41
pon.\, a, 'tJ,: %Zot" w*JUt, orn,bolo¡ O \,$*" a va^oLt: o,r',),J', q"L\, uooV'lnu¿\ 0- (x'A-t x'f rry,o ll= /{B+e $ '(x'n\ ' x'(x tsi e) {xr¡l ' l; e fi =ii'o)'l'Álb l fl- ut{x'r)rx'€ aB\,rr,.1" vuL nr¡',,/a fs u en(^tn , 9; \rvtg*"j;' FIÉ: - F[\B+[ffiN't'e] y, r¡,,.,¡eUet *\ u,L o sn,o,ta E[fi]= Bt (¡,¡¡'EL/t'e1 c^ orol¿,o,J) €r-ilW=o1 "r rl,,,- [^vr!on,*rlu *i o,l,^-,]" É,r, "S'Pgi onrLo¡^" yrr$t"\"+ * vo*[La o^)r.jo_, C cr,,*,tnt\^oo !'u<., rth't d q*c.^[¡,..,.;b ",\r-rl,-, €=dd+ol E [l.e] = Etff(6¿+q;)] = E[x.6,¿1f EtxtCI] " S,cr-{^ v*[[. orn,f,J..l -ca,¡,!-f", .Ore\ ¡to"cob ELfFü+o(=) Grr(X,¿)fo t\ "ih*1" óLS estq"/, E¡¡-e] = dqñ6+E[Á.0] ÉtÍ'e] Éó

Notas Econometria Algebra de Datos Panel

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Notas de clase de Datos panel, comprobaciones, etc.

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  • pon.\, a, 'tJ,: %Zot" w*JUt, orn,bolo

    O \,$*" a va^oLt: o,r',),J', q"L\, uooV'lnu\0- (x'A-t x'f rry,o ll= /{B+e$ '(x'n\ ' x'(x tsi e)

    {xrl ' l; efi =ii'o)'l'lb lfl- ut{x'r)rx'

    aB\,rr,.1" vuL nr',,/a fsu en(^tn , 9; \rvtg*"j;'FI:

    - F[\B+[ffiN't'e] y, r,,.,eUet *\ u,L o sn,o,taE[fi]= Bt (,'EL/t'e1

    c^ orol,o,J) r-ilW=o1

    "r rl,,,- [^vr!on,*rlu *i o,l,^-,]" ,r,

    "S'Pgi onrLo^" yrr$t"\"+ * vo*[La o^)r.jo_, C cr,,*,tnt\^oo!'u

  • fr,v,, orv Xf*L ao Crao G. n\ t^.o&lOB,o=(ilY\-'ff)

    = L ftx\' /r xr.r\ n " v- v/Fr+/D= fl " ^i \,i ^ /) db* i = lkv+q- ft ux)'(; rrxnrc:)= b u*)'$ro ) t[* n{'(n re)= tbiG-u'u)t*O*o pn^ O=fx.x

    l8oo= tBt e-ttFeQ = dC+O q"Jr\o^,0" .,611,^

    ,* fr.-.d,{b r 0, x.e)[\'^ ur.= ts+ Qt pt,^& *'4 pe,o A --4610)

    = Jb I O' 1},. fi x"(da,+u) r.'" pl*il"t+o$,*1".r 4 D \ r llo of G,neslanle . | |

  • +,

    Sq m,vooa\. [rL-,h" ^'.Sn''rdo "\

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    I- EIu,uJ EEUI. E1o'ail l-ri o o^ I Eto,oJ rtot ttq-rl |

    " {'L o

    EI$tD"l= t "'\,tillLrto"rELohuJ Efono^l L" o v'r

    o ^"{r' n-?/0., o rl

    Ett0t\)'l--v'\ o o:1", ? \=u'SlrL o o v'3io'lS*\^,.t\ ""LJ n;.$"nlM*-l."tJ lq vc,nor=rnrrh,l al o\*'J^ LS \,"pyx\"J,&tq"$n,l-r el

    uc"*, V...\tt)s "

    r'uhc

    t\**- s V.'qk\

    nlr* ,),,,*,AA**o

    rn"tlro

    -hrL-*,rL, gnyn,G&

    !or. ffi1 = \o.[ lB + [,n]r /ttf=r(tx)+lu.x fftf)tlflW Xnourlr 8,8st

    \urffi '$,8.tr)rXcx ffx)+. S, .f,S \Jr.r*&rtr

    "dr Xh G\&U^ owur J mqgh,.[r [,, OLSncr,.^^ \ur$1. w"t \oc-\,r s"sJ,'L 1[,spcu+Ur F S^ \n" yr,"yn"J"l\-e lLd'tvc6! q

    I

  • (t { ettuw,lo *$. ^\'o', .n\n^ J--l4rrr-o Plltrnv ,ltrt

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  • Dfttps Q$GLf*gy*,- Xb*l Cc ws,[. G*6,*n1" &en*, ONN]crob" l" fqvs.ov'r

    D'ft il eun orcolar, $n ^*f,^.cle[r.,rz,vt"1[,r 4lrrn,iio Krl d'kn-Lrti''Je\G^*aVfu\ en"r,aev":L J-t# tcre u.lr. onL, r,l*\*oqr er.: ,, \,r L

    U,o - Y; t\;r lt'= lbfi "-+f '!'^l/dl o '

    \[f"uobvvu

  • V1 Se6^r*i e.
  • \ert"1to.A ( \c*2\nJ'Jou5cu=z)]YiL:.Yl lll.,uu pxo\u.of,uar ( K.

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    x,,,,

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    I rz,

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    X zzt

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    K

    2l I l(ri!')l

    our=fill?v:lYrlt6t.t at+ 6/,3

    Y,l liTrl = 'n

    lB,

  • 1 -1tTtrHW Nrx\)r

    uE"* lue n)poot[- ao,n",*, 1,r'.' ll u(sr,.

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    i)UJ*t.'+,.o ( .\u*'.r.cr )oraftt oor'n\.r,.,,^n\" e\ \'n*noon\ tl'^ 'n "'.or'17,' 1"5dor,,) o*.^\" o\*n'o *I'\ot, k,b'rrl \os paa'oc'r*r lnei\:^f"-y*.

    \o.^ m;s fec1,*cc \aa T* oo:)A4 -n),,'oi i":N''tJtu"r'''t A""""un'li '--- -'-' - .- -./

    --+- \p c,l'-"['dg

    C!*.p- 'T-.r

    ,rn, l'tr-ti; {ti, q(' '1 ii t:)'.} t'q J.^t'-T' U L ""'\"..'.,' 'r "it'\'t} t&2 :

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    irn\\1t\ \'-,i,, l=\i,i 'iiir,,l;:o,r\!1}$;

    ',j, =

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    \,1, ,L o o \\ - ! \'1,'1, -' io*- Z \ o"'J, 'i, I

    \o"'h /, I'\a^\rner pbto c^\u\^ \'vnn \^.;o@ i t)'tn b ell^pl-q*tr,*= T*E\ =tu@ * T Fn Xrr"qoJ'.r,r *i ,.,j,,.\u f,uuori..

    trrrr = \[{@ i)I ir',t TP tt e \ uo*J o $ o\x"'"^e5 o \',uuot 'ol i'o''"n '

  • Aarrc,: I peah\t I" S'9u*\, x>' @

  • A!r"l **."o*/o*o SJx llq Q$' f,7{-@ tr e n\nes ;+t,#i {t eu-,) *"lrp\.;'(nrx $lsrt 'lf' Kr.r,brtt"q*

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    .1 o {)\",,1" olg*t r^uPoo[,,t *l

    A @ E D.n[",'

    ^!

    -r.(.fitau

    'l]r'[] = d)1vr

    -t.- (J_TT

    gr^rL'or'= rfp f)0 (t_ol; )

    .^i t*'t"M ^\'rd r**v"' (A@ CCDtd I '

    twt = T*'{*8 '{

    &.\il}n ft+fr h*Th-,v* nt'x.,lo Tr@*- = n'@fu-l sr#rr= T-oi ff- P=I*@l)Iouoll-rn'oo: 'c'oo-t U *ilr* 14,onf =,@, E:*i'''p:fo.cD0-[f-e+")

    in-rn$l]-r(Tn8{t)' ---

    (..rn\u poecL q "

    Ail b &pb) = .4 c6 $ cil'r ':19 - $ *6tif I -611'$ * 4)'\'(nue+1) (lery)s\ -n G^ \ ;,i; *",' I 0 fl" = J-,*P =T*b + VY {io"r T'TOEE

    6tf - Irr&rrt

  • ll& ,;)C )''irtr;\lt\u), ff ;,

    \ti\ p ar\ tt Dociri,pli

    l\ | A /a 4 I\\ l"s t''1V-1 ..' . /ntr,./b, ,rl\ x"iTcr'" r.. .1t."r.t/.

    . II '-.t,t,' ''1,.'; ','

    .ro \,IC,I IOI

    thdd, & &"Ls $s",r\-.-^ir'

    " PAp\\e (r,\o l: ct5wa\ cro ioJ (c'''[i(r(r,v'., e',prk,

    "r^y rporc h, T,o, o h, o-'n,.,,;,5\ \ *-\Q)\aco',\ir.,l rq\,a]c. ){,. ) !,n ,.Jcif f,: (O()

    " 6\ Hualu 4.i \*-

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    v\ r l'r

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  • , Hqly,r .' obglcrJc^L zu,- s,x.r,eAb..

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    -B v[, p.',,ffaan l"t*r,s p*oro'obLu' ,ln')"J"dp [n,n,r,vr -, Cu),oJ.s a-nunJrL, J",*7 (LS UV ) g,.J col"puf4,

    d,4*fXts +?tr{tVrad'-\Nr IQX\B} efu + qv

    Qero Q?r=6r '

    Qtur-*Obr^,/ Q-F:o^ I =[X* |D*,*']tu.

    =tru.-F**ort4r i*"-ffi*1T^11;'=Lrrr. -+fteihff?.n I 61= 1*, - ru.= 6- tnwt'wt,, '1 Q[=0

    QY_

    Q = t, -t,Q '= Q oeb

    I

    (

  • Qur^, urr, = Q *rr*., X ur* B*r, I VwYl6\a e u^4, Nts,c^ *l'**^r,

    1 = f u+v^d""r, ,.i u[*Jo *9 n: (],, - f) sL \= Ol, c.'"!*d;*J" *o (X,.r* -X,.,) y"," a K-.rrrno t1nl. K=!,"1r. .,K\nil*/, *rl\,,*r - OL)

    -6= ('o x)'KoYC,^ q\1o\" eigo,,clo

    E[n]= EWQx)'x*o(Tu+vD= |lt (rOx) ,f ev

    s'ry"e \|: O er\,n

  • " 6{ nt},*".1* 6 []waok' hi"!o Fro\'.,, p^l'o^'&' *"1\.**" tr,th - N*,J[-iowl\

    ffic/'aff.nY'r = J AX,, )ry; tv,r

    \o.r,ncL f,*t s,L elt-"-r,f;= a.i 0T, + tr, +fi

    SxLr"^r!, Y," - Yi *lF* +.*/" = f pX:c*/l *V,"Y, " drf5}: tft, fl

    "n\r*r

    (Y,,-\1 = At/,fil t,-V)(1,,-= p Cx"_g,,_T)

    1o*.,*-0o ur. rrcneJo s"i* U", los ofuuocay=Ct&itV

    \.I

    \p \.roos"^o*t g \^p^e ry I trt, =e , sb $1.* Cqa,nq\e,..'' o,h\-qr-,o s,I* [* c-i]-t, * \o^.,L,b, br*1 p,,ru rulr\. ttl'vo^,r& v,n*1f,1 J,*rr o p"[t ,,lloLnnW. '

    o

  • \rJ

    i)

    . S$roJ, h q* rro cllnno, p'"hs,fic

    = o1+ AX" I fl; * V,rJ" p.r". .lf** fb '1 6-fD *r)** lklrJ"crxp'e'"9p'")t,Sp ovq esJf*,, d 9 fl; ew*Lr*"le') t^r^" [ *** rr = o,o*y"\*,bb"h*rqrt, *"rt GrorS;exs\.L rrT*r>"bk+[ *;

    , , x,-I -- l}C,"-X)+,r_i)\ 5, C"IA" \rs lBd n = ,-6]/, l:o&e)xan al-, *o^ 7=r(+lBXtV,\ t-^, :- t4 v.-q ) M' = Y'd - tsX; p>&A**Ve,,",^ X =o

  • @q\

    ;rf s;e\ r^nado *"\ awLu'Y :6+vir ll +v

    d)

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    t

    t|, nl^ I* T- a n\o.ffi"do LSDV e c^c,rt-nEsr Teslr: 1\}*rer,,.ptnel q"renL,*" B oc^,.81peco e\esl,,,/* *L, uJ"rj^ ln),**L, At;) i.^rf*V *4" 't* e\ ponnro + per.,.etr or

    "^\- -t '

    ,))iN c,e ."

    Cu^"l' e\ *oLlu wo&co et, Y =fr+Unfltv

    A n*,,*r)^ +L*o,.^.,. Y-dlX; BJcs.

    "* "if,f- *y{ he,*.}r*,Ja \nr^sn[nf,/ ulns.rvlos *[s:lfts: 6'F, dff + wn.1h) or,l,i*';-^;;.,*uLJ el,rnt/tr darrmr1 lnol,,rd*b (urnolo pll"l $, ubrunh

    '$A(-l

  • @Po,o to,.io: Ef'; pon*l IB p* ]' c?s'#lt*d ":!tT AS,n u\\o. i^tku.no$s . 6l'sl'" 3 o rortnoc'cr*s'

    'N us\^"r|,, tt,{h'n \ , tr rii) f :uv \c^\ rnsnnq rcs'r\.d"tiri) &\*.d^ P ilore"r )'J,o,r"r."

    atrn ln'Nflnrr 5"u nl nwlo a[" J^' ,

    anry,to 1., o\**oo*, til-

    '^llfiol[;*il;= il,lBM/n-'lvi@1Yi = @tX'lb + d,&rd f er\ Wfi = X, tsJ:0'

    agruta/o S"\'e G/" c^oo l^ \J,rol*, $hI-n [7,-1 rvtiu i =lE lo'. lq li l-i ltu'|i;i ttiir/p I tX,J LV_L

    *

    &PErnlfpl(" p Q,6&,0CQ-'\=o

    .l4r= E-*il.ler= n- +(rfq)

    cle a

    f\rrca\, a c,^rfr.nenht "on\ e,r* \to',sl*odo

    Y = Xn+Vo\x,,rq Te srgtVWl+rn- j fr,u =6r, voal,.-t

  • r,I xit \i,l

    {p5\,^odo, VE d,"[,Jo\4" OLS Lf_,o*q*'"6,,= C"w\'wy

    ., sr fi= [l] "- rl=ril:

    = ( ftT)'?,F Lilr= (*, r*,0)"c ox)' i {*,, *,f *,1/,,= ( (nc*o) o, Q\@Yr pe'o @W =@ nsSI

    t)--T-/^i*t

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    x: &'llll-L ..- r

    = {I Xi4xi\ - f\ r:r / Al: !

  • b"l S{rrrse D.,1 V.r^;obb (tS Uv). $" o\ ^wlo

    aplo J*o '

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    = [!t' t f,l= [ry ryl tl

  • Lq So\,o* ! t4 0n @,haer u*l ,n1, l, *o1''' ln poo pu\'n^")o aalr-Sljlrnq qn{encl^ j e3 &or

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    al-.,1. col,u,/' wih NturutW\u ap Ccttecdcn',

    a\a"ao$yu!"' fp ,J Sc-.., do e(o.oc,rrr tIDY\B+ urod = D./ W,u l|=ltx,x\-'l -(xv:'tl"Dd]

    fibenn0\, )do

    ,,D:^ l(/t"x\/ il'/-(x,x, Dul + D*oo = Do/uH"\\rp\,c-1, k',o1 p

  • O ^

    --1--P \YsA dorin\qrero'.QD= T - lPo

    ch"i, $r,gc6o=[Tu,- It,'J@* S-11"1] ]'r1r

    = nN. -Tu0 \t(

  • S"q e\ l'{rrp\, C\arccd"f,owqtY -$Yz

    ri)' V@}q eJ.,L,. 1,, 10geJ,",, l,f* loi ),;)vc,(,,,i r.i,icL ,),,, n.,,le ejdao r), _.\ 1

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    /' bd I illD"}, =$.b | b.xlB

    Dloi^.,t. d r.t-oE"tDblb: \N/- DtxB\D,.,Nd = Dt[y-lD

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    ^r",'^,,,::r::-y.,.I) = E[00.]

    =y.V?-rrYlV(trri{ ivi:=If(h/rv"r( ll,fii i ,v,J- tr T+,lt ,, I=tr twt t\v lll ti-t r lvV_J

    = El'b, rr tt.)t.dlTh r lt\t,l r rNV !: [H1|.lfi|':]f( + tt,ifN\,,, FLVVI{; rr,: ![,f/S']=O

    "I*o,*& = L[iDO'.= ruf)1'.7rfu"" i{V',V:

    .\ -

    1-^\t\tn sJle(r\n&pn,J*^L'

    ,) 1", \$rr\e\

    I

  • -A =E[ol(lrnl- +frEtfuy"Jry +FnAd @9',.,o 4 -- T-01 J"'*,(V

    =[uu.1=ftN60t//"]6uOt\+ Ff\wu] [o@TuI" p,T*ta, *\ 1r.J*["f,..cnh. @OCc4r!)= nc1gD '*4=E[u 0"]= [r.n,r 611{ffFtprJ+ EtwlrO rfto E[y1tJ=Sl*oT', A Etvv] q-3Ts@xr

    ^,*,-o= Er0\lFl= E* oT-r)q-or)+ (r-our

    "tt 1- )ro l'pccr Itvqoc/*o Vor(g,)=q'r* V, Wf' o. J"u""'l H\\T* \" c*f

    "*# on"l)^v^.|s"LA \.*- at* -1",;t*;,;\ *;i:ff; "^*"''' Gr1, J lJ,Ll*t,

    6(v,,rtJ5)= \'5t Pra r=-,--S rP''66J r- | " p"ro i=J * s 1,,)"L' h,,Lt ,L 6 e o-p Per''o'/"1 4Jt"'k

    r ..,\ r\o Hdre+ Go"loo."< es

    Vc.fc{ t=J.t t=S,_] \)'J"\ yuro r= J t+S

    Pn

    1-?

    /u lrfr

    a

    A_' EL)O"J= s(I@$ + q (uro r)

    CoacIoc rCF) =

  • I r 1 r /.. I1v er^rlr, L..n Z\.,)..,.i..0. (ut-) t ' I1""'1"' i'' r'')"'li' l' 'i;!p.,rrt,, (.r'.,\.-, \'" 'n:;,"'' '?' ft"'"'r "'"" ')"""u' *"oL t'o 'L']'tc-fL.r\ u',.'i c,",,--'.

    ?al{ it 11."'r

    -, I,, ;-'lDwl'l

    ..r I

    ) r)0r)

    'ltlt rl , Iir, ,, i,

    { ) ft i: ti,i f-r() ;;,iI-

    \rof r \lI r'{ lu"l,ro

    it \ oolt, ooloc)\ IIOO \ {

    \T?1-,rr ,i I\t':'ir"ii;l" o llo o

    /'.\ 'A: t 4r!', ': -\i_, :- [\t l'df j \ J'i'. l-\\ / i "' \ if'

    :

    t;t\7

    ?\o \;? i,\/zrr\ (zvr \ \

    olrlfT'il= i+ r\\JJI

    \\ OIor

    ^ "1-

    yA I tf,@j

    \r D\-\I- \'!N- iO t I

    T*oI ='L\.1 -IlL

    t-e//fli,(s'-

    I I Oolr oooo I Ioo It\ O Ool oooo \oOo Ol

    lc \lL'TL t*

    1"r+

    Iru@tfT = \!uL ?ti.

    Or>{JO

    ot

    c1utr1'f1

    tl

    _q__ r

    \ ,*c IO

    o';2vr)'

    'U y\'.1f

    o

    Dql1{?

    ^:l'Jr

    .8- -, q-fr f n )OT.-)+l] ff,gTrr-\ ,", ar\r**r],"t ",0.1".

    "'i.,,.,.-,'i .-q,L lo",\,, n Sl sc.

    \: fnsfrros, o \af,r.,rnl'n ,mcxerL,.j,crt f i R, ,ln] ^ (^ono"r, .* b[rj*rJ *U,") &51,c^c"'o\ S\ro"\ !*n,

    "rl*p,\,,t6*dp\ fnrrro \r ,l,u tto

  • rt

    6ne$Coso CaGdt'otA elct^or('o J^& Iu nor\+ * ,

    \c{hol+cl q Coto.rronlol nlor errorej eJ n !

  • _4= rru\l'l=(r rf +az)(uu6fr)f ci (fN@8")pero Tu@ i. = P, I ,po,a Tug Er = Tu @ ([r-A

    = T* e n, - I-C t F'" X ^C 5:P'1\ ,+\X-- -.r+- R\

    ,,NU rT = ]LUt - y

    nt@t, = 0un\*.^

    -a = urq)rJ = rlnlri') 1p + .4

    ol,*o\,rn HJ

    A Pe,o lz' (rafrlfr) 'iA'D>c.^o56-n"r,6.*l.j *

    -C d**t3 ,1 !- fo,,l lqs 8o,*, Cor*i^*:ao

    -A

    F,, fP@ =o g^-\*,.,Lt uexis\en$:JI cr,+,lotP*," fPfP=lP r 0@=0 r'.it,,,"Eli,s? f='L

    ll';\ttvt,

  • l\a) \eilorlta I ;,d

    e'rno'lc.i 6 kno?,q fl S- .hSarooJr.r 4 s rocoiqno

    ;) S"> p,"$tn'\ oJto cr 4[S e N!o'crr

  • u",Lql= rt(&u)'@,ul:Et LD.O"O 0\ffi

    -

    ' '.

    (f1) = [[(],r. ro ul

    prr, 0t0 = trp,Or) p,*,, o**1.'., coj-r.|..r.,.,1

    + pl' tr"l ,v sr.u-g A l4cJ :

    r ^ tr"(l;)--Ef g.pg]

    o p** dbrnd,rrn gua:E [ 0 -lD 0l=e tv re6cp

    [u,, ECo r) _r?, r#F

    (oo9u

    = \.c [-0 p-l

    il,.,o 4= frt i[ q1 0,-r*,,'t,[ffi\]+tlQ p:

    Pera \Pp F 1 Do =g uil, *,,= \r[viPl

    [),ro F(.,4) =clrA) ,)**,F|ID"PC = q-]l'(lP)

    \eD Qc, Q q 0Q=@

    u'.(s.l) = E[ g"@CIJl.. 6cqs =k (tUOr)

    +--Q AtLlcaS ,

    lar (o$).Ef 0'@01P pe& caonc\\rt"i

    EIIQ0n =Ftrt{rloy

    = \[[(CIrD\@lp',[0b: :-Q, nn\^* 1

    JCTP @:vo O= q}\)r C+ e *J^*,

    =-viidpi( olol=1.[(Gl

    taWl, ei,tr?l

    i'

    (1- trfnt^r1"! - (- c_'.,wv l

    v-?= EilD"p0l"

    _

    \rflpJ_

  • l> eY \ten

    I l1'Wl cv L ,_)

    _/\ ^(1- L -\.

    I.o\

    /p 6ClP)=N

    (\'\Y:ef4cro&rn -q- W.

    NT1 r'.lr,J -r\l T'/AA\T.I l:7

    U;. - 0;)trlAJenpt.

    (o.\,"\,s P{os xrqrer "}'"t*t nL )r-"

    So**o.n nn!-t'

    0'p0 Grpo_-r,al-

    - ----

    _: 6.CI0 d^eTC@)" N(r-rr C&)

    (fL,JJ

    -/ ta

    NCr-4

  • E"s"d *l^ n*,\Ldo o#*.u &nr,tpn * J,h[ o^ o"*tr*-nte*L s**trwkrr\*q-.

    [mrcf,g-ortl f /'r o\-r\rc,u; ;;,iia-''L', [; ,;Jl

    ;,,(L

    _\rll' t\- -vt -!V-r

    DoW o co\ilr l vqnanvs y.,, FdLs se pa* n^.1*. "A

    t'\ V^*= X"@ "vxy

    = Xh[)lDx = Bn,1= rG-Trr)}

    0.[: r K\O x dq) r x" (] {*) x ( /)}'x til"ov (,61) r "{ n5 *)y( /qt]tn,\f ,\r^/, aa,Ao,lnv *\ onn\"r, n", 0f n,\**r'-

    u'

    ct-rv/t,a.w , l.zt.\.,,i^ . .l-r -

    rl nt \ .1bff = I x' ox t (a,/r) x n {_\ xl-, x ro r n Fqe) x" F _T *)lxYP-u*)X

    QqLs= L\ni Q']b*-f'r,\n r + rH)nxx J L*rux,1t cp-ts*iu,LtqrJ= W[W** q Ortsr;]-J

  • tt*\o de e)fu otl^., [ns].\t\Va e I f{au to :

    Y,, - /iD +d;Ei X;d,l= @

    S"" e\ )e,r,o e) evro( 6 i" = () )lL,CLb,1,sJ : EICt+fZ,)(0, lniJ]

    =Eroi:;:;:i;l,:o,,rr H,;ffik**^= Ert-ll]1 EI),r]\Efn,_rrrr r,-,^ _,1'"""'-_i

    ' u,--,-""uu

    Ef,.,J = E[ol]] Ft rLi,Drsl rv;Lt EL,L'0"i1\

    Xl"T."4'Lt c

    a/.

    ftotq ge, Jc^h C,^oY,, =l X,: [3 to,lp,,

    E [x,il,]_o[D,l X,_l *_o

    tnc,eJrv^co- eh,.nb *p^ru*[ "ffi & Copron*-] ch 0,,

    U, .?. \rJ o,crr)f['''.- 1l (o, q)

    r=s ;? EroSltE[0,ff],]:

    :0, - Froll

    = \-fr "lu

    I l)''Na undgn*,)"/

    \ Q,, &or,

    qtfi rlu"ers

    _ ll Crr\Rek c,nn1.re LI l),, [,"]=N ll *\"r {.,*,nuJl/e:\c.,sht

    Si

  • '[t"u t+5

    yrrlz, ;S

    'tClUrn,doS

    C .)(,,e)=l ]" -( q|tr,i

    n\\", v cu\, C,*,.

    ) = Gr (,,t;,

    en\nu*^r.rs Voq1

    Gv

    I c^n["^ *\"Cofi('.6,

    f-1 r r\ /\ (sitr ) ((l\

    (c 6.\ -

    (3\Lrt)uu ,/ - : {itafunc,\ YrYd n"t,r*CbS.,

    f .'"zI tuI. \ \ (\slr

    corL,r., ,, )={' t

    It'1

    [ra'r r*S..

    ')\rl

    .-l f)\

    I^u

    ?ur

    FJ(-\,-t\

    .

    -l -X){c' L+ \r, \"- 6,"n\uc* ai.l\r.1;,,... . {,, a,uWJrd$?vny?crer cer,r

    ,9 io1 "J".1,1\,

    J "

    l*L aobw*dq

    -

    Cor

    gH,\"nt

    f*" 6-=5/',o*,\*1,

    Cov[,,.6J -: @ r0,, i{5 \ 1""t"'} ry['^,*k l": ,/.]off

    r"""bs.,* coH l. s ld,ro(r3

    T,J r,r f;sl

    2\lv

  • J lvcCa,n,: oi..F-n\ woa\o l^o "t c"tVroru'rq el\rrn 0o^eh"+" @

    f"'Re ( r rt \\,^ olft^* o esfcrnf)c,t., alvrtrol s,l",c* :

    A-r=i')t4-'lz' ,,^uS.CJ,J, ;.'d ;[^*d" *l'T^o'

    a-t/ = !-'lzWi E +$)l't'7'' ' 6+6'

    d^e Et6r,'l ='l'E'',t' U,\bi, g,)'l' Lfftlt {,{,:g't'1--

    -a'] ELt,{,')-a:'L* f"t EL aq:l=O= _p-'lz_p4:'t,t i,o e et!,*hrq,_ 4,1@'14) u

    E[C4'] = TT -+ I-t,nfu'on\,rn1* kca oil-,,y'+6tr rc{ [rr.r oL\ f)" 1t Ci=t[k,^ ," b '&,,1\""n".

    '.'

    =l,m'$ :Hl gl\',o * *, \+l1' lm-\ , [ot

    = (f'I*\I i w''\ )3

    ^ _

    (A , \,) i .*,O ,I,Ion =(,] Nl-o'M') i,,

  • 'l (l f l,t rtt\r, ,at ,.!,..5 ,6L\ 0,,,,', f' "''

    "n- ' I t '"""]"n

    I tt \-f4,1, 0',r:

    "w) l *'i-'/'-i\ \.: / iLfin= tS x,1; 'tTrrl\,,* C; -.--, (; tI - - CS {rcffir''rir ii it'tt'''t" I i3

    '?iS^p\ - '[ d ii',i ] *, .Iilo5 ?,, 3

    . u\\l^,/., r,rr,ir!,\ rn y"h.nn r s, pdc ,oor*t\*r1v..T/, = iS+ ttl,-ltrt,, J, .n T- {).-1"

    p,urr)=olr+ l*,e i]l tZn,.Tf' t ,

    ,3 [ - ] --

    '1, ff,- .on

    ,'=6)t_+o; - {'--, ,' fnrai'f|A\"i --r* / - T.r.',\t*ffi

    , \J i^l ,., o,,\*.'dn L 1L,n p^, F tulnnys", = X,; IB + n* !,* ='.,'' - 'aLrt X'.-X,-)l

    *-, 1 lSi* P-r-"

    IL:Ln n- f-h-J I +,rrl,t - u rZ

    fa^o,'r ( | (.- *(ra1'...,." I .1 t-1,

    \0^&;_

    Ic)'nlo. I'I

    I t\1,i.,( " '

    .,lo r(1*

    en \rt)( el j-,^\tr

    ..\ .* l:J-i r r, t rn

    c., .,,

  • lr) ke cll1 ",

    , Jp''--'LlLJ

    , \ frgr,/'l \ | l'\ s-L\ e\lrllodct' lJr:' t

    tt -\ ,, r ,r? n -r-1," , , h1rnu.'(LS -

    -VVrx \ '{ ll1rv-,

    _r J1r, t Q itsq .

    r-\ \ F\ eit ffoULr

    $,orr'n-= Voi 'Wl,1

    S*'**= tsl ts*1

    i_A.qt r- ,-, .

    --lfi.. , ,4 \\]ur - )rro, r q*.J -L\u..

    , dl Rrr_;= \,r., , F lB-l' \trq r Mir"\ qr'ts";]l h-\,,, ,

    fr,oii ,")' r,,^,)o a&cr"tudrrnb \Wxx\yJ;i- \ B*'D;l un\,.",t

    . --r',Nr ti'$i'h.,'r )), Bd,.roq {U,aL

    r- l \Y

  • o\&**se g*e;) s {-r co ;

    ^ +-- rA a.ee^lclras IU6LS-IDe-l

    ffi=Ntl..\qhnd'

    S Q= + u,nl*.

    '\fi j,--i to?t t.,',)--.o-> --7 Q*'wr\'-t'-v/--- $ \)lr4.ft,)P-- a l\1 . ,*r

    -.J Wt r Drr\

    rZryr *>@\lt

    $*^ -U:.-$,{t*ao-**^\Jz

    Aag F.. , ^ -1,,, K ,, L 6tDqrs --l$xr | ts*il -V.lxx\Bu*h,nF I

    t?,- tv +8"-'vfnfi*,{',^ = w:O*ir nif sr w,) B,^ ll:\i@ 0lL \^gyvrr*tci,b lrd,h *le,upu,,

    ','

    tk"fl '&ry*n -FrT

    ^' 6l n ) * n!, t'a n\no

    "nt voil

    s; h>v*^ ff i .,*")tr"yK"]**u"*).*,*,ll

    ,\pn, nl e[, ,, &nl^,., *\ 1_rgr"" '

    '

    ui) L. !Y^e^ *i" "!: !"t qLs, c* \)r,,.c,:Lo G,cc,J, a &rane,&tes Lu c{ f,un, rt4ls e. aSrnLrf.o^o,le

    "L,"n-l.Jrr, l.J---..c

  • -liln?d

    \I"r, d t-p*t$t oo lo urr*ri 'J,J *rlcs P:,)'o: & C.tq e I, 4^r^ 64''tp,6^),1 1L( )=

    '*5-r-l'u"4-'tl

    n-+vl

    A./n

    I

    'L( )= - ln an '/L\n l-ot-/z -,lzarfraa loyn\,*,*Lw,os^,llol

    peto Q =

    q p+O ,,\\r).^o, A,J*J"," ofl-s.X;7,*.

    =q3;FaJnr-r"rff n 't-- aJ =

    "i [9, iP+ @-l ,pu,, r=s- (i F* al = *+ ;:: r=[io,e-l' r4=(+,.q^; | 'g' I\^ L( )= - \n ,f,^'!-\^ \ o l- /'- ,/, u,tr;fi-,tl

    vr, (/, = c,=-\,.2r-'- l: \O L tu,[c+)rl.lru

    I

    \^L( )= _ \n,n_1,,*bf_frt*qrr

    l-Ql =ffi'f*lu)- "t^S \.r@\- \r[r4] , i.l,q= u

    = (r?)" ho,u(u3)u

    ,

    ",_*],:,ft)*u" ,' ($ = f

    \"vl q '9nfn.otn-\n L( ) = _ ,b \n(,)_, I,t.naliTQ) .l

    - fuln "lrot^Lc ) = -'r)*'@d-J -* ru.{",