9062 3 97)( )2 BK& .%L BK& )L G)&&2 > : ∩ 3 E; > = = : S 3 = > > : 3 E; 3 G)&&2 > : ∩ 3 E; > = = : S 3 = ; ; : 3 E; ;H ##06 D #))), -) )6 0), ; #))) )6 )&=) &), ) #)06 G # ))0)X 9062 ) 06=#% & H)2 BK))60)L ; ! ; ; = = = !, >! : 3 = D ; + "#&& H)2 BK^0L BK;^0L A G)&&2 : ∩ 3 = : 3 : S 3 : ∩ 3 = A E ; = = = !,>! D > ; U))( ) # ) .062)( ))6 )# ))2 :∩3B:3:3 :E3 ) &):S3B:3:S3B:3,) ,# &'&6. #&'&,6 ')( ),;,>)6 # ))2 :∩[3B:3:[3,≠[ :3 :∩[∩O3B:3:[3:O3≠[≠O :A3 9 ) :3 ) (.& ) ( ) )6 ) ) # ),)6 # ) $#)2 H9)))60),-#-& ) 5E# ) 9062 97)( )2 BKE0 UL ;BKE0 ;UL )#0) #&2 9BC,;,>,D,E,F49;BC,;,>,D,E,F : 3 = ; ; 4 : ; 3 = #&.06#'& H)2 : ∩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∩I IB:∪∪3∩I IB:∩I3∪:∩I3∪:∩I3#&.06# H)2 ! :I3B:∩I3∪:∩I3∪:∩I3 :I3B:3:IS3V:3:IS3V:3:IS3 %8( H)2 :I3B!,E!,!>V!,>!,!DV!,;!,!EB!,!>A T& 2 9 ) ( ) , ;, O #) # 06)#0) 9 -2 3 ∩ [ = ∅ , ∀ ≠ [ 3 O ∪ = 9 = 3 : 3 > ! , ∀ 6#( 2 I B : ∩ I3 ∪ :; ∩ I3 ∪ ∪ :O ∩ I3 )8 # # &)%2 O : I 3 = ∑ : [ 3 : I S [ 3 [ = :3 !U_) #&062$# ,)#=-#0)& )7. )G#)8-X 9062 G)&&2 : S I 3 = : ∩ I 3 : 3 : I S 3 = : I 3 : I 3 # )-2 :I3B:3:IS3V:3:IS3V:3:IS3B!,!>A ))2 : S I 3 = !,E !,!> E = !,!>A >A ) H)2 : S I 3 = ; 4 >A : S I 3 = ! >A T& 2 : S I 3 = : ∩ I 3 = : I 3 O : 3 : I S 3 ∑ : [ 3 : I S [ 3 4 = , ;, , O :3 [ = $#2 &$& & ))&$& E& ))E+&$)&= & 9 #, & # & (&$ 9062 %8( H)2 DS S; ES ;SE S; >SE ; #&H) _) H)2 : S 3 = : ∩ 3 : 3 : S 3 = = : 3 : 3 : S 3 + : 3 : S 3 D D ! ; = = : S 3 = D ; > + ; ; E ! ; : 3 : S 3 ; E = = : S 3 = > : 3 ! > )#) ) 3 +)60).&BK&LOBK&L 97)#0) 9#2 9BC:O43,:O4;3,:O4>3,:O4D3,:O4E3,:O43,:&43,:&4;3,:&4>3,:&4D3,:&4E3,:&43F 97)( )2 BK&&L BK&#L BK&;L H)2) )))% )&7 )2 3 {:&,3:&, ;3:&, >3:&, D3:&, E3:&, 3:O, ;3:O, D3:O, 3} 3 {:&, ;3:&, D3:&, 3} &3 {:O, ;3:&, ;3} 3 {:&, ;3} 3 {:&,3:&, ;3:&, >3:&, D3:&, E3:&, 3:O, ;3:O, D3:O, 3} .3 {:&, ;3} %3 {:O,3:O, ;3:O, >3:O, D3:O, E3:O, 3} =3 {:O,3:O, >3:O, E3:&,3:&, >3:&, E3} 3 {:&,3:&, >3:&, D3:&, E3:&, 3:O,3:O, >3:O, D3:O, E3:O, 3} 73 9 O3 ∅ 3 {:O,3:O, ;3:O, >3:O, D3:O, E3:O, 3:&,3:&, >3:&, E3} > ;3 +$# &)) #% )=)))) 6# &I 3 )#0) #$# { ( )( )( 9 = (I, I ; ) I, I ; I, I ; I,I ; )} 3 ( BK8$=)# & IL {( )( )( = I, I ; I, I ; I,I ; )}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a< 9b 9 .062 97 ξ $# 9 )#0 ) ))& $# +.06I,-))&& ) ∈ 9 I:)3(8( * #) 06T8.&2 9 I D ) I:)3 ); I:);3 )> I:)>3 P06<8( *)& .062+(8( *I )& ), () #))5() I . . . 8( ) 06 #) (8( * )& I , .- , )#&.& # #) ) () #))5(), 7 & # & ))) () )6 $#))) ".*,-%8.& .06 :I B $3 B :$3, .06 # (8( *I) 06:$3) ).")&01)2 !E ∈ :;!3 3: $ 3≥!,∀$ 3 ∑ : $3= :;3 $ G- .06 - ) ).0 ) &01) & .06 # D; P06) 06 (<8( *)& .062 .06 ) 06 & ( (8( *)& I, # #2 P: I 3 = : I ≤ $ 3 = ∑ .: $ 3 $ ≤ $ :;;3 (8( * )& I, ) )." ) )% ) ##)2 3 P: I3 = : I ≤ $ 3 = ∑ : $ 3 $ ≤ $ ;3 ! ≤ P: I3 ≤ :;>3 :;D3 >3 P: I3 .066H&)& ,) 2 9 $ ≤ _ , 6 P: $ 3 ≤ P: _3 $#)2 H0 )) 97( 2 IBK&) )L IBC!,,;F :;E3 ! #) 06T8.&2 9 I :&,&;3 ; :&,O;3 :O,&;3 ! :O,O;3 %8(2 S; S; S; S; S; ; c; ; c S; c; .06 :I B $3 B :$3, .06 # (8( * I ) . - % 8( H)2 ; : I = !3 = 4 : I = 3 = 4 : I = ;3 = D D D P06#.-2 IB$ ! ; :IB$3 D ; D D ) 06 :$3 .06 #, (" - ) ).")&01):;!3:;3 !A ;H ! #0), > ) -) . )), $ H) > #0) :) #)063 97 I #0) . )) ) H)2 3 (.- ) (8( * I #) .06 #4 3 &&:I ≤ ;3 9062 3$BC!,,;,>F& 5I + ") 06\#% & H)2 > A $ > − $ , $ = !, , ;, > : I = $ 3 = ! > > A ! > >E = : I = ! 3 = ;! ! > > A ; > = : I = 3 = ;! ! > > A ; ; : I = ;3 = = ;! ! > > A > ! : I = >3 = = ;! ! > ! #) 06T8.&2 :, , 3 > :, , 3 :, , 3 ; : , , 3 : , , 3 : , , 3 : , , 3 ! : , , 3 P06#.-2 IB$ ! ; > :IB$3 >E ;! > ;! ; ;! ;! T8.&:\) %3 :$3 !,E ! ; $ > 3:I ≤ ;3B:IB!3V:IB3V:IB;3B ;! ! >H& ) &=I(d#5 , ) &=(, (8( * & )% ) 06#2 :IB$3BO:>H$3:DH$3,$B!,,;,>:O&) 3 3 & (O4 3 - # = & - &= -#5X4 &3 -##)& 4 3 -#& 8$ 9062 3 ).06#2 ∑ : $ 3 = ∴ > ∑ O :> − $ 3 :D − $ 3 = $=! $ O[> D + ; > + ; + ! ] = ∴ ;!O = ∴ O = )) H)2 : $ 3 = : > − $ 3 : D − $ 3 , $ = !, , ;, > ;! 3 :=& 3 : $ = ! 3 = ; > = = : > − !3: D − !3 = ;! ;! ! E &3 :#)& 3 : $ ≥3 = − : $ = !3 = − > ; = E E 3 :8$3 : $ ≤ 3 = : $ = 3 + : $ = 3 = : $ = 3 = > + = ! ! ! > = : > − 3 : D − 3 = ;! ;! ! ;! ! DH97I# )-#&7% 6H(& 3 & ) 06#I4 3 &&:eIeD3 9062 3) 06#I , ) $ = ,;,>,D,E, : $ 3 = !, &)& 8 3:eIeD3B:IB;3V:IB>3B D> = ) 01)7 )#<8() *))& ) 9 I d )6 (8() *) )& ), .) .06 #&7 Id#2 : I = $, d = _ 3 = : $ , _ 3 :;3 2 :;A3 3 : $, _ 3 ≥ ! 3 ∑ ∑ : $ , _ 3 = $ :;3 _ + .06 # &7 # I d # ) #) # - # &7 , & #) )% # ) I B I[ ) )H) ) ) )=&)# $[,) : d = _O 3 = ; : _O 3 = ∑ : $ [ , _O 3 , O = , ;, , [ = :;3 G+ [+Id _ d d; d I :I,d3 :I,d;3 :I,d3 :I3 I; :I;,d3 :I;,d;3 :I;,d3 :I;3 I :I,d3 :I,d;3 :I,d3 :I3 ;:d3 ;:d;3 ;:d3 I ) () :$[3 ;:dO3 )6 &=) .01) %) #,#. )#)) ))()) %)- ))2 ∑ :$ [= :>!3 [ 3= ∑ : d 3= O = ; :>3 O -#))& &2 ∑ ∑ : $ , d 3= [= O = [ O :>;3 $#2 - )% #) .06 # &7 )(8() *))& )Id,#:$,_3B:;$V_3, $_# )() ) )-!≤$≤;,!≤_≤>,) :$,_3B! )) )&))H)2 3 &) -#&7 4 ; 3 (&) &4 &3 :IB;,dB34 3 :I≥,_≤;3 9062 3 -#&7 2 _ ! ; > ! ! ; > ; > D E D ; D E A ;; ; E D; I 3 .06 D; = ∴ = D; &3 : I = ;, d = 3 = E = E D; 3 : I ≥ , d ≤ ;3 = : ; + > + D3 + : D + E + 3 = ;D = DD ;D D = D; A <8() *))& ) # ) 97Id(8() *))& )9)( )IB$dB_ )6 # ) # $ _, 6 ") - I d )6 (8() *)# ) &)2 :IB$,dB_3B:IB$3:dB_3 :>>3 $#2 N) - ) (8() *) I d # )6 # ) 9062 > .06,)Id)6# ),() # $ _2 : I = $ , d = _ 3 = : I = $ 3 : d = _ 3 : I = ;3 = ;; : d = 3 = D; D; : I = ; , d = 3 = ;; >> = = = = D; D; AD ; ;D ) : I = ;, d = 3 = DE E D; E , 6)(8()Id)6# ) ≠ D; & <)-):3]!, 62 : S 3 = : ∩ 3 : 3 :>D3 9Id)6(8() *))& )) )2 :2IB$3,:2dB_3, 6$#))6:>;3) 2 : d = _ S I = $ 3 = : $, _ 3 : $ 3 :>E3 2 :$,_3B:IB$,dB_3.06#&7 I d:$3.06#%I )) :dB_SIB$3 &= .06 # && dI $#2 H) 06&7 $# , 2 3 :dS;34 &3 :dBSIB;3 D 9062 # 2 :$, _3 B : ;$ + _3 D; : ;$ + _ 3 : $ , _ 3 D; , # $ = ; − )2 3 : _ S $ 3 = = : $ 3 : $ 3 :D + _3 :D + _ 3 D + _ D; D + _ : _ S ;3 = D; = D; = = ;; : ;3 D; ;; ;; D; E : ; , 3 E = D; = 3 : d = S I = ;3 = ;; ;; : ;3 D; ;H)8)#) ),--#5 = (8( * & ) 06 #) #2 :I3BO:EHI3:DHI3,IB!,,;,>,D & # , -- #5 =, ) #) )2 3 $ ))8)4 3 ))8)8$4 &3 $ ),)#)) 8#) 9062 & ()#&&8&O9)-2 E ∑ : $ 3 = $ D! > = 3 : I = ;3 = : E − ;3 : D − ;3 = D! D! ;! ; 3 : I ≤ ;3 = − [: I = >3 + : I = D3] = − + ! = D! ;! O: ;! + ; + + ; + !3 = D!O = ∴ O = &3 "&& #&& H)2 : I = ;3 = : I = ; S I ≥ 3 = − : I = ! 3 D D! = D! = > ;! D! ;! ! − D! P06 ) <8( * 5 9(8( *# ))() & (,(8( * & 5) &),%8.& # 8)#& &(&#) )% P T+YP+fg9 < a<I .:$3 I ! .06 .:$3 - ) ).0 ) ##) ; )% &= .06 ) # :.#3 (8( * & 5I 3 . : $ 3 ≥ !, ∀ $ ∈ :>3 +∞ 3 ⌠ . : $ 3 $ = ⌡ −∞ :>A3 # I ) &# . #2 : < I < 3 = ⌠ . : $ 3 $ ⌡ :>3 $#)2 H # &)6 #0 & & )06 (8( * & 5 & .06 ) ##2 ; . : $ 3 = O $ , ! ≤ $ ≤ , $ & ) =) ! , &)& 8 3 O4 3 #0 )&= &) && & & )06 G # - )D!!=)4 &3 - #& % #0) & ( !! D!! =) 9062 3 .:$3≥!,# !≤$≤ .:$3() ).":>A3)) H)2 A +∞ −∞ ! ⌠ ⌠ ; ; O $ $ = ∴ O $ $ = ⌡ ⌡ $; + O > O $ = ; > + ! O= [ ] = ! O [; − !] = ∴ A;O = > A; 3 G):!≤$≤D3BX D D ; $> ⌠$ = $ $> = A; > ; ⌡ A; ! [ ] D ! = ! : ! ≤ $ ≤ D 3 = D = D − !] = [ ; ; = = !,; = ;,Z ED ;A &3 :≤$≤D3BX D ∫ D [ ] $; $> $ = $> = A; A; > ; (≤ I ≤ D ) = D [D −]= > = ; = A = !,;; = ;,;Z ; A; ;D ; ;H.06)#<I #2 O −; $ $ ≥ ! .:$ 3 = ! $< ! & 2 3 (O4 3 :I];34 3 :H>eI≤D3 9062 ∞ ∞ ∞ ! ! −; $ −; $ −; $ ⌠ −; $ 3 ⌠ =− O O $ = O $ = O ⌡ ⌡ ; − ; ! [ ] ∞ ! = ∞ =− O O = − − = ;$ ; ! ; ∞ =− O O [! − ] = ; = ∴ O = ; ; ∞ ∞ ∞ −; $ ⌠ ⌠ 3 : I > ;3 = ; −; $ $ = ; −; $ $ = ; = ⌡ ⌡ −; ; ; : I > ;3 = − ; [ ] ; ! − −D = −D = !,!> = ,>Z ; ! D [ ⌠ ⌠ & 3 : −> < $ ≤ D3 = ! $ + ; −; $ $ = − −; $ ⌡ ⌡ −> ] D ! = ! : −> < $ ≤ D3 = − − + = − − = !,A = , AZ >H # 06 -5& (8( * I & )% .06 ) #2 & $ ; , ≤ $ ≤ ; . : $ 3 = & $ , ; < $ < > ! , &)& 8 2 3&) &4 3 (I > ;) 4 > ; &3 < I < 9062 ; > > $> $; D 3 ∫ &$ $ + &$$ =∴& + & = & − + & − = ; ; > > > ; ; ; D& + E& A E = & + & =⇒ = > ; ;& = ∴& = ; ; ; ∫ > E 3 ⌠ $$ = =!, EA=E,AZ ⌡ ; ; ; >; ; = !,D = ,DZ &3 ⌠ $ $ = ⌡ ; DA P06 ) 06 ( <8( * 5 .062 .06 ) 06 & ( (8( *& 5I,#2 P: $ 3 = : I ≤ $ 3 = $ ∫ .:3 4 − ∞ < $ < ∞ :>3 −∞ G.06) 06& ( ,(8( * & 5 I, . &=&, (8( # $, #H) .06)#:.#3,("-2 .: $ 3 = Ph : $ 3 = P: $ 3 $ :D!3 ;! $#)2 H # &)6 #0 & & )06 (8( * & 5 & .06 ) ##2 $; , ! ≤ $ ≤ , $ & ) =) A; .: $ 3 = !, &) & 8 & .06) 06& ( 9062 P: $ 3 = $ ∫ .:3 = ! ,)$e! −∞ $ $ ! > $> P: $ 3 = .:3 + .:3 = , ) ! ≤ $ ≤ = ; ! ; −∞ ! ∫ P: $ 3 = ! ∫ ∫ .:3 + −∞ ∫ ! ∞ .:3 + ∫ .:3 = = ! + + ! = ,) $ ≥ 2 $> , ! ≤ $ ≤ , $ & ) =) ; P: $ 3 = , ) $ ≥ ; ;H97 (8( * & 5 I & .06 ) 06 & ( #2 ! , ) $ ≤ ! P: $ 3 = $ ; , ) ! < $ < , ) $ ≥ & .06)#I 9062 .: $3 = Pi : $ 3 , 62 ! , ) $ ≤ ! .: $ 3 = ; $ , ) ! < $ < ! , ) $ ≥ D )#0N 8 &<8( *)& .062 =H) )#0 8 & (8( *)& /))# ) ))))()#))5()# ))#) 9#=) - < I )) ) () $, $;, , $ & #),;,,,)72 IB$ $ $; $ :IB$3 ; ;; 6#.062 : I 3 = $ + $ ; ; ++ $ = D ∑$ = :D3 )#0N 8 &<8( * 5 .062 (8( * & 5 I & .# .:$3 .H))#0I&2 +∞ ⌠ : I 3 = $ . : $ 3 $ ⌡ :D;3 −∞ $#)2 H - )% .& () #) ) # ; &# ) ) &# )) )) = ) #))#& ()& ()#:()# 8- #5)3 IB$ ! ; > D E :IB$3 ; ; D ; ; ! ; > ; ; ; ; 9062 : I 3 = ∑ I : $ 3 = ! $ ; D ! > ; + + ; + > + D + E + = ; ; ; ; ; ; ; :I3B;,D()#8- ;H # )# # &= # )- &% # W ) (8( * & .# #2 O $ , < $ < D , =) .: $3 = ! , &)& 8 ;> & # - & &= .& . )# 9062 3 8&O D D [ ] O ; ⌠ ⌠ O$ $ = O $ $ = ; $ ⌡ ⌡ ! D ! = ! O [ − !] = O = = O = ; +∞ D D D −∞ ! ! ! ⌠ ; ⌠ ⌠ ⌠ ; 3 : I 3 = $ .: $ 3 $ = $ $ $ = $ $ = $ $ = ⌡ ⌡ ⌡ ⌡ D : I 3 = $> > $ = > ;D [ ] ! D ! = [D − !] = ;,A =) ;D D! <?&)(6<8( *)& @.8&&(8() *)-#) ), # . ) () #))5() <7) # $#, ) (8() *)Id,)#))% )) 01)2 IB$ :IB$3 E E !,E !,E :I3BE!,EVE!,EBE dB_ :dB_3 ! ! !,E !,E :d3B!!,EV!!,EBE (), ) ) ) (8() )6 ' &), # ) ()I)%# ::I33,- -)() d)& )#)) )) ), &=& ) , 6 ) # ." .'&)) & ) () (8( ) ) ;D )) (, 7 & , "H) #? , (?&, - % .) ) )06) .06297I(8( *)& (?&)) (8(.#2 <: I 3 = [: I − : $ 3] ; :D>3 .* ( # &8& (?& # ) &&. )% 2 (?& % / .0 )#0 8 & - (8( * I - ) )#0 8 &,)72 <: I 3 = : I ; 3 − [: I 3] ; :DD3 2 : I ; 3 = ∑ $ ; : $ 3 :DE3 $ ) 062 [ ] <: I 3 = [I − : I 3] = : I ; − ;I : I 3 + ;: I 33 = ; <: I 3 = : I ; 3 − ; : I 3 : I 3 + ; : I 3 = <: I 3 = : I ; 3 − ; ; : I 3 + ; : I 3 = <: I 3 = : I ; 3 − ; : I 3 )) 2 <: I 3 = : I ; 3 − [: I 3] ; ;E >H)))$&5& :() #) )#;&# ) )&# )))),& <:I3σ:I3 IB$ ! ; > D E :IB$3 ; ; D ; ; ! ; > ; ; ; ; 9062 <: I 3 = : I ; 3 − [: I 3] ; $&5& :I3B;,D()#8- 8&:I;3 : I 3; = ∑ $ ; : $ 3 = $ : I 3; = ! ; : I 3; = ; D ! > ; + ; + ;; + >; + D; + E; + ; = ; ; ; ; ; ; ; D ;D ! D E! > ;E; + + + + + = = ; ; ; ; ; ; ; <: I 3 = − [;,D] = ;,!> :()3 ; ; " - :#) (3 (?& &=H) )( #6 ( &) 2 σ $ = <: I 3 = ;,!> = D; , ()#8- ; D <?&)(6<8( * 5 .06297I(8( *& 5(?&)) (8(.#2 +∞ ⌠ <: I 3 = : I 3 − [: I 3] = $ ; . : $ 3 $ − µ ; ⌡ ; ; :D3 −∞ )(#6)8#2 σ$ = :DA3 <: I 3 DH ) ) ) $&5& ; : # )# # &=#)-3,&&(?&)(#6 +∞ ⌠ 3 <: I 3 = $ ; . : $ 3 $ − µ ; = ⌡ −∞ D D D ⌠ > $D D ⌠ : I 3 = $ ; $ $ = $ $ = = $ D >; ⌡ ⌡ ! ; ! : I ; 3 = [ ] D ! = ! [;E − !] = >; <: I 3 = − [;,A] = − A,; = !,A ; 3 σ $ = !,A = !,>> ≅ E ) E P+fj9< a< 9b 9 97Id(8() *)))#0) 9"H )-d.06I,9d#)#) #dBT:I3 $#)2cI,I;,IVc)6.01)I&T:I3Bc$,$;,$Vc U 97Id<8() *))& )&dBT:I3 ;A 62 :D3 : d 3 = :T: I 33 = %: $3 : $3 + %: $ ; 3 : $ ; 3 + + %: $ 3 : $ 3 : d 3 = ∑ %: $ 3 : $ 3 :D3 = ;U 97Id(8() *)& 5)&dBT:I3 62 +∞ ⌠ [T: I 3] = T: I 3 . : $ 3 $ ⌡ :E!3 −∞ $#)2 H97 I <8( * $&5& : () #) )#;&# )3.H)dB;I,&)&) #&& I()H)2 3 &) :d34 3 :d≤D3 9062 ) 06 #) (8( d # ) &.-)%2 dB;I ! ; D ! ; :$3 ; ; D ; ; ! ; > ; ; ; ; ; : d 3 = ! ; D ! > ; + ; + D + + + ! + ; = ; ; ; ; ; ; ; : d 3 = ! + ;D ! ;D ;! ; D + + + + + = = k E,; ; ; ; ; ; ; ; : d ≤ D3 = : d = !3 + : d = ;3 + : d = D3 = ; > = = = D;,Z ; D A ;H #:=)3%) # &&$&06& #(8( *&.##2 O −> , > .: 3 = ! , ≤ P T+;YTaP P+fg.: 3 .: 3 9H) - & k E!,!! # = = # ) &) ) - ) > =) k D!,!! # ) &) ) - >=)),- &) &) X 9062 97dBT: 3.06&) 2 E! , d = T: 3 = D! , < > ≥ > ; 3 8&O2 ∞ ⌠ = O ⌡ ∞ −> =− ⌠ = ∴ O ⌡ −> ∞ =− O = ; ; O O ! − ] = = ∴ O = ; [ ; ; 3 ) &) 2 ∞ > ⌠ : d 3 = : E! 3 : ; ⌡ −> −; −> 3 = > ∞ > ⌠ = !! ⌡ ⌠ 3 + : D! 3 : ; ⌡ ⌠ + ! ⌡ −; = − !! [ ] > − > ∞ > = − !! − ! = − !! − − ! ! − > > : d 3 = − ∞ − + ! = − > = > ! ;! !! + !! + = = k >,>> > > > >H97 I <8( * )& & ) 06 ##2 IB$ H; H ! ; :IB$3 ! E E > ! E .H)dBI; & 2 3 ) 06d4 3 :dB3 >! 9062 <)#))5()d2_BC!,,DF 3 ) 06d : d = !3 ⇔ : I = !3 : d = ! 3 = : I = ! 3 = E : d = 3 ⇔ : I = − 3 ∪ : I = 3 : d = 3 = : I = − 3 + : I = 3 : d = 3 = > + = E ! ; : d = D3 ⇔ : I = − ;3 ∪ : I = ;3 : d = D3 = : I = − ;3 + : I = ;3 : d = D 3 = > + = ! E ! )) H) )% ) 06 # # (8(d2 dB_ ! D :dB_3 E ; > ! T" H)2 : d = _ 3 = ∑ $ 2 d = T: I 3 : I = $ 3 :E3 > 9N@ < l ^ 9&) , 62 :3B :E;3 <:3B! :E>3 ;^ 9&) I<8( *, 62 :I3B:I3 :ED3 <:$3B;<:I3 :EE3 ) 062 { } = {[I − : I 3] } = { [I − : I 3] } = <:I 3 = [I − :I 3] ; ; ; ; = ; [I − : I 3] = ; <: I 3 ; >^ 9I<8( *)6&) ), 62 :I±3B:I3± :E3 <:I±3B;<:I3 :EA3 D^ 9I,I;,IO)6O(8() *), 62 :I±I;±±IO3B:I3±:I;3±±:IO3 :E3 <:I±I;±±IO3B<:I3V<:I;3VV<:IO3 :E3 $#)2 H97I(8( *$H)2 3:I343:I;34&3<:I3 IB$ ! ; :IB$3 D ; D >; )#) 2 :I3B :I;3B>S; <:I3BS; ;H97I(8($&5&.H)dB;IH)2 3:d343:d;34&3<:d3 9062 .06#(8(d#)&. -)%2 dB_ ! ; D :dB_3 D ; D + ").01) )#(?& H)2 3:d3B; 3:d;3B &3<:d3B; >HP"H)>)#)&#)& (%) 2B!,D;B!,>>B!,&=)#0 8 & & ) 9062 & ) # )# <8( * I-#)))()2:& 3&#B!,D! :3,&#-BH#B!, >> )) H)2 :I3B!,DV!!,B!,D) H)2 :I;3B!,> :I>3B!, 97W & ), 62 WBIVI;VI> :W3B:I3V:I;3V:I>3B,>& ) DH&= )#0 8 & (?& ) # )-#),0))2 9062 972IB# )# I;B# ))% ) () #))5() I ) #) )#& (), ) 6 #) )-$ IB$ ; > D E :IB$3 : I3 = A + ; + + = ; )()#))5()I;)6' &)I, H)2 : I ; 3 = A ; >D .H)2 W = I + I ; ∴ : W3 = : I3 + : I ; 3 = : I3; = ; A A D + = =A ; ; ; ; A + ;; + + ; = E,A 4 <: I3 = E,A − = ;,; ; <: W3 = <: I3 + <: I ; 3 = E,D σ: W3 = E,D = ;,D; EH ) # ) 5&), # && #& ) 8- 8 & #& ) 8%##);!!%)# , #,%#&)68-,#) )) ))&)(#6>%)9H)- % #) &) ;E %), - )(#6#) #& X 9062 97I#) I(8( *&2 :I3B;!!%4σ:I3B>%4<:I3B%; #) #& #).&2 W = I + ;E 2 : W3 = : I + ;E3 = : I 3 + ;E = ;!! + ;E = ;;E% <: W3 = <: I + ;E3 = <: I 3 = %; ⇒ σ : W3 = >% H# ,)#)% (8( *&;E%)(#6%,-)8 )(#6#) X >E 9062 #) :I3#)%:d3)6) <8() *) # ), 6 #) . (8( W &2 W=I+d : I 3 = ;!!% 4 σ : I 3 = >% 4 <: I 3 = %; : d 3 = ;E% 4 σ : d 3 = % 4 <: d 3 = %; ))2 : W3 = ;!! + ;E = ;;E% <: W3 = + = ! %; ∴ σ : W3 = ! ≅ >,E% AH+ #&)) .&06 #" #0) & #) ;!%)(#6!,E%) )#0))6&&)#& ) " & ) %) #) >!% & )( #6,;%G)(#6#) #& X 9062 I = #)#0,B,;,,; 97 d = #)% W = I + I ; + + I; + d = ; ∑I = +d (W )= (I + I ; + I; + d )= (I ) + (I ; )+ + (I; )+ (d )= (W )=;;! + >! = ;A!% < (W )= < (I + I ; + I; + d ) = < (I ) + < (I ; ) + + < (I; )+ < (d )= < (W )=;!, ;E + , DD = D, DD% ; σ (W )= D, DD ≅ ;,% H+ %"06 && (.& - & 8 :3 #(# I#)% $#))62 B,<H!,HD,E > 9H)-#0( 8:<3 ) 06 k E!,!! )( #6 k ;,!!, - &) 8 :3 ) 06kDE,!!)(#6k,E!,- )(#6& 8X 9062 < = 0< = ) + 8 : <3 = E! 4 σ: <3 = ;, !! 4 <: <3 = D, !! 97)(8() , 4 <:3 = ;,;E :3 = DE 4 σ:3 = E! , < − !, − D,E3 = , : <3 − !, :3 − D,E = : 3 = : , E! − !, DE − D,E = EE − D!,E − D, E = k!, !! : 3 = , < − !, − D,E3 <: 3 = <: , ; <: <3 + !, ; <:3 = , ; D + !, ; ;,;E <: 3 = + , ;E <: 3 = D,D + ;;E , σ : 3 = , ;E = ;,E H )% 8H) ) ) 01) #) ) (8() *)# )Id.H)2 W = − ;I 4 + = − I 4 = I − ;d ; H)2&&(?&W,+ IB$ H ! dB_ ! ; :IB$3 ; > :dB_3 D ; D 9062 (?& ) (8() I d ) 6 #) ) )%2 >A : I 3 = ! : d 3 = : I ; 3 = > : d ; 3 = > ; <: I 3 = > <: d 3 = ; )) H)2 : W3 = : − ;I 3 : W3 = − ; : I 3 = − ! = <: W3 = < :− ;I 3 <: W 3 = D < : I 3 = D > − I :+3 = ; :+3 = : I3 = − ; ; ; <:+3 = < : I3 = D ; : 3 = : I − ;d 3 : 3 = : I 3 − ; : d 3 = ! − ; = − ; <: 3 = < : I 3 + D < : d 3 = A + D = > ; > A 9 + fj9b 9 99 9 A ) 06 )H)$# * ))% )&01)2 3 #()# )4 3 &#( #))) )2)&)):3,.&)):!34 &3 # )&)) & #( &) , )7,:;S3B:;3B#,)-BY#4 > ))& (8( * )& I % )&))) ))) #(), 6 # ( & $ $(") (),#.06#2 m : I = $ 3 = # $ - − $ = # $ - − $ $ − $ m : $ 3m :!3 ) 06 (8( * I #) )&))), 6))#))5()())62 IB!,,;,, A ? )) 06 N2:I3BnB# :3 <?&2<:I3Bσ;B#- :;3 $#)2 H&;("))(&)H)2 3 -#) &X 3 -#) )&)X &3 -#) )&)X 9062 #) &#B!,E,# 2 ; 3 : I = 3 = : !,E3 : !,E3 ;− = !,E ; 3 : I = ;3 = : !,E3; : !,E3; − ; = !,;E ; ; & 3 : I = !3 = : !,E3 ! : !,E3 ;− ! = !,;E ! > ;H9H) - DZ ) #0) #") # & 8- )6 . )) !#0),& 3 $ )). ))4 3 );). ))4 &3 - )( #6 #0) . ))X 9062 # #0 -- ) . ) # B !,!D, # 2 ! 3 : I = ;3 = : !,!D3; : !,3! − ; = !,!ED = E,Z ; 3 : I < ;3 = : I = !3 + : I = 3 ! ! − ! ! : I < ;3 = : !,!D3! : !,3 + : !,!D3 : !,3! − = ! :Ie;3B!,D>V!,;AA!B!,DBD,Z &3N2µB#B!!,!DB!,D )(#62 σ = A; #- = ! !, !D !, = !, ; ) 06\#% & .06297&7 ),)-) && 5) & : ≤ 3 9 $ 5) &) ) )#)06,(8( *)& I,% ) $ 5) - #)) . && 5) &, ) 06 =#%  − $ − I : I = $ 3 = , I = !, , ;, , :>3 D! A; ? )) 06=#% & N2 : I 3 = <?&2 <: I 3 = :D3 : − 3 : − 3 : − 3 ; :E3 $#)2 H ) & ! ), > =) ") 9 ) ))6) ) ,-#2 3 ) =)")4 3 = =)")4 &3 #) =)") 9062 3 97)( )2 BK) =)")L > A ; ! = ( ) = ! E ; 3 BK= =)")L > A ! ; A = ( ) = ! E ; D &3 BK#) =)")L :3 = − : 3 = − A = E E ;H+ .! %)),D&. )) ; & . ) %() 9 ) %) )6 )&=) : #*) ,)#)063,& #-2 3 ))7#. )4 3 ) =. )%()4 &3 #))7#. 4 3 8$)7#. 4 3 $ )7#. 4 .3 A> =) =. )%() ) 06)) <) - ) 06 .06 # #2 : I = $ 3 = # $- − $ , I = !, , ;,, $ :3 P"→∞, &) # αB#,-. I,.06#) 06#))& &2 : I = $ 3 = − α α $ , $ = !, , ;, α > ! $m :A3 -..06#) 06)) .")→∞, 6#→! ,#)&&- ) 06 )) #&8( ) ) ( ) #-) #)&'& ) )) ) 06 # ) 06 )), ) - )7 % # )7 #- #8 &, )) #$06% )#≥E!#≤E,&:I3BαB# D; ) 06)) ". )) 01).5)&)@ )#)&(, ( #( ) )&2 &=%&)&" 4&=) .`&)& 4 ))6# 5&))) ?& (, & A> ? )) 06)) N2 : I 3 = α :3 <?&2 <: I 3 = α :3 )(62 σ: I 3 = α :A!3 $#)2 H ()6 #%8.& ( &=H) ,E ) # #8% ) !! #8%) (, ) - ) 6 #&) ) .&)#6#) ) 9062 #6 )#8%2 : I = ! 3 = −, E E , ! = −, E = !,;;>= ;;,>Z !m )!!#8%)())#-2 !!!,;;>≅A#8%)6#) ) ;H&=) .`&)-&=%& )%) 06))&# 3 G # = &= &=% & X 3 ))&=)&=%X D> 9062 : I = $ 3 = − $ , $ = !,, ;, $m 3 : I = !3 = − ! = !,!!;E ≅ !,;EZ !m 3 : I ≥ ;3 = − {: I = !3 + : I = 3} = : I ≥ ;3 = − {!,!!;E + !,!D} = !,; = ,;Z >H&% 8.%. ( #7 )) #( 06 ) (5&) &=% # #( , *% #+%=.") )(01)$ () ))) 6#) ) H 9 + fg PGQR MN <o+9N + U<o+9S PGQR N + :MN9<fj93 ! >; ; ; > ;! D > E A ! A ≥ ! ;! P2))-) 9 - $ E (5&) # 5( &5 & &% 8.%-&, #))5( ) % #)) DD 9062 )) )-2 ∑ I. I= = ! + >; + + ! = ;! I = ;,! = α 2 ( I = $ ) = −;, ! ;,! I $m ( I ≥ E) = − ( I ≤ D) = − !,>D!> = !, !! = ,!;Z DH=1) &=% #*) "6 ;, &=1)S= # &=% ') ) &=1)2 3 #5>! )4 3 #5=4 &3 #5;=) 9062 3#5>! ), α = ;, , = D ; (I ≥ >) = − [ ( $ = ! ) + ( $ = ) + ( $ = ; ) ] −, D , D ! −, D , D −, D , D ; + + (I ≥ > ) =− = !,E = , EZ !m m ;m 3 #5=,αB;, :I≥>3B!,E>!EBE>,!EZ &3 #5;=),αB;,$;BE, :I≥>3B!,AB,AZ DE G+HN <9 9 + fj9 N , 99\ TN@ 9 + fg N 99 \ TN@ 9 ) )))5() )! )!∞ )! )(01) %)&))) %)&))) %)&))) .&))) .&))) ? ) # α ,, ( ) # ) # ) # ) ) ) # ) α & 9 + fj9b 9o+9 ) 06+. % .062 + (8( * & 5 I . ) 5 ( [, ],)).#. #2 − , ) ≤ $ ≤ . ($ ) = !, # -)- ) () %8.&))) 06) 8#) .%> P T+>H 9 + fg+ PN .:$3 − !I :A3 = " # " = %& σ = + ! − !$ − ! %'(#) % * &+&) ), #- '(#) -.(( α − α' ' > / ' / ' ≤ / !0 1 (# -(# 2+# '(#) (2 345*678%49:64;*4<=11>>?47@ ' α / ! '(#) α = µ = " # " = σ = %& σ = ! !! α α ! '() 1 ( & A ) ( )# # (##(A&+&)),.(( B − /. // ' = / ' '≥/ '</ ?)#)&)BC D) () ( &. ) ( #(A.(//AEC # D)(&(E 9) ?&+&)),#-. ∞ ⌠ B − /. // ⌡/ ' ' = ∴− B /.// [ ∞ ⌠ > // = /. // − /. // ⌡// > // = /. $/= $/.F # = = = 0// A α /. // − /. // ' ' ] ∞ / [ = ∴B = /.// ' = − − /. // ' ] ∞ // = $ %>) %*&+&)),#-)- .()( ' = σ π − ' −µ σ .−∞<' < +∞ ! GHC σ H&(C σ I/ D J (## K &+&) ), 2 )#G& # σ . 'L>GCσ / 1 (# 2+# ) 7 #& (& #& )#&5.((#20 345*670M%49:64;*4<=1>167@ 7 ) #- () (.K ( # (' N KOP#&Q-#C & ( (' N # ). 2C # N # ((N 2-).K 2( #2 $ () R 7)#)G.( G8SHGTB.#2 345*678%49:64;*4<=1>167@ R 7 ' &) +' ( ' H G. . G C $R 7'(),#'#. J )'H/)'H/ '→8∞'→T∞ R 7'()'('HG±σC 0R 7#)&( 3' = σ ' − ⌠ π ⌡−∞ ' − µ σ ' 0/ R 7)(##$H/ ###H$ $ %)(U 7 3'. ( ( #)# ().U8 U= U = '−µ σ $ ' ' = σ U σ 5 U = σ U ⌠ − π ⌡−∞ U σ' 5 U = ⌠U − π ⌡−∞ U U 0 K #) ( &+&) ) (UU 7 )U # & )GH/& # σ H. VL>/C .(&+&))(U+( 2 U = π − U .−∞<U<+∞ ! 0 $$ :)&))(U 7 ) (U ( ). )U8 2#>K '. &) )(./UU#+)#)U#( )5#()#(W+A#A 2! 345*67!8X67316>?4%7@7:7;@7%7?*6"7>167@ $ )((&)&) 8* (# # (U ( # #( 0// & ( / D) (#2 (K /0/ . F /0 / 0.F # !/0$/ .!F #0/ 0.!F '0 .F 0/.//F #0// 0 8%+#&)(U( /≤U≤. $.F 8/.≤U≤/ 0.F # 8/.≤U≤ . .$F /.≤U≤. . F U≥8. .!F U≥/. /./F 2 U≤8/.!.$F /≤UY. !.F A $ 8 98 K &+&) ), ) #µH/σH$.#)#)2() 'I!.F ≤'≤$ !./F # 'H/.//F '≤/ 0/.//F ≤'≤/ .F . /F 2 ≤'≤ .$F A Y'≤$ !≤'≤ . /F 81 #)#)-# µH/.()2&(σH/./ ()28 D)()K )(/.E $/.0F 1 ( #) K) )# K #+# /./ 0 D) () ##E . F 08*(##(A #&(0A?)#) 7()(K/A .0 F 7()(K0 A !.F 0$ # 7()( 0/A 0./$F 8 98 K ( (U ( +# 2 ) # /. 0 ()2 &(/./ ()2*(# 2) /. / ()2 2) /. ()2#(#)((U() +#E!.$/F !8 7 ) ( # ( Z & //A&(0/A?)#)() *) (K8#//A0.!!F *) (K8#//A.F # *) (K8// /A!.0F *) (K8////A/./0F 87')3-#! & # 98 K /F )A ) & # 2 7 D) -K)&(#)#8#7E$.0 F 8*()-###. (#0/B2(#.#&(.B21 #) '2 K. ( # # # # B2. #(2U6[/.//(#?)#)( )$///##.K)+##U 6[$.// 0 %D8D 9J V. V . . V υ . υ &+& ), (. ) -. # U & # &+&) ),K8K χ .( χ = V + V + V υ = υ ∑V = (( χ = υ υ Γ χ υ − χ − .χ ≥/ K8K χ = µ = υ / " # " χ = σ = υ %& σχ = υ > ,) . 8 2 # ( . ( Γ .()2)(,( ∞ Γ = ∫' − − ' ' . > / $ / %8K Γ = − Γ − H.(&. Γ = − \ 0 00 D J (## K &+&) ), 2 K8K # υ 2 ). χ L χ υ 1K$'(&)) χ .K χ > χ α. υ = α ! ) K $ ' . & K + α #)A #) 2 ) υ #)K7.&)#/2).+ ()/./0( χ /. /0. / = . $ ( &))U#().#2 χ > χ /. /0. / = χ > . $ = /. /0 *((#A##((& χ . # # ] S &+& ), ( χ . χ . . χ S . χ # υ. υ .. υS 2 ). (#&. χ # υ + υ + + υS 2 )^ 0 %9 9 V L > (/. ) _ L χ (υ) . V _ &+& ), (.&+&)),( = V _ υ 0 (( υ + Γ = υ πυ Γ + υ υ + − . −∞ < < +∞ ( υ 2) 0 9 = µ = / " # " = σ %& σ = = // υ υ− . υ > υ υ− / / 7 9 # ) H /. K. ( υ → ∞ ) ( ) # U & #)(U D J (## K &+&) ), 2 9# υ 2). /$ L υ 1K'(&)) .K ( > α. υ )= α / ) K ' . & K + α #)A #) 2 ) υ #)K7.&)#/2).+ 0! () /./0 ( /. /0. / = .$ ( &))U#().#2 / > /. /0. / = / > .$ = /. /0 *&UK #)U. K − α = − α .J. /. 0. / = − /. /0. / = − .$ %39# 9J&+&),( χ χ .U ( χυ υ υ χ υ = 3= χ υ υ χ υ υ /0 (( υ υ − υ + υ υ 3 Γ υ 3 = υ υ υ Γ Γ 3 + υ υ + υ ./<3<∞ / 23# υ 2) υ 2)`2)&# 3υ. υ 39# υ 3 = " # "3 = σ = υ − . υ > /! υ (υ + υ − υ (υ − ) (υ ) . υ > − ) / 0 %& σ = υ υ− / 739##(&)W K8KC ( υ υ # )')')W D J (## K &+&) ), 2 39## υ 2) υ 2). 3 L 3 υ . υ / 1K0'(&)) υ υ .K ( 3 > α C υ. υ )= α ) K 0 ' . & K + α (-)#)A2) υ υ #)A #) #. (#& 7. &) # 0 2 ) / 2 ).+()/./0( 3/. /0 C 0. / = $. $$ ( &) )U #().#2 3 > /. /0 C 0. / = 30. / > $. $$ = /. /0 0 917%"764X"497@7:a6479 9L> µ C σ .J(. bH7±7 ±±7L>µcC σ c ? µcH7µ±7 µ ±±7µ $ σ c H"cH 7 σ + 7 σ + + 7 σ '() 7()#N(##( &U&+&),(.# 2N)AN L> /C.$bL>C$. %8 : # &) ()#N & U %P: D) () K K)K (- & U &) ()#N J ( 6[$/E # 9J"H8b4("" 9) : = + b : L > µ : C σ : : = + b = / + = $ σ : = " : = " + " b = . $ + $. = !. : L > $C !. : − µ : $/ − $ = V > − .$ : > $/ = > σ: !. ) → /.$ + /.0 = /. $ = . $F V > − .$ / .$F & U (8 &) ()#N(6[$///////.// # " H 8 b H &) ()#N &U %" " L > µ " C σ & µ " = " = / − = σ " = " " = .$ + $. = !. " L > C !. / :167?>:67@%1@44: 9J. .. KOP# &+& ), ( # = µ . = . . . 0 " = σ . = . . . 3bHT TT#N2.b )# µ c = ∑ µ ! = σ c = ∑ σ = ? ( b L > µc C σc ) ≥$/J+()# 2 () ('N&)N( &+& ` K ('N N ;)()) '() 9J . . . /. / &+& ), # ()( ' = ' . / < ' < C =. . . / 9JbHT TT/8 1b ?)#)bI 9) ) : ? @ b L > µ c C σ c [ ] ⌠ $ ⌠ = ' = ⌠ ' ' ' = ' ' = ' ⌡ ⌡ ⌡/ / / [ ] ⌠ $ = ⌠ ' ' ' ' = ' ' = ⌡/ ⌡/ " = − [ ] = µ c = / / = $ − ! − = = = ! ! / $0 = / " b = / = = ! ! $0 b L > /C / = b > = U = − / $0 = − /.$ b > = V ≥ − /.$ = /. ! + /.0 = !. !F 6@7<=1>:67%49:64;*4<=1;4>14>7@%14991> > ). 2 () ( #(,'U.&>(+#.# #&.≥0/(≤0#) ('()#αH(. − ( ( ' ) ( ' K − ' = . = /. . .. '\ ' / → ∞ (→/ '() 8 #U +2 . () ##/.// 98KWA( ('///##U.K)()K ##K)(- 9) *)U) H///C(H/.// CKH/. /// ( = ') = (/.// ' )' (/.)/// − ' . = /. . . . /// $ ≥ = − [ = / + = ] = /// / /// /// + = − /.// /. /. // /. = / = − /.$0/ + /. !/! = /.0 ! = 0. $F ? #+)#) )A ( (' ( . J α = ( = /// /.// = ( = ' ) = ( ' ≥ ) − '\ ' . ' = /. . . = − [ ' = / + ' = ] = − = − / \ / + − \ = = − (/.$0$ + /. !/!) = /. 0/$ = 0. /F 88 /./ () & (,)# 2 ( K ( Z# ? . // ( ( Z#. K) ()K '#((,)# ()#((,)# # +' #((,)# 9) *)U8 α = ///. /= ( =) = − = /. /!$$ = !. $$F \ − / ( ≥) = −(' = / )=− = − /. /$ = .!F /\ # (≤ )= − / − − + + = /. $ = $.F /\ \ \ $8%()A&( //.'-2)A+(' F ( 9) ))8 // = = /./ /. = /.!$ = .!$F )8 α = ( = // /./ = = = − = /.0 = .0F \ 6@7<=1>:67%49:64;*4<=1;4>147@>167@ 9 2 ( K (,' U. ) ( (' ( )#H("H(K ? ) # ) #- &#A## 0 :) # # # K () # &) 2# ' ). K&) #)#) () # &) ' − ' + ).J S + − µ' −µ ' ≤ S = ≤ S + = ≤ σ' σ' S + − µ' ≤ S = U ≤ σ' S + − ( ≤ S = U ≤ (K $ YS8 S − −( S − − ( −µ ' = U < < σ' (K (K '() 98 K /F ( (U ( +K ( (K ?)#) () K // ( # ( #)& / ( '#)&#.J≤'Y / 9) *)U)8 // ' = ' = /./ /. / ' // − ' . ' = /. . . . // ≤ ' < / = = + ' = // // ≤ ' < / = /./ /. / + /./ /. / = ≤ ' < / = /./! + /./$= /./ = . /F )).)U:?@8 ( )= ( = // /.= / " ( ) = (K = // /. /. = σ (' ) = = . 0 ( ≤ ' < / )= (!. 0 ≤ ' ≤. 0 )= E V !. 0 = !. 0 − / ) − − /. 0 → /. . 0 V . 0 = . 0 − / ) = − /. → /. /! . 0 (!. 0 ≤ ' ≤. 0 ) = (− /. 0 ≤ U ≤ − /. )= /. − /. /! (!. 0 ≤ ≤. 0 ) = /.! =!. F $ 6@7<=1>:67%49:64;*4<=1%14991>>167@ 8 K &+&) V = −α α #(&+&))UC ) α→∞ −α ≤ ≤ α = π −V ∫ U 0 7()Kα→∞ α≥$/('J+ ! * )& # /. ( (+2 ?)#) ()#!//)//(+2 )& 9) 7&8 αH/.d(+2Hd//(+2 σ = ∴ σ = = D#)#) !/ ≤ ' ≤ / ? #. KU###7 .0 ≤ ' ≤ /.0 = V . 0 = .0 − = − . → /.$! V /. 0 = /.0 − = ./ → /.$00 ∴ .0 ≤ ' ≤ /.0 = !0. 0F 7e*9:7>:1%79%49:64;*4<f9:a64?79g9%49:64;*4<f9719:6749 1()JN,#WN (+#. (. ( ) 2 # ) ,# ;). . >). #. & U J K)J1(#) A(, )U ( &) K J. N K8 K.+&#(-)$ '() M%//) 0 &+)&) # .  K Z &+)&)#K2 >h >h) / !0 $ $ 0 / / 87J) 9) 9K))( = ' = ( ' K − ' . = / . . . . 0 ' (()&+)&)K)K 7 ,# µ H ( H 0(. Z &+)&) &+( ' = ∑ ' ( = / = !0 $ / / + + + $ + + 0 = /. $ // // // // // // 42) µ = ' . 0( = /. $∴( = /. / K = /. 7.)J+ 0 = ' = /./ ' /.0 − ' . = / . . ' ! . . 0 *)U '( ! 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" ! µ 7 σ 7 " Xσ! ! !!! ! & H Y = µ 7 = µ H# MK !L! !!! ! + H Y = σ 7 = σ H# % 4, ! 4 ≤, ! !!! ! H#9 & H Y = µ 7 = µ !L! !!! ! 1 !8 + H Y = σ 7 = σ ,− ,− H#< 3H#<2 H# ,→∞ #< + !1 , . !2 ! 6 '!!! )! % 7 !!! !! 3 ! 3! X !L! σ !!! ! ! Y !!! ! & H Y = µ + H Y = σ ! !1 !2 ! Y 1 2 = Y −µ σ H#E !1 !2 2 H#E!!! !! ! # !L! K# #< D '!. . '4! +! #< !1 !2 Z H#E!!! 7 !!! !! ≥9#&#<! 4! % ?! Y Y Y ! 4! 8! = Y −µ % H#G !!!%ν[3 ! #<9 - $!4 % Y !1 ?! !!! ! µ !L! σ & ∑ (Y ! = ! −Y ) = σ χ − H# ' '!!! 7H#R3 ∑ (Y ! = ! −Y − ) σ χ − χ − % σ = χ − → = →% = − − − σ H#M K )!! ! H#G σ 3 = Y −µ σ Y −µ σ Z σ =Z →= →= = σ % % σ % % σ Z χ − H#K − !!! % !! [ # ν → ∞ !!! ! # !L! H!!! !2 &7 3% " !=\<GM#] .3 ! ! 8! 4 H ! ! !!! ! ! !!! ! ! ! ! "? ###9#< " ! 1"! !!! ! 1"! !!! % ^D! = !8!7 8 ! , , 4 4 K ' ,[E[ ,[E[E µ = + < + G + M + # = G# E E σ = ∑ H 7 ! − µ ! = , = H − G + H < − G + + H# − G = σ = M9 E ! HH<HGHMH# H<H<<H<GH<MH<# HGHG<HGGHGMHG# HMHM<HMGHMMHM# H#H#<H#GH#MH## ! ! 9<EG 9<EG <EGM EGMK GMK# ! !!! ! µ7 = + 9 + < + + # E# = = G# E E ! " µ 7 [µ F3 ! !!! ! ! ! G# ! K9 !! !!!E7 ! !2 "! σ7 = H−G +H9−G ++H#−G = # E ! " 5 ! σ7 = σ σ7 = M9 = # ^%! - H HX[G#σ[M9 E J1 [# 4!! H<HGHMH#H<# H<GH<MHGMHG#HM# ! ! 9<EG EGMK ! !!! ! µ7 = 9 + < + E + + K G# = = G# # # ! " µ 7 = µ K< '! !!! ! σY = H 9 − G + H < − G + + H K + G = 9 # ! ! " σ 7 = σ ,− , − 5 ! σ7 = M9 E− =9 E− 3( 4E##! #! <&7 !3 <K 5 D! !! @ ! !!! ! _ • !3 µ Y [# • !3 µ Y [# @ ! !!! ! _ • !3 σ Y [## • !3 σ Y [#K 93( "1! ! ! ! E#&! 3! < ( 9G ! ! ! '! !! ! ! <K E !! "! " ! ! )MGG<` #< '!!! .5$F! / ! % !"!! !! !!8 [3 ! !! ! ! . 7 KE !! ! S! 2! !! "! D! 8! 4 7 8 ! 8! "! !!! 5 ! µ a ! σ a µ a = σ a = H## ! µ a = σ a = ,− ,− H# ! #< + !1 , . !2 ! 6 '!!! .5 % "!! !!! 5 !!! !! 1 7! !!! ! !L! , 1! 7! !!2 ≥ 9# ?7! #E ! !1 !2 ! 1 2= a − H# D !!! 5 !!! !! H! 7! H8 1Z!! " KG a ± 2 = − H#9 &7 R( "1! 2S!9`"! (! !!##.3 ! !!! 5##9 ! !!! 5## !! !!4 7 !"!KGE` "!9MEK` 17!F"!G<` #<9 '!!! % '!" ' )! ! !! '! . 5 . ! ! D4! % 5 ! ! µ µ !L! σ σ % Y Y " ! ! ! 4 5 ! !!! !" &H Y ± Y = µ ± µ H#< K !L! !!! !" ( ) + Y ± Y = σ σ + H#E #<9 + !1 , . !2 ! 6 '!!! % '!" )! % 5 7 !!! !! 3 ! 3 ! µ µ !L! σ σ % Y Y " ! ! ! 4 5 !1 !2 ! Y ± Y 1 2= (Y ) ± Y − (µ ± µ ) σ σ + H#G #<< '!!! % '!" ' )! ! !! '! . 5 . ! ! '4!% B ! % 5 ! ! µ µ !L! 4! σ σ % Y Y " ! ! ! 4 5 % % " !L! ! !!! !" &H Y ± Y = µ ± µ H# KM !L! !!! !" ( ) + Y ± Y = % + H#M ! ! !L! % 6 5! % = ( − ) % + ( − ) % + − H#K ! ! !L! % % ! % = ∑ (Y ! = − Y ! = H## − % ) ∑ (Y ! = ! − Y ) − H# #<<+ !1. !2 ! 6'!!! % '!" ' )! % 5 7 !!! !! 3 ! 3 ! µ µ !L! 4! σ σ % Y Y " ! ! ! 4 5 % % " !L! !1 !2 ! Y ± Y 1 = (Y ) ± Y − (µ ± µ ) % + H# !!!% υ = + − ! KK #<E '!!! % '!" ' )! ! !! '! . 5 . ! ! '!"'4! % 5 ! ! µ µ !L! 4! σ σ % Y Y " ! ! ! 4 5 % % " !L! ! !!! !" &H Y ± Y = µ ± µ H#9 !L! !!! !" % % + Y ± Y = + ( ) H#< #<E + !1. !2 ! 6'!!! % '!" ' )! % 5 7 !!! !! 3 ! 3 ! µ µ !L! 4! σ σ % Y Y " ! ! ! 4 5 % % " !L! 8! ! Y ± Y 1 = (Y ) ± Y − (µ ± µ ) % + % H#E ## !!!% φ ! φ H !3b4 ( + ) φ= + + + − % % = = H#G H# #<G '!!! % '!" ' .5 a a !1! 5 ! % a a 7! ! ! !!!5 ! H 1! ≥9#! ! 5 !!!5 !5 µ a = µ a = σ a = σ a = H#M H#K . "!! !!2 7! 6!!! ! !!! !" 5 a ± a = ± &H H#9# !L! !!! !" 5 a ± a) = + ( + H#9 # #<G + !1 , . !2 ! 6 '!!! % '!" ' .5 % "!! !!! !" 5 !!! !! 1 7! !!! ! !L! , 1! 7! !!2 ≥ 9# ?7! #E ! !1 !2 ! ± 1 2 = (a a ) − ( ± ) ± H#9 a a a a + #<'!!! + !L! % 4 ! !L! σ . 8 8! χ = ( − ) % H#99 σ 8! χ H!3 H#99 !!! !3 υ = − ! ' $!4 ! 7H#993 % = σ χ − − H#9< !!! χ υ = − ! ! !L! % σ σ σ ( −) = σ & % = & & χ − = χ − = − − − ( ) ( ) H#9E # ( ) ( ) σ σ< σ< σ< ( ) + % = + + = − = χ − = χ − − ( − ) − ( − ) H#9G ! !!! + !L! ( ) & % = σ H#9 !L! !!! + !L! ( ) + % = σ< − H#9M #< & 8! ! 6'!!! + !L! χ = ( − ) % σ H#9K !!! χ υ = − ! #<M '!!! '!!!$% % ! ! 5 !!! !L! !L! ! % % ! $= % % H#<# !!! $ % υ = − ! υ = − ! ! #9 *+,- . /*0 ! ! !!2 ! ! L ! ! 4! &! 8! ! ! ?! & ! ! ! Y ! % ! ! ! X! σ &%-B)-B+.,-(*&B,-&/+*/ 8! ! !!2 ! L ! ! ! ! 8! !! =! ! ! L =! L ! ! 7 ! Y !!2 ! ! ! X !L! % !!2 ! !L! ! σ ! ! ! ! 8! ! ! 8! ! H !! ! L ! @(*B''&%'&()A)&%-B)'/ !! ! ! ! &! 3!! '!23 ! aθ L θ ! 3 ! #< () & aθ = θ H !! !H+"!! !" () + = & aθ − θ H ! !! Y ! 3! ! ! µ ! Y! ! = & Y = & ∑ () µ &(Y ! ) = µ= =µ = ! = ! = ∑ ∑ &! ! '!23! aθ L θ !! 3! !L! 2 "!! H → ∞ () () & aθ = θ ! +/ aθ = # →∞ H9 ! !! Y ! 3! ! ! ! µ ! () ! +/ Y = ! →∞ →∞ σ = # H< &! "!! ' ! ! aθ aθ L aθ !23 aθ !"!! aθ 4 ( ) ( ) +/ aθ < +/ aθ HE % ! aθ aθ " 3! "!!F! ! aθ aθ 1"!! #E ( ) ( ) +/ aθ +/ aθ HG 8 7 3 ! !! ! !! ! ! ! µ !L! ! + (Y ) = π σ σ ! + () ) = 5!!! . "!!F! ! ! ! !! ! ! ! µ 1 ( ) +/ Y +/ () ) 9 σ = = = G<` π πσ &%-B)UT./B,-&/+*% % L θ .{ ≤ θ ≤ } = H−α H ! ≤ θ ≤ ! ! ## ( − α ) ` "! L θ 7! H ! !!!"! !"! !! 4! ( − α ) 4 8"! ! ! θ − − θ 4 !! #G 4 8"! ! ! L: !!2 8!KE`KK` @ ! 8 "! ! 1 ! ! ' 8 "! ! " ! !" ! θ ! ! "! = !"!! ?! " ! ## ( − α )` "! θ " ! ## ( − α )` ! ! θ , 1! ?! ! "! ( 2 ! 1 ! θ 21"!7 8 !! 8"! "! ! ! [ ] ! θ ## ( − α )` "! < B,-&/+*'&D,$B,U./):'B..(*DB,*X 8! !!2 ! ! !! Y ' ! '! ! σ 4! ' !!! !2 3 { } . − 2 α ≤ 2 ≤ 2 α = H−α HM 2 = Y−µ σ HK %!! HK HM ! µ 3 ! "! ! ! µ σ 4! # σ σ .Y − 2 α ≤ µ ≤ Y + 2 α = H−α H# '! ! σ 4! @ 4! ! !13 ! σ %% "9# 2 !!! %. ≥9# % σ 4 !!! !2 2 " "! ! #< ' !!!%3 { } . − α ≤ ≤ α = H−α H = Y −µ % H !!!%ν[3 ! %!!HH! µ 3! "! ! ! µ σ 4! 7!!2 % % ≤ µ ≤ Y + α = H−α . Y − α H9 &7 3( ?! 9G ! "! ! ! <M% 3 !! "! 7 8 < #M !! "! KE` ! ! % . Y = <M = 9G σ = < H3α[KE`' H 7→ Z α [±KG %!! H#3 < < . <M − KG ≤ µ ≤ <M + KG = KE` 9G 9G . {<G GK ≤ µ ≤ <K 9} = KE` . ! KE` "! ! ! 1! ! ! 3( ?! # ! "! ! ! <M! E<'!! "! KE` ! ! % . Y = <M = # % = E < ν = − = # − =K H3α[KE`' <H 7→ Z α K [±#K %!! H93 E < E < . <M − #K ≤ µ ≤ <M + #K = KE` # # . {<E GM ≤ µ ≤ E#}= KE` #K . ! KE` "! ! ! 1! ! ! E B,-&/+*'&D,$B,U./././UT..(*DB,*. % "!! !!! 5 !!! !! 1 7! !!! ! !L! , 1! 7! !!2 ≥9#?7!#E! !1 !2 ! 1 2 = a − H< %!! H< HM ! 3 ! "! ! a a a a a − 2α a + 2 α . ≤ ≤ = H−α HE &7 R& ?! ## 2! 1! !"!3 # "! '! ! "! KE` ! "! 2! 1! % . a = = ## # = # #E ## H3α[KE`' H 7→ Z α [±KG # %!! HE3 # #E (# KE ) # #E (# KE ) . # #E − KG ≤ ≤ # #E + KG = KE` ## ## . {# #KM ≤ ≤ # #M#} = KE` . { KM` ≤ ≤ M #`} = KE` . ! KE` "! ! ! "! 1 ! ! ! G B,-&/+* '& D,$B,U ./ %) & 'B$&/&,U &,-/& '(% ):'B%..(*DB,B% µ & µ 8! !!2 ! ! !! ! Y Y ' F '! 5 ! ! σ σ 4! ' !!! !2 3 2= (Y ) ± Y − (µ ± µ ) HG σ σ + %!! HG HM ! (µ ± µ ) 3 ! "! !" ! ! ! (µ ± µ ) ! 5 ! !4! σ σ σ σ . Y ± Y − 2 α + = H−α + ≤ µ ± µ ≤ Y ± Y + 2 α ( ) ( ) H '! 5 ! ! σ σ 4! ! ! ' !!!%3 (Y = ) ± Y − (µ ± µ ) HM % + !!!% υ = + − ! %!! HM H ! (µ ± µ ) 3 ! "! !" ! ! ! (µ ± µ ) ! 5 ! ! 4! ! !7!!2 . Y ± Y − α ( ) = H−α HK ≤ µ ± µ ≤ Y ± Y + α % % + + ( ) '! 5 ! ! σ σ 4! !" ' !!!%3 = (Y ) ± Y − (µ ± µ ) % % + H# !!!% φ ! φ H !3b4 φ= = ( + ) + + + % % = − H H %!! H# H ! (µ ± µ ) 3 ! "! !" ! ! ! (µ ± µ ) ! 5 ! ! 4! !"7!!2 % % % % . Y ± Y − α + ≤ µ ± µ ≤ Y ± Y + α + = H−α ( ) ( ) H9 B,-&/+* '& D,$B,U ./ %) & 'B$&/&,U '& '(% ././UV&%..(*DB,B% & 8! !!2 ! a a ! !1 5 ! ! a ± a 1 !2 ! 2= (a a ) − ( ± ) ± H< a a a a + %!! H< HM ! ( ± ) 3 ! "! !" 5 ! ! ( ± ) 7!!2 a ± a ) − 2α . ( M a a a a a ± a )+ 2 α + ≤ ± ≤ ( a a a a + = H−α HE B,-&/+*'&D,$B,U./+/Bc,DB..(*DB,* σ 8! !!2 ! !L! ( ) % ' !!!!3 χ 3 . χ α ≤ χ ≤ χ α = H−α − HG χ = ( − )% σ H 9 8! χ H!3 H !!! !3 υ = − ! %!!HHG! σ 3! "! !L! ! σ 7!!2 ( − ) % ( − ) % . ≤ σ ≤ = H−α χ α χ α − K HM B,-&/+*'&D,$B,U./'&%+B.'/T..(*DB,* σ 8! !!2 ! ! % D! !2 !! ! "! HM 3 ! "! σ " . ( − )% χ α ≤ σ≤ ( − )% = H−α χ α − HK &7 3 ( ?! ! ! " ! H> 9##E9<E# '! ! "! KE` ! !L! ! % . Y = G = E % = < % = EE υ = − = < α = # #E ' 9H 73 χ α = < χ α − = = = # <M < χα < %!! HM3 (E − ) < = KE` (E − ) < . ≤ σ ≤ # <M < { } . #M ≤ σ ≤ # #M = KE` . ! KE` "! ! !L! 1! ! ! 3 '! ! "! KE` !! ! ! % . { } . #M ≤ σ ≤ # #M = KE` .{# K9 ≤ σ ≤ < <M } = KE` . ! KE` "! ! ! 1!! ! E 1 -* 2*2 2- ! !! 48! ! L θ 3 ! (!!2 !!! 2! 3 2= Y −µ ∴ 2 σ 7 = Y −µ σ7 H " 2 = Y −µ 3 H = 2 α σ 7 (!!2 !!!%3 = Y −µ ∴ σ 7 = Y −µ σ7 H9 " 2 = Y − µ 3 H< = α σ 7 )%-/0&)*&-d/B%B).*&%D)/&.%BUT& σ D,J&DB' , ! σ 7 = σ %!! σ 7 H! 3 2 α σ = HE 2 α [ 6 1 !!! !2 ! 8"! H3α G σ [! [ !8H! )%-/0&)*&-d/B%B).*&%%&)/&.%BUT& σ D,J&DB' +! ! !!! ! σ7 = ,− ,− σ HG %!!HGH! 3 = 2 α σ , H,−+ 2 α σ H 2 α [ 6 1 !!! !2 ! 8"! H3α σ[! [ !8H! &7 3@ 4 "!! ! ! !"!! ! ! E KE` "! !#<_ % . σ[E # [#< H3α[KE`' H 7→ Z α [±KG %!! HE3 KGE = = G# 5 # < 3@ 4 ! E### 5 ! ! EKE` "! !#<_ . ,[E### σ[E # [#< H3α[KE`' H 7→ Z α [±KG %!! H3 = KG E E### <M### = = E9G 5 MKEMM # < HE### − + KG E 9 )%-/0&)*&-d/B%B).*&%D)/&.%BUT& σ '&%D,J&DB' , ! σ 7 = % %!! σ 7 H<! 3 α % # = HM M α [ 61 !!! % − ! ! 8"! H3α %[! ! # [ !8H! % # < ! 1 1 ! "!! ! L θ < )%-/0&) *&-d/B %B).*&% %&) /&.%BUT & σ '&%D,J&DB' +! ! !!! ! σ7 = ,− ,− % HK %!!HKH<! 3 # = α % , H,−+ α % H# α [ 61 !!! % 3 ! ! 8"! H3α %[! ! [ !8H! % # < ! 1 1 ! "!! ! L θ K &7 R( ! 4 [E ! !"!! "! Y = <G 9# ! %[KM<@ 4 "!! ! ! KE`"! E`_ % . %[KM< #[##E<G9#[9E H3α[KE`' <H 7→ α < [±#G %!! HM3 #G KM< # = [ 5 9E D # > ! ! ! ! ! µ 3( ! 4 [# ! E ### 5 " ! Y = M# ! % [M# @ 4 "!! ! ! KE`"! <`_ . ,[E### %[M# #[##<M#[K # H3α[KE`' <H 7→ α K [±#K %!! H#3 # = #K M # E### 9< << = = GG 5 <9 M9K K HE### − + #K M # D # > ! ! ! ! ! µ E )%-/0&)'%././UV&%D)/&.%BUT !1 !2 ! 1 2 = a − a − ∴ 2 σ a = σ a H a − 3 " 2 = H = 2 α σ a , ! σ a = D 4 3 ! 4 ! a %!! σ a H! 3 a a 2 α # = # H9 2 α [ 6 1 !!! !2 ! 8 "! H3α a [ a =− a [" # [ !8H! % # < ! 1 1 ! "!! ! L θ G )%-/0&)'%././UV&%%&)/&.%BUT , ! σ a = ,− D4 , − 3 ! 4 ! a %!! σ a H! 3 a a , 2 α # = H< a a # (, −)+ 2 α 2 α [ 6 1 !!! !2 ! 8 "! a [ a =− a [" , [ 4 # [ !8H! % # < ! 1 1 ! "!! ! L θ &7 3( ! 4 [ E ! a = !"!! " < = #G @ 4 E "!! ! ! KE`"! E`_ % . a [#M< a = #G # [##E H3α[KE`' H 7→ 2 2 [±KG %!! H93 # = KG #G #M< = # 5 # #E D # > ! ! ! ! ! 3( ! 4 [ # ! a = 9 ### 5 " ! E = # E @ # 4 "!! ! ! KE`"! <`_ . ,[9### a [#E a = #E # [##< H3α[KE`' H 7→ 2 2 [±KG %!! H<3 # = KG # E #E 9### = 9K 5 # #< (9### −)+ KG # E #E D # > ! ! ! ! ! ! " " " # ! " $ % &! '' ()*+,+,+,#-,).#, ,& / $ &0 &! 1 02(13"04 1 0 ! 2('13 " 0 05 6 0 7! 0 ( &80!(' , "9 &7$ #0!% & 3 ( 1 (' ( µ = µ ( µ = µ µ = µ 1 1 (' µ > µ (' µ < µ µ ≠ µ 2''1 # & 21!! 21 21 !! ! : "#%&7& !4! ' ;+<)=+,>+#.+)#?@6+;+A+)?@6 1 ;%& #& 2;#13 " %& 0(5 1 ;%& ;7& 2;;13 " %& 7 0( 8%&&B " %&2;.1 ' +;;6>6)6) B 7 0 ! ': +;;6>6)6)) B 0 'C D-E+F>+,)<D)).GD.)# B 4 7 ) + % 3 α HI7(J(!K 2'1 D4" !%$L'L5LLC LL' C # ))"3 β HI(J(K 'M 2'1 ;),.6,>+6N#>#,>+>+.),=+, OP#>;6'';),.6,)D+;+D+,#6N#>#>+>+.),@6 >+.),@6 ;+#F)>#>+ (LE (L #(L >&.2'α1 +))2β1 ;7(L +)2α1 >&.2'β1 OP#>;6'>+.),@6>+PN;6+,,6; ;+#F)>#>+ >+.),@6 #(L #!# ;7(L ;!# (LE (L + D&+ >&.2'α1 +))2β1 +)2α1 >&.2'β1 OP#>;6'Q>+.),@6>+PNNB>).6 ;+#F)>#>+ >+.),@6 #(L 6 ;7(L D&6 'R (LE (L 6 D&6 >&.2'α1 +))2β1 +)2α1 >&.2'β1 +,OP+N#<+;#F>+PN+,+>+()*+,+ D & 0 ! %3 M 'S +0( S +0!(' S !%$α :S > %&7&0( CS + ! MS ;7 ( ! ;;;# 'T +,+>+()*+,+#;##NB>)#6PF#.)6D#F9 'S ( 3 µ=µ S µ ≠ µ ('3 µ > µ µ < µ S !%$α :S> %&7&3 'S.3>!& S.3>!& R CS. 3 /= −µ σ 2':1 'S = −µ , 2'C1 S MS.3 1 / > / α > α 7(5 1 / > / α > α 7(5 1 / < − / α < − α 7( + 3 'P 4 % ! " CL ,!&": , M & ! " :T "&" CL !%$CUV ,&3 'S(39HCL S('39≠CL SαHLLC T :S> &%&7& >& / / α H±'WM CS.4/3 /= :T − CL = − R : M MS .&3 / < − / α H'WM 7 ( 7 " "" CL !WCU !& M !" ! " :T ! & C: " &" CL !%$CUV ,&3 'S ( 3 µ = CL S (' 3 µ < CL S α = L LC W :S> &%&7& >&5νH'HC αH'MT CS.4+3 = :T − CL = − LL C : M MS.&3 XαH'MT7(7 " ! & . "!" CL 'W +,+>+()*+,+#;##;66;?@66PF#.)6D#F 'S(3H ≠ S('3 > < S !%$α L :S> %&7& CS./3 /= − 2'M1 MS.3 1 / > / α 7(5 1 / > / α 7(5 1 / < − / α 7( + 3 P % WLU Y ! % + LL ! % " ! 'ML %& " % & ! %$LL' ,&3 'S(3HLWL S('3XLWL SαHLL' ' :S> &%&7&3 >&/αHLL' /αH CS.4+/3 = Z= 'ML = LT LL LT − L W L WL' LL = − :R' MS. / X /α H 7 ( 7 %& & " % ! %$ LL' ''L +,+ >+ ()*+,+ #;# # >)+;+D?# +D;+ >P#, NB>)#, 6PF#.)6D#), µ + µ 'S ( 3 µ' − µ = L S ('3 µ' − µ > L µ' − µ ≠ L µ' − µ < L S !%$α :S> %&7&3 ''L'# ! σ' σ & ''L# ! σ' σ & % ''L# ! σ' σ & ''L:# 2 1 CS. 3 # ! σ' σ &3 /= [' − [ 2'R1 σ' σ + ' # ! σ' σ & %3 = [' − [ , ' ' + ' 2'T1 & , υ = ' + − % # ! σ' σ & 3 = [' − [ 2'W1 ,' , + ' & , φ % φ 2% " #\ 13 φ= !' = (!' + ! ) !' ! + ' + ' + ' ,' , ! = ' − 2''L1 2'''1 : # 2 1 = , &, υ = − ' % # ! , &3 = ∑ =' 2''1 ∑ ( , = =' − ) 2''1 −' 2'':1 = [' − [ " ! MS.3 1 / > / α > α 7(5 1 / > / α > α 7(5 1 / < − / α < − α 7( C ''' +,+ >+ ()*+,+ #;# # >)+;+D?# +D;+ >P#, ;66;?=+, 6PF#.)6D#), ' + 'S ( 3 ' − = L S ('3 ' − > L ' − ≠ L ' − < L S !%$α :S> %&7&3 CS. 3 /= ]' − ] ' ' ] (' − ] ) + ' 2''C1 ] "33 # ! ]= ] ' + ] ' ' + ]' = 2''M1 ' ] = & ! ' ' MS.3 1 / > / α > α 7(5 1 />/ α > α 7(5 1 /<− / α <− α 7( M '' +,+>+()*+,+#;##E#;)GD.)#6PF#.)6D#F σ 'S(3 σ = σ L σ ≠ σ S('3 σ > σ σ < σ S !%$α :S> %&7& CS. χ 3 χ = ( − ') , 2''R1 σ L # χ 21 2''R1 & υ = − ' % MS.3 1 χ < χ α '− χ > χ α 7(5 1 χ > χ α 7(5 1 χ < χ' − α 7( D χ ! χ '− α χ' − α ! /3 χ '− α = ' ' χ' − α = χα χα 2''T1 R '' +,+ >+ ()*+,+ #;# # )<P#F>#>+ >+ >P#, E#;)GD.)#, 6PF#.)6D#), σ' + σ 'S(3 σ' = σ σ ≠ σ S('3 σ > σ σ < σ S !%$α :S> %&7& CS. 3 = ,' 2''W1 , # 2''W1 & , υ' = ' − ' % υ = − ' % MS.3 1 < '− α > α 7(5 1 > α 7(5 1 < ' − α 7( D ! '− α ' − α ! /3 α '− = ' ' ' − α = α α 2'L1 T '': +,+ >+ ()*+,+ >+ ^#;F+ #;# # )<P#F>#>+ >+ _ 2_ ` 1 E#;)GD.)#,6PF#.)6D#), σ' σ σ a 'S(3 σ' = σ = = σ a S('3 !$" S !%$α :S> %&7& CS. χ 3 χ LM = ( − _ ) % . _ ∑υ =' , −_ _ − υ % , =' ∑ 2''1 3 = _ ∑ 5 υ =' . ='+ = − ' ' (_ − ') _ ' ' − = ' υ − _ ∑ 2'1 2'1 # χ 212''1 & υ = _ − ' % MS.&3 , χ > χ α 7(L ''C +,+>6OP)OP#>;#>6#;#;6E#>+#>+;bD.)# 6 0 !! & & 7 0 !! $ & P 0 " W 3 & & & & 7 0 & 40 & 0&% 02 1 6 0 !&7&" + ! & % Y_!,7 6 Y! " ! # & /0 Y" ! + #"3 χ = _ ∑ = ' (6 − + ) + 2':1 # χ 21 2':1 & υ = _ − − ' % c $ &/0 P ! & 8 % Y D& 4 $%!! Y !:C& / #% % Y & ' C, Y 4 Y ! 7 # Y ! & " _ / 6!& :L D d e & " :L c %"%'3 χ = _ ∑ ( = ' 6 − + − L C ) + 2'C1 ;3 'S(3 7 0 S('3 &7 0 S !%$α :S> %&7& CS. χ 2':12'C1 " :Lc %"%' MS.&3 , χ > χ α 7(L + 3 7 / &W':/ α HLLC #%Y! 4 [ P !/ Y c & C Y :' #^+F#'' ;+OfbD.)#, #AP,#>#, ># >),;)^P)?@6 >#, )>#>+, >6, PD.)6Dg;)6, ># +N;+,# [ >),;)^P)?@6D6;N#F )>#>+, ;+OfbD.)# ;+OfbD.)# 6^,+;E#># 261 +*;).# 2+1 ':ChTC LR LR TChCC '' '' CCh:C 'C ' :Ch:WC 'L '' :WChCMC LR LT 6D+>6,>#>6,^;P6,3,;( P !/ ` :L / 2':1 3 χ = _ ∑ = ' (6 − + ) HLC + # &%&7&4 3 υ = _ − ' − HCQ'QH H !/4 $ 3 " µ ! & σ > α HLLC υ H χ L LC HCWW .&3. χ < χ α (L 7 7 0& ''M +,+>6OP)OP#>;#>6#;##,,6.)#?@66P)D>++D>bD.)# 6 χ &2Y1"/ & !4! %0 /& ! & % !4! ! & %/ %Y . F % !4! 4 ' : #^+F#'#^+F#>+.6D)D<bD.)#. F E#;)gE+F^ E#;)gE+F# 6#F .%' .% .% .%' .% .% 6#F 0 % Y ! ! ! 07!6! + 7 %Y . F & 88 % !% %3 + 7 = ⋅ 7 ⋅ ⋅ ' ≤ ≤ 5 ' ≤ 7 ≤ 2'M1 # " 2':1 & χ 21 υ = (. − ')(F − ') % . c c P ! & 8 % Y + %Y! !%3 1 3 ! C #" !/&d4 χ , ! C 5 1 .3 χ ! '5 : 1 . F3 χ " %c " %M ! %$ CU 'LU M !%$'U6c " !! c ;3 'S(3!4!& S('3!4!&& S !%$α :S> %&7& CS. χ 2':12'C1 " :L c %"%' MS.&3 , χ > χ α 7( + 3 ! %$ CU % % " & # % !! #^+F#'#^+F#>+.6D)D<bD.)# ;+OPbD.)#,6^,+;E#>#, D6#D6+,+ >+,+N+D(6D6+N;+<6 ;/4! ^ ^ MR M: C 'CM N" : RM CM 'R: # 'L R RL ''W 'M ''T :LL :: ,&3 ;3 'S(3 %& & S('3 %& && SαHLLC :S> %&7& ;70 χ ≥ χ L LC : = W :TT CS. χ 2':13 # &2'M1!Y ': #^+F#':#^+F#>+.6D)D<bD.)# Q;+OPbD.)#,+,+;#>#, >+,+N+D(6D6+N;+<6 D6#D6+,+ ;/4! ^ ^ :M: MM :ML 'CM N" C'T RLW C' 'R: # LT TC LR RL ''W 'M ''T :LL , ! Y ! 0 2':1 3 χ = (MR − :M : ) :M : + (M: − M M ) M M + + (R − LR) LR = :LTW MS.&3 . χ = :LTW > χ L LC : = W :TT 7 (L 4 & & % ! " # $ %& ! " '! ( $)%& $ %& * + (" ,", -./0)1213405-6078640'940#216/))0:06;<# ( & ( " 2 ( = ! > = µ + α + ξ > µ ? @ α ? @ ξ ? " $,",% A ,",", B *81 ,% ( ! > σ = σ = σ = = σ = σ @ % 6 ( (@ C% 6 & ($%@ % ( ) ξ E - D& σ & & * (" ,"," 'B *0!F $FG% # ! ! > ,% BD> µ = µ = µ = = µ = µ % B,> µ ≠ µ C% : + ! α % 2 ! ( (BD % 6 & -#3 A% 6(> ) > → & ν = ( − − ) ! " ,","C 4 ( ( # ! -#3 (" '4'81-'#) 1/181-'#)2 8#)'4 8 ', ' """ 'H +,, +, """ +H, +, + """ +H +, + """ +H +, + """ + H I, I """ IH J ) ! > -?K F?K$% ?K$%>,"""H ?K$ L%>,""" 8 > I = H 8 > I = ∑I =, =, =, - $,"% ∑∑ I H ∑ I ⋅ I = =, - H - = ∑ $,"C% =, ,"," 13 M -#3 & & M $ M * % M$ M+ %" 6 L * $BD% ! & L * $B,% "/ L * ! M M ! I H ∑∑ =, I − I &> =, $,"% ) = ) + ) H ∑∑ =, I − I = ⋅ =, H ∑ I − I + =, ∑∑ (I H =, =, − I ) $,"% N > ? (@ ? M M+ @ ? M M* " ( > $,"A% = − ,","", 3 6 σ & K " 0 L * ( ( ! σ " 1 > H ) = ∑∑ =, I − I =, - −, $,"J% )O'" 1 & L * BD & M " ,","" 3 $% ( $ % ! $-F% ( σ & BD ( " P ∑∑ (I H ) ,",""C = =, =, − I ) $,"N% -−F 3 ( $ % ! $F ,% ( σ BD & & ( & − ( ( ) − µ & σ " ⋅ ) = H ∑ I − I =, $,"P% F −, 2 :& BD &( ( σ *+ ,"Q &:& σ BD B," ! -#3 (" O724#,",-./0)1213405-6078640'940#216/))0:06;<# )#821 O7242#) $)O% R47)21 /0S14221 $R/% 1 F, = − 2 -F = − '#'/ -, :#-'121340;<# $:3% O7242# 8920# $O8% 1)''T)'06 : = D O724#,"-./0)1213405-6078640'940#216/))0:06;<#)08Q/0:062# :3 )O R/ O8 1 F, = − 2 -F = − '#'/ -, : = ," -./0)1213405-602#0)640'940#)216/))0:06;<# ( & & & "2& ( = ! > I = µ + α + β + ξ $,",D% > µ ? @ α ? @ β ? L@ ξ ? " $: ,%& L $: % ( > 8 > / I = ∑I =, / $,",,% , 8 L> F I = ∑I =, $,",% F 8 > F I= / ∑∑ I =, =, $,",C% - ,"", 'B * # ! L *! > ,% B D, > µ," = µ " = """ = µ /" $ L% µ = µ = = µ $% % > µ > µ C% : + ! α % 2 ! ( (L *BD,BD > :α/ [(/ −,)& (/ −,)(H −,)] → $ L% :α6 [(H −,)& (/ −,)(H −,)] → $% % 6 : A% 6M> %) :/ > : α/ & BD,@ %) :6 > : α6 & BD" ,"" 13 M ,""", 3 ( ' = ) = H / ∑∑ =, I − I =, ( χ &$%! " $,",% ,""" 3 ( ,U$% H ∑ 6 = ) 6 = / ⋅ I − I =, $,",% ) 6 ( χ &$%! " ,"""C 3 ( U$ L% / = )/ = F ⋅ / ∑ I − I =, $,",A% ( χ &$%! " ,""" 3 ( * 4 = ) = H / ∑∑ =, I − I − I + I = ) − ) − ) 6 / =, $,",J% ( χ & [(/ −,)(F −,)] ! " 2 (&> ) = ) 6 + )/ + ) $,",N% 2 ! (& M ! ( σ & M ( L ! L $BD %" C /⋅ H ∑ I =, )6 = ) / = / ∑ I − I =, $,",P% $,"D% / −, H = − I F −, F⋅ ) / ∑∑ =, I − I − I + I =, $,",% $F −,% ⋅ $/ −,% O724#,"C-./0)1213405-602#0)640'940#)216/))0:06;<#)08Q/0:062# :3 1 L )O R/ )/ / −, ) / = )/ / −, ) = ) F −, 1 )6 F, 4 (/ −,)⋅ (H −,) '#'/ -, ,"C O8 ) = : :/ = : = ) / ) ) ) ) (/ −,)⋅ (H −,) 6#8Q4;V1)8W/'0Q/)1-'418920) + ! & (& L& (@& L &(&& L " ( & & MK + "1(L )& ! K M + " & & ! ) &-#3& & ! " 3 = ! " )( ! & $'HXF& )-F& S )L%& M " ' ( :-#3 ! " ,"C", ''HXF$B)2% # B)2 $BX ) ! 2 % ! ! ! -#3&" > ) = I − I , + , ) $,"% ( $ A& + ,%& F ! -YF! " ) α& (F @ - − F ) & L * BD > µ = µ " ,"C" ')-ZF$)-F% # )-F ! 'HXF&+ ( (K F + & K F[ " > )[ = I − I ) , , + $,"C% ( $ A& + ,%& F[ ! - Y F[ ! " ) )[ α& (F[@ - − F[ ) & L * BD > µ = µ " ,"C"C 'S # S ! α & > α S = α $,"% α ! !+ K M " 9 L M Y ( Y ( * (" # +(! > S = I − I , , ) + $,"% () υ ?-YF! " ) S αS & - − F & L * BD > µ = µ " A ,"C" ')L - -#3 (& )L µ µ ( & (> − ≥ ∆α > , , ∆α = ) ⋅ (F −,)⋅ + ⋅ :α [(F −,)@ (- − F )] $,"A% --#3 (& L& I" − I" ≥ ∆α $% I " − I " ≥ ∆α $ L%&> 1> , , (F −,) :α [(F −,)@ (/ −,) (F −,)] ∆α = ) + " " $,"J% 1 L> , , ( −,) :α/ [(/ −,)@ (/ −,) (F −,)] ∆α = ) + " " $,"N% > "&"K L @ " &"K @ I " & I " L @ I " & I " @ 1+> ," 1 K & +"6 + ! ! + ( & ! $!%> # ,> N&, N&C N&D N&, N& J # > N& N& N& # C> N&N N&J N&P # > N&C N& N& N&C N& N&C N& 3 + ! \" ) (> ,% BD> µ = µ = µ = µ = µ % B,> µ ≠ µ C% α ?D&D % 2 (! ( (> H,?,?C -F?,N?, Q> :D&D$C@,%?C&C % 6 :> O724#,"-#378640'940#216/))0:06;<# :#-'121 340;<# )#821 O7242#) R/ O7242# 8920# 1)''T)'06 : 1 D&JC ,?C D&C D&C 4 D& ,N?, D&D,J D&D,J '#'/ D&PJ ,N,?,J =,&P A% 6(>:G:D&D $C@ ,%?C&C& BD&&+ ! " 6 -#3 ! & 'HXF)L " N ''HXF> 2> , = @ = @ C = C@ = A ) = D& D,J@ H = @ D& D ( @ , ) = &,,, I , = N& @ I = N& @ I C = N&N@ I = N& C Q> ) = I − I D& D,J , , + O724#,"6#8Q4;<#218920)Q1/#'1)'121'7F1]F4814 #Q14.40#) D& D& ( @ , ) ) 6#-6/7)<# , C&C &,,, ( ,C N&P, &,,, , ,&JP &,,, ( C &AN &,,, ,&AN &,,, ( C J&AJ &,,, 3 C ! (!+ (" ')L> 2> , = @ = @ C = C@ = A ) = D& D,J@ H = @ :D& D (C@ , ) = C& C I , = N& @ I = N& @ I C = N&N@ I = N& C Q> , , ∆α = D& D,J + ( −,)C& C P O724#,"AY6#8Q4;<#218920)Q1/#'1)'121)6B1::9 − ∆α #Q14.40#) 6#-6/7)<# , D&N D& ( ,C D&CD D&A , D& D&, ( C D&C D& D&J D&, ( C D&P D& 3 C ! (!+ (" " O D,&D&DCD& = ,& C" 2 L *" ( + ! L" ! L * ( + ! " M ( +" 7 α ?D&D" Q41/B# #Q14.40# D, D DC D , JD AD A N J AD AD C J AC N N ) (> ,% BD,> µ = µ = µ $ L% BD> µ = µ = µ = µ $% % B,,> µ B,> µ C% α ?D&D AD % 2 (! ( (> 2> :α/ (@ A ) = &, :α6 (C@ A ) = &JA % 6 :> O724#,"A-#32#0)640'940#)216/))0:06;<# :#-'121 340;<# )#821 O7242#) R/ & C,? & CNJ&D ,?C ,P&DD C& "C?A C&P ,&D ,,?,, 1 L 1 4 '#'/ O7242# 8920# 1)''T)'06 : & C&P ,P&DD C&P = D&J = C&P, A% 6M> % 6 :/ = D& J < :α/ = &, & BD,& & ( + ! L$ L%@ % :6 = C& P,> :α6 = &JA & BD& & + ! $%" #'HXF)L 3 ( ( L (" -& & 3 + ! " ''HXF> 2> ", = C@ " = C@ " C = C@ " = C I ", = J @ I " = A,@ I "C = AD @ I " = J ) = C& P@ H = @ D& D ( @ A ) = &NPA A, Q> ) = I" − I" C& P , , + " " O724#,"J6#8Q4;<#218920)Q1/#'1)'121'7F1]F4814 #Q14.40#) , ,C , C C D& D ( @ A ) ) P&A ,D&D ,C&, D&NJ C&D &A &NPA &NPA &NPA &NPA &NPA &NPA 6#-6/7)<# ( ( ( 6& D, ! " ')L> 2> ", = C@ " = C@ " C = C@ " = C I ", = J @ I " = A,@ I "C = AD @ I " = J ) = C& P@ H = @ :D& D $ C@ A % = &JA Q> , , ∆α = C& P + ( −,) &JA = A&,, C C O724#,"N6#8Q4;<#218920)Q1/#'1)'121)6B1::9 #Q14.40#) − ∆α 6#-6/7)<# , ,, A&,, ,C , A&,, , , A&,, C , A&,, ( A&,, ( C C A&,, ( 6& D, ! " ! "##$% & '( $! ) ( * + $% , ' !) - . , , % / ! ' ) ! + ! ) , 0$!+ % 1( 234+"!5"$! +!5$! %%% ! +!5$ 6 ) , ),37β89β"2!6 ' ,4 5 = β 8 + β"+ + !7"!!%%%! ":%"$ 4 +7 ' +2; 57 ' 3; β87< *!; β"7< *!,; 70!6' 456 β= 8 + β=" + $% > 6 ) ? < * σ ) 0 6 $! ',% ":%" @AB ABC 1&@ DE A&@ ACF@ 1& FA&1& 1&@ GHB &@ IJ11&@ & ) ! < β8 β" ! ) 6 ) 4 ∑ =" = ∑[ =" ( =8 + β = "+ 5 − β )] = @ 33 − (@ 23 ) @ 22 ":%$ 4 @337 ) ' 5 @227 ) ' + @237 & @33! @22 @23 ' + K 4 @ 33 = @ 22 = @ 23 = ∑ =" ∑ =" ∑ =" 5 =" 5 − ∑ + − + =" ∑ +5 − ∑ =" ":%>$ + ":%L$ ∑ 5 =" ":%:$ L 47-' ,K & ) + K 4 =" = @ 23 = @ 3 β @ 22 @2 ":%$ 4 @3 = @ 33 ! @ 2 = −" @ 22 = −" @ 23 (@ 22 )(@ 33 ) =8 = 3 − β =" 2 β σ = = I ":%M$ ":%N$ = @I ≅ " − % @3 − ":%#$ 4 7, ; @37 3; @27 6 2; I 7I; @I7@) ; σ 7 6 % ":% IJOP&DD1BQ3DAB12 0 ( * ! ', β β ! 6 ), 5 +% : =8 + β ="+ 7"!!%%%! = = β 5 ":%"8$ * ), 3 2 ! ! 6 % ":%> RJHOS@TBHBQUCB@ @! ! ) , + 3 2 ! 6 ,K . 2 3! 6 ! ! ( 6 * %, , %H 6 % ,K % ":%>%" R,D { = α β + β = = → = = α → α = = → = ":%""$ ":%>% R,+ { = α β + = = → = = α → α = = β → β = ":%"$ ":%>%> R,V'0B β = α ± = α + β = ":%">$ ":%>%L R,V'0BB { = α − β − β = = → = = α → α = = → = ":%"L$ ":%>%: R,V'0BBB { − = α + β = α + β = → = ":%L ":%":$ HUTB@1CBEHWB1X@@P& & 4 5 = β 8 + = "! ! %%%! ":%"$ H 5 <-!β8! ,0+%&( M ) . , * * + 2% D β8 4 =8 = 3 β ":%"M$ ) 3% ) 4 @I7@33 ":%"N$ H ( ":%"8$!) ) * ! ( , β=" % H ! β= 8 5! ":%"8$! β= 8 )+78%H ! ) 4 = ) ( − ":%"#$ < ( ( R @$% H&C %%!57β89β"+9$ ' ! 6 < %%!57β89$% 6 )4 ∑ (3 − 3 ) =" = ∑( = − 3 3 =" ) + ∑( =" = 3 −3 ) ":%8$ " &"'" = " &"'" + " &"'" %% !" #$ !" ":%"$ N D4 = − = ( )( − − ":%$ ":%>$ ":%L%"1 ',K '' ) ) ', χ − " )6) 6" '$% ) @I ', χ Y − " )6) Y6" '$% ) @I ', χ − Y )6) 6Y '$% ":%L%D *0 ,+ ? )? *0 '+ ? '+4 "Z V 4 β = 8 + $ ZV"4 β ≠ 8 + $ >ZR+ <α LZ1(, (, ' ', R @! Y6"$ ' 6Y$ ' ! ( , 4 # χ Y − " R(Y − "! − Y ) = χ Y − " − Y Y −" = χ − Y χ − Y Y −" ":%L$ −Y 4 R(Y − "! − Y ) = χ Y − " ":%:$ χ − Y ) ) @I ', χ " )6)"' ) @I ', χ − )6 )6 '$% :ZW ) 4 @I R8 = I Y −" = @I I −Y ":%$ ) ',R@Y6"$ ' 6Y$ '% ZW 4 R8 > Rα! (Y − "! − Y ) !(6 V8 % D < α! *0 V8 ( R > Rα! ("; − ) %&' )! ',R";6$ '!.''$α% H ) H&C ! * @ I A @I$ . @ I M8 < %,@I A@I$ @ I @I$ [ [ ),@I <$! * @I @I$% IJ1&":%"6IJ1&1HUTB@1CBPHWBH&C$ R&HA1 CBOP& @& 1IJ11&@ ="@ 23 @I = β XJ@1 TB/11 6" @I = @I − @I 6Y A&AT @I = @ 33 6" ":%: IJ11& F1B& I I = @I XT @AAG@ABW R R& = I I @I = XT W&RBWBHA1W&TOP&$W&RBWBHA11A BHOP&$ W 6 04 @I 7 @I [ @I 6 ' ) 36 4 @I @ 33 = @I − @I @ 33 ":%M$ )@I7@33%1 '6 4 @I @ 33 ="− @I @ 33 ":%N$ ) 0 , ' ' ,K 3 ) + 2 ( %&0 \"] ' M" +%J6 H&C'6 ,$!)8"% = @I ":%#$ @I H ! ) , ! 4 = @I @ 33 = (@ 23 ) @ 22 @ 33 = ":%>8$ & , ρ$ ,6"≤ρ≤9"%@)* , % & , D $!4 = @ 23 (@ 22 )(@ 33 ) ":%>"$ & , D 23%A6 - $% I 7 6"! , ! ) ) 7 "! , %D78!+ , ! + , % @ 8 ^ ^ 8!M:! + , % @ 8!M: ≤ ^ 8!#8! + , % R! 8!#8 ≤ ^"!+ ,% + , 6 @ $ $ ) M ) ρ ) ', _ $% ":%:%" A *0 , I , ! * , ρ % 1 !' *! ) + , 2 3% )? *0 ', '+4 "Z V 4 ρ = 8 Z V" 4 ρ ≠ 8 >ZR+ <α LZ1(,4 :ZW 4 8 = − " − ":%>$ ) ',@ υ 7[ ' '*0 V8 % M> ZW 4 > α ! (6 V8 % ":% @JD&@BOS@@@&WB1@& &1T&1X@@P&TBH@B DT@! CT&@@D1&@!&@6D1P& W 6 ) , 2 3 ) 5 = β 8 + β"+ + ! ="! ! %%%! ":%>>$ ) β 8 β" ,! 6 )4 • 2! ! 2 * $; • ' < σ % & ) 4 , β=" β"! (4 ( ) =" = β" β ":%>L$ 1 @ β=" β=" 4 @ β= = " σ = @ 22 = I @ 22 = σ = @ 2 −" ":%>:$ ML , β= 8 β8! (4 ( ) = 8 = β8 β ":%>$ 1 @ β=8 β= 8 4 @ β= ":%M 8 " 2 =σ = % + @ 22 = I " 2 + @ 22 ":%>M$ BHR`HWB@@&/&@DE A&@1& &1T& ":%M%" B ,, & , + ) < ! , "6α$6+%@ ,) $ ' < σ= ! < βa $! ' 5$ 5= $ ' ' ) ',K % ! , ' ',@% J "88 " 6 α$ b , β844 D =8 − I ! − " 2 + @ 22 ≤ 8 ≤ =8 + I ! − " 2 + @ 22 = (" − )b ":%>N$ 1!"88"6α$b, ,β"4 I I = − =" + D β ≤ β" ≤ β α α " ! − ! − @ 22 @ 22 = (" − α )b ":%>#$ M: ":%M%A *0 ' <, R)c (6 < * − * * 0 ' − % D *0 6 4 "Z V 4 β 8 = 8 β 8 ≠ 8 ZV"4 β 8 > 8 β 8 < 8 >ZR+ <α LZ1(,4 :ZW 4 8 = =8 β " 2 I + @ 22 8 = =8 β @ β= ":%L8$ 8 ) ', @ υ 7 [ ' '*0 V8% M ZW K 4 $ > α ! (6 V; '$ > α ! (6 V; $ < − α ! (6 V% @ R @! 6 ) H&C4 R = I I ":%L"$ ) ', R "; 6$ '! ' *0 V8% D <α!(,V8 4 ":%L$ R8 > Rα! ("! − ) H , β"! R % 6 )'6 4 = =" β I @ 22 ∴ = β" I % @ 22 = (@ 23 ) (@ 22 ) I ⋅ @ 22 @ 23 ⋅ @ 23 I @ 22 = = I I = R ":%L>$ ":%M%> B , *0 3+8$ W (3 + 8 ) = β= 8 + β="+ 8 ! "88"6 α$b,3+8$!4 MM D = 58 − α I ! − " + (+ 8 ) −2 ≤ (3 +8 ) ≤ = 58 + α I ! − @22 ( ) " + − 2 + 8 = (" − α)b @22 ":%LL$ & , .) + 8 − 2 % D 3+8$ η8 ! 6 4 = 5 8 − η8 − = I ( " + −2 + 8 @ 22 ) ":%L:$ ":%M%LB, &, !! (5 8 ) ' ,K ) '! +8% B , 3+8$$) *$ ' ,K 3$,+8% (5 8 ) ' ,K ' +8+ 4 Y 58 = ∑5 (=" 8( Y ":%L$ )Y- ' ,K % J "88"6α$b , ' ,K ' )27+84 =8 − α D 5 I ! − ) 5= 8 = β= 8 + β=" + 8 ( " " + −2 + + 8 @ 22 Y ) ≤ 58 ≤ 5 =8 + α I ! − ( " " + − 2 + + 8 @ 22 Y ) ":%LM$ = (" − α )b MN I7",- ' ,) '27+8% & , 2 7 +8 ), ')27+8! ), ( ) .' ,K % ":%NDTBW/BTB111& &1T& ( 6 4 $ . ( '** ( % F + ; '$ * ! σ $ ; $ * + , ! +,K + ' ; $ , % J 0+ " ) 2 3 %H )2 ( 3 6 % ,K 2 3 ) . ) !., % M# +4 & ( ,K 3$, ' 2$%D ": %& '":%"%D6 4 $ 23; '$ ,D ; $ < β 8 β" ! β 8 β" ! *0 β 8 β" ; $ + ? < :bH&C$; $ , ; $ ,#:b < β 8 β" ; $ , #:b 3! +87N; *$ ,#:b3! +87N% A/T":%"6 H&A@ @AAG@ABW WUTWJT& 1 J &@A TAdB 1 ": TJH&@ 1& DB B& H& 1 @AAG@ABW H&A@1@AAG@ABW H&A@1WUTWJT& 3 2 N8 @,4 $ 2 7L!L8; @ 2 7>!L 3 7:!#8; @ 3 7!NL '$ ,D + ":%>"$'6 4 78!#::N $ W ! K IJ1&":%6W&RBWBHA@1X@@P& H& W&RBWBHA W 2 &D1P& !LL:" 8!MN: 8!8M8 8!>M88 @BXHBR% !8N# ""!MML 8!8888 8!8888 = = ! LL:" + 8!MN: 2 D4 3 $ + ? < :bH&C$ IJ1&":%>6HUTB@1CBEHWB1X@@P& R&HA1 CBOP& A&AT XT " "> "L @& 1 IJ11&@ IJ11& F1B& "8>!>>M #!MM> "">!"888 "8>!>>M 8!M:"> R ">M!:># @BXHBR% 8!888> W 4 D6 ' ) + !'' ≤ 8!8"% $ , + ":%#$) '6 4 78!#"> N" W 4 ,K + #"!>b ,K ! N!Lb % $ ,#:b < β 8 β" + K ":%>N$":%>#$'6 4 IJ1&":%L6BHACT&1W&HRBHODβ #:b$ D< TB T@ β8 β" $ ,#:b ! )+87N + ":%LL$'6 4 D [ N!8" ≤ (3 + 8 = N ) ≤ #!L>M> ] = #:b *$ , #:b !)+87N + ":%LM$'6 4 D ( !M># ≤ 5 8 ≤ "8!M# ) = #:b
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