53
A(4nltoo " q&$

rps cw i wyk. am2

Embed Size (px)

DESCRIPTION

rachunek prawdopodobieństwa ćwiczenia i wykłady

Citation preview

  • A(4nltoo" q&$

  • ' ) -

    v!L:

    { o,' 5 zl,iv a,,*e/r^-,,,fo.7 /.'kne--sfr[tt lleril'tn{sX""rt t rO ) ; ("r) I (d") ; (r,l) 3 'Za'a" za**^ elr,*,t ^ -,gJ,,,< o, lo7

    ,/ i:,q.e zt-G-,-n:,^La b>e4p itAr'r,r,.ilo LoL

  • ,6 - "tta-'

    Lctor:1cl.' aruJJz.qa-r!,/rrq kJri-rrg > pr,\rzbto^o.,'r c2 sp,el-,.,,.lE.l ' ;.:.Pr'u,\',1 1*,,L+' y Otyipl= ?t4{i; r(

    .1is r':'or" 1 P( b ) :/. (:ln15icD *fr'W1o,zai,nu,.^-s..{si-o-,.*,r-.e- :o i/ D ,. I -- P(CnDi

    -

    pf-Q) = i zs'X1-31'-"'J't"-s-'^t: t' ;r . ytuLl t ) j ?(h) - p@l- ' , p{ [ - r , (4r , )oR) :_

    At, ' r . . , 4.nl ' , ?(4. ,"4.r in) = r \ ! : l j : - - j j - - - -1- :" :

    :f" 1

    .

    r (n, ' r l ) " (n".rb)t . / ? (4n.o}+ ?[ , i r .ntr) ? [ t , ,nh)- , ?f&r] llcol-=- '"?i 'Fi ' ;- jJfffrr " := ?( A. / r l ,Pt A. /ht v :

    ' \111 l 'J l \ \ ' t 'Lt t ' /J

    ;

    :

    1

    a.

  • t|Z ' | :^ , 1, . t7, . - , -6\4= [" . ]

    J R- | . r r - t r , ! ) t !J(a I f',il =

    a1I-o ;1

    L?-

    4^ / \ - ' , ,/ ' , L t

    l rn l= E. i )

    t [,rn i1] --

    ,!-:'- \-

    .J

    al62

    t ,a^ b)----..:=-=D

    Le.

    ?'"rr 'd, ' r . , - , . , : " -f'e"--uyrn to p---r.1"p.-'r.t,t n"t t- :4r:;;111.'- }(Av lij) = |J1d_!(D/A")

    Cr;I,-q,t**^ | .-12rJoS,r1( t:t,e ,,., 1i-.- .r, W n.g..r) .z /)J-{,1/1 i Dt nl

    / {-'u n_.,3!.':* 3L ,11.>,-)trr".c L"r1 bir.7 '-

    Cr;l.q'r**^ p .-12rJos,1(,t:t'e ,", 1\-.- 'r, W n.p..r)l'' n.-.-:,3,:,i:,: z-1Lc>')'-r.".-c t"r1 bir..7

    ?(.tr'/nl =Utrl-tnlr') = '4+ -

    !---t i )

    ?i, r ,1=! ?( r lIZ frf7dit *:t

    -

    A t'?aO ' - , ) T

    P(e,)

  • -Y' N ie:c.i.c,zrrc,5. .' &t-n:.')''

    ZLo.'.0--.".,:. A i 1b ^o-zycr'"r'1 ov{ta'Lrt'""f"'I'}9

    m,4/D)= 41)?(i\1i)- P(b)

    p^ercir11C,l-c t- re r,5-:'.-

    +-a,- \ a- l - : ^I I ' -^ ) i -

    1??a,aob)- 4) P(B) - '1'\:t'"*.q1p[Anb)

    = p(4)?(b)

    ? (,r .. h) -

    Plb)--.--=-

    P{^)

    /'1*X*,')L!'" ;)i{. L- I (

    X"-',tt" a lt>o,'a

    Z'-s"r1lkzo'3owr.^/:"trl dg' 'Jn3 I':^:L* qry'2

    '6''cr''';{J) zLr'r ' 261" '" "';1.,;*,J..., ,,{rL.

    -i)r,,.>' tt"h "-r,c'{-.cj'15tt' X '7 '

    9,"*,CoSdrrdr,"-,,-'l 9-'xz,uI IT tt't,^':- tt Ct *\txvr*

    ?(/.-3)=4 ****oL,,e,i,tn,, . r-v);tJ\1,"e b)c"o' X b /l.rU-J. *""F "?)L-cLr-L ' r r, a lx'rrQc't'

    Z'".arn,"o kOo.,c. bLoLcu+ ieot to L'i'.,t-,a'n;r'L [^j'otQ-+c)"- zL Dw'\'\to- bLoVc u

    ikDr loI

    r?-:;\ ^C (,arC- 4-

    fr:"^LgS p"c-,crc qrfb,c'i5t-,c' "^uyo''*l p^yfW w-6"^:', U":L-t:."{"n \Lh \UDLOJ

    (o,o, . ) ;3io.o''r) -> 2-l =

    ^irc' ""'o1 -> ,l[ * ,o o)-) 4'ft',-,o)-; -1

    fr ,o,.r) -)- '1fo,rr, ',.r \ -) - 4( ' r1,r ,

    -

    ) - ) - ]

  • ? f(() = f onuo ,"...< ^3

    I "o at^ - 3( r '-

  • lo-/ 'i;llgo"u=o

    GGGC=GGGGGGFCFFFeF

    +e

    i

    :

    i

    I

    l

    t1il

    ^ - i f 't^ ) art * toirti,, zq' F' (x\ rst''urXu

    l { tx l= /.

    t.-' \ O di3n po.csrot/^".*iIl8rur,n"rp. (aro,,o- l"*?g"n"a$iz"*x,unq r-o q*itr*f.g !1Y ) .:%A-Y ff,f3d*'"9:y4

    "1".--$h*1* Yd"'at"y*@*i n,^\.**^lo","r-u"

    Va-"uf^M*ltU l) iPtxcr ' Yt-trvr/,

    e Odrs.- -s j (GC,

    a

    x(Oo)O

    ilo" x>On'o.zt lod

    q{x

    k/

    l: K}-

    'K

    k',(,1r1, ...

    += ) L,,-.vx;o ^r"1f",y .rcql!r,'d'ttu,"'n q-# "**X;5:T*W:YvrXf:ffiY|ffi*Og X +,a+U',LtL t'4^fch'W.;c.oaol'

    kairrra af.'d'n-ittluo Qi'ae'r"at

    1/.

    Zr";lrrr.6- n[c[-ci,'c- a'"-'1'-*@

    -ci

  • aY::t"*- 1s:oet^ {'taci t-,}"rt4-/.;-czj{). c"?o4ea. rnc"kf ot1 c$r.t3b *5 *".""r- pra-L-.> t?.r,1

    rr.,5) =_,ir:j f;,ild't

    F(e'(Ku,{ tr ,Al= |' t

    pn^*r,J I.rr,7).

    FFFFFFR5lJ

    /F)

    !z

    n ,AI K*61'It odl-

    2

    0'rzZ.c4Cu-A

    9' O ' ' l5l- z ,Lt ,

    - - i

    {{ , )=olto * e (a

    t \cal) I r"t *' 2lot)

    I o,. l ia X v &x j

    o#t . furre i- pt,-'-.r"11'"."..sr

    .fu "LW ('1 mruz'ya,,."^ ]pttor*2 proa

  • IIil

    : rI

    l.ri1,,

    Aolc:-*Fq-:r**..q fsot'-1etf c.tgolo rn*)?Dl'r-'L''c5c-\L>+ :

    ht '

    nf . \ r ) r . l ts4t*,9)= F(*t{ \ j / F,Fn'yr. )it O t tt ,4 G( ) i )

    t f 2 e, ,*

    ?(x.o ,r=e)'Lz ?(x=o)p(v'o)= L+'2 y.. :, ?[x.o ,v,41=k ?((=o\?fY=0]' ! +.1, 2,,*a,,w,s,.to71 , :?rx'; y=o)-4 ?(x't)?(v-or4V=i r7oilrvL.t- ' tsc-* :?1x=l) , Y',{)= \ ?lx''tl ?(Yt) =t '!b= + :

    tlP,re"&n"^"^-7lL8/.b'

    , ( ' \a.^Qr- x Y n'^a' J') '1L'44')L'/"\- V"X* -' "

    Yrt

    ?."O^',Il'.{ 'z**t^-r1 {'ceCqrtl t' - - 'a ^ ^

    'rl 4n t-t. cpz.J

  • . - , i \ ! ,( \r,1)i{n:!c_ 2rL?-1A5rAv}."A _\. erL "-LCSt i- 'rtc,?i"( b
  • ,r.w,$^n &vr6adax -l

    -" .+ , i t ..

    -aA,,l,-_i..-r

    /

    ^or. E(x 'Y'J " l 't

    ,nr.,r = E [Cx-ff)'(Y-r

    I(t>..-"n^* zn"-ervn1d"' bf3*u CX,Y )'/*,,,' El({-Ei} (Y-rf/J

    .iCoru656, Lc-,o,*ozvy

    ov,(x,Y)= E(x v- 17y -Yf* +[dEr)= f fxYl- E/EY-r/E\: E({Y)- EiEY

    ,Trl.r& Zrvwtrr,rra- LOa,i try t2 odrzc.&-i, rq- b i.U, f,1'.41"r':',rLcl*- 1t-,$-'"r'z'"C O(1o ao-otr- r^rc' lear pra-,r'l;ztzx-)

    frot-Uor"t^'try8-(fY) 1.o!"-.-^,* to'r^or:.n 1zr- /,r,r.L'.,.. (c'so.-,. I i^+4 ,tJrEfkc?ELOdAru; '

    u_

  • XL -( ? \pt a. :ec

    " j ' l ;h'-t ' . J i t

    Fd. 1 f i .0 {, '- l t .9, ) ' i \ ' .o/r t ' l ; ' : i - l

    L -t.: .)L a1'"ur,,-.k v.c4 !!'- ,'r$

    ) o 'Yl-- t "v{^ v '

    r $x t)Y

    - l ln

    , \11,^-i\4J1L 'nU' 'rV! ,/.\! :r-l".1-

    -4

    ' . (2 ' ,5=43

    L

    ,J (\,\ l . --. - .),;) {/a;3 t r Ii,.,- . - )

    . ' b. t . \ ' l { X r l 1. . .J .(

    l \

    aiLc,

    Z3

    J

    L\ \

    - .1f i =

    t l ' 1. ' * ; i 1" , ' ro' t r . { ' t ' ?1:l3,ir -/Y_ll_ g.Ej!:

    -b 16 I .) .)

    , )5L_'r: - 6

    :D'( -

    ' l ' tv -

    t j{.* t- J,( i;f '-Xer-,.r5L,\.\ L)\-')-& llt-S't? z'",u"C,r,l".itu,,'{:l':':L1ru" .

    y2r.) 2",.-.,u,.. t..>,r... .i.-l[..]-,1',1-,-o.,r,,..,, r'].-.."'i )u.'\',!-1

    : a J -,t-'-'- l*Lrrrrn,e. /-.-t.: Y: ,o.,r.,. Y

    '-r Ii ) a-k i

    t

    0< i1i( O i lioO,,. ri-(!?.1\-'.i ,rrrcilJ\, a: Zr,rtcry'4d14.,11 llr,:,.-).-(1r,..

    i .)< lg t< "),5

    3 5< tgl< o,,Tt--(qi< 1i

    51.,,..* "r..-), i:-:.g: i-,t 1i".

    6 i . ! , ! - ' , '2*(- ' i t ! . - , , (

    t r.1l^,.-" ,l;tr;:-.rr,-s. \ "\f i

  • Y'*A-P'A

    I

    4r-vtcfx 9"5 rtrcari-r,r"c

    f-1.:l4la!.B".-\ Qi p a5zn"z]ll!.-."mc)o* La'GE ,eit6u bg-' et"cn'i9ftru"cl'rzt I-

    a,(&, s)' E f{' 1* x,, 1j!2+.^"ntA'

    aiv-{D\a

    .&*f_.Dy

    )'Lo-d..nlg,.Lr^t'lcrLo. n P\rrYvlulJr'u^0V L

    ,a. LY-,o EXr

    i.x-. F

    c-t't(fJ@-P'.-f

    TL

    T'v ' t3

    'tb>|occ;,e- *,ri-irt? p-e

  • r ^

    . ) . - ,1\

    3. Xt"ra"n " "*4'tt yL "q'lni

    b Un'

    rn=o F: i M(o,),1 lU-"rur.aa"iri,-o,b?Ta OsT,z"dr^x4r.q tX.O_t.: d-:rJ- y'=-I:t4' n-it ek"".-pt"%",9l-crrrLx>. E{tnn CIX-d ln "t ^ t-t S-tr:*,ra /=3I

  • 9oY' . , nrrn f . i. \ rv\v l" ' r

    I t-2 ./ 9-\ -

    pf Y < O,6y ) -- qvc"?tx ql= / - PU "'eoz-y""1 LttJoe r'L& ?LL,\/):E(E

    9,.

    i

    r l - /1 ,a\I \Y,uV ut ' \ - ' , " " '

    4f=l i 5r ' r

    E# .^a-p--2(lb"** n"J'lnd \l(tr;T 'l)P'")^g(yo, )sc) W N (a/ lL ,,=p[yo, 7/pci\ = P (fY; 7rt*\-Pt:+-= a Q 7;)) = )- 0 t-,t) = "t- t4-or4ll= d("1) = o',ac I

    .lrl- t I )) l '^ l '

    EY^= ?.n' OtY.n=l*

    ' -zL

    !

  • (1btt :L,-o.r]*i.el.i 51,.,:lo-r..{c-

    i",,'.u""""s,b,so-'s- X "'--

    ,",ot.i'J ft (C 4ly x'*J \tLrvl'1-L.UJ>rrr- tgv*1:iL:I5Cl,r,cf .]sg-rr4ii'!i tt( dn,,E=1 )

    ,r'l nn'.tCO ftrui.'t wn- afo:

  • P''1!J)1,'."r;*VJ{* /. 1.' . / tcc' t:t -'t^ru ';r;i- )1-\' O lv\ . i r .n / / . rJ I - ! r -

    -tt ) .

    |F

    FstsF.et-

    -{s+s

    s

    +

    s3

    :

    : l :3

    Il i^ ; .2 \1r

    1 ."\

    ' " i ; . t i --qt )'rr,

    .-LL r.1.-

    -

    r-\ i) ' } " ' l . QI?> | +I l - ; -

    ' ' | ' \ - -1 l l ' ' l\3

    / i Y \1 . , - , f ' t ; .= . ) . r . r 1; 'l

    .i

    Q-"r." t*Ltr;Lit Lutrt hat- 'i;r''LLtiP

    ' -

  • i i A- lYtJ i ' (V 1\ iYl l -Ei I i f iG"l i f t

    J1t,l--,..yr.-- 1i,r\ i'l 1'r.1,t., :-cto, r lzl,:rl;g L )l-\l] tz.

  • kJ'

    fp

    /1. lrq-

    -1

    7

    \ . '6]

    ",, ,t)

    T^-1

    n.{>tx.-.",.J'=: [4#f 1rr ro,l\) ., E,li"Xcz,]-. c-cius- X .rl,4> f 1=-r-,. ' $tX

    = EZ

    \1, . i

    ;,-D).vt,

    J'

    2

    t^=* T.t-.mr*LoAa,l,,"d*''"'t o-',,..-^."L.A Af (p' @

    ("*.*r""-g

    to et"fyotpl-l- I .,^*,.cdo'od, ol1r"'pfo!"-^L oryrn{'(^{urt* ,* )

    /A, /.tl,1L o-D1-i -o:,t-{F {'} \ o'\1v-pfo

    l.qovmt mc r'"a L"'rI

    t'J (0, i)

    3r'lL,-oa qaric6c,' Lz\hloscr- 5c"1'i cr>"c

    Vw zr"^;*"v e. Lar-'lo- (.n rnt:, r)i";;ol

    ;* ?( lu.-s l() ' /

    L.,.u LUrn' q,rt, O

    Slotpt'\,A4 lL- ^rrr'g,u,n7t eatS''"eio

    \y.,stc"" ot

    'J l*ry'-y2$:cLwetrr- itlL J,2. ninbuT'zrtr'''y.t't',

    '1tttV FUo, = (Q

    b o*1ry:toloz.w"e ^ P:a)-7>+-^Yn

  • ?(\ i t ._ l l ( ) . , izl n*.11-.:"'2i'g;:\rr'"r-'-'err'

    A.'l:

    ' . r I t " . , .1, r - ! ! ! i t ! . l

    L , ' : \ ' , . lQu)

    ) 1e>Lr'

    r*{ l - l \L-r. r L\r l \ '^

    :r,s1.r'-flol4c ;.ru-L .m;ad C't rJ "1/-{na

    e.

  • r r''r'J- :'I\^-i4lr'r,r)11, ( 1^ :1 ,J ^-)r-r\\

    ' . - ' . ( ) : '1: - r : . . t , : - - - \

    t

    .i, ,1.,,.,,-r 1 1. -.1 ,; ,, .; ,.,._,:\_

    ' i ! - ;e . . .1{

    : \ l

    ' { , . " , r t . ,1 .* , -011, ' , t ,1 i . , , r [ , ; .1.1 . : l - . . -

    ' ] {

    -r/_ L -l_ni._ , ru]-L!!,.. .ij\

    4y: r;,". -l ;

    \ [ r11,.,'.1in ri "'

    f ,,. i':,.r r- ".t--

    F i ' r ( .1 1/

    O

    Jl I rir-riL li t7

    x - .

    f) ,.i

    L. . : . (4#l' asrs?t-Qsr:)

    mV 4r04,F5m 7r tt 2o2

    t-,J1,.t'jr,ztyr^r,,a rnw-rv_./-rv\*6;;7;,65 ;-; J;ffi Rtrh" t"t"""b;;fr6".-.

    =o,o3) - * . C.195

    m// qt oosl

    n V lOt'l

    Lir,,u.b.nc6c p'o6{ toJ. o.O*,CoO otna(,a-'o^rn'a . \

    i

    -l

    t (= o,-o/

    = I u/o

    bo/o

    mVt^

  • l\ (rr\, o Jan: Ll .-^ /

    5=o,3/-p = q3)

    $ ( i ,c l ' i -.1 (**)=.{ l ' l '58

    oi915

    NQ goz"a*r; ul'"-"tu o'f,' )dci.x1i,n,.*-e- 4ic-""d"-*'J'.o 2r'"^e1:11"-

    4,3. p ' ,7- ,PLuct ' l+

  • ,L,-r 4JR4 ..o-'vzc*.i- gd{E.1.n^} p'X1t

    ;*;:"/'c- p -'>>'e;io;'2

    cr--{i.i.- p!- vS, t tiwvr'li*

    ^^^t f f i c . l tL" \ iJW

    "ti. \ r:

    t=Y'!;1 Wfr ="1,b u+a, ct,-i-Xrtyr.,. for*,1 /t'e'l''

    d, -p9..-.a1.r- 1519{rrro:ct . OtOl- Arl

    ^rq"**; *;,"'1 Po** iriilarose'" Qo 5

    kTfH.ffi':frrff]-p.jj-.*2 w::tz*"4.' on'rx;z'*"Y( N

    -

    K-zbr.v OrfA*7 1,r6s.a,' 4y-Y

    1,D/r'4A

    tn^lo1jl- {fih".- ie,bl'*""'*5 tc\Otg O.tLrLl"J,,

    L o=oirnv>16lw

    rn; i r< - at \ )a- l iJ\ g,rvt

    'r- ' I

    -

    - . , \ ]

    , , i2l l . , rm =' fl ' { a1 .*vr)F : ;

    _ = I_ge 57l - \ )

    K=(ki ' - )? { l r . - ,1 77V\=Lr-

    ;

    I

    t

    I))))))))),

    tD

    t { ) / ' r - r - r ' \ rt ' \ l I r tb l / /V

    ..;, --r---'.,-\.\;*^ k : t, '{ I- ' ! ' (=(?, /2r

    l=oFu[r,rz),Pl

    ' (

    O,CZ rnfll dt> ttdrz'u'c:-'ar\l . 1, ,6 K.) ,42

    t . i 6k=2' t I

  • 5p.nt--.1,.- *,-,n [u'1'1.'.,ie-r"- z'' od"@e Acv"
  • LTg"t X l/\'.i/L /'-i;a4r".;-t"Qa .:v{.g,-Lgt

    -c;r ':.at-r-/

    '11 p]Tg3; LL:.-.r 't, . L"r,-ft,.- c,.1( { 16- ih,r- 'l'c zr*i-)-L1l1 rprlo:,:" rr-dc,'"c-f*^: ?4n"."-u.-a t\o

    igol . ' l ,2.e tvw.. , -1 l ,A"_,As, ,An A

    , p.""rr-=-;c* i-r..--.- , 4, , A. 9 i\-" -. u A t

    N r -z-d.t,.,,"b' Gsrr,,:,' Oz-"ar-aa,.i'* Lr,zn l -q *1t"f,1, 1r '- l*

    ,r\,cfJ'ri.:",h- *; pr-.r:J.,l.r,.Ct". -A< pk =.r l ,C' l

    .p t' 1t"a--tLpc 'rr-'6rt ,n:t.c r-r- i4 o ieotP'oz,.i.-+. r r, --

    \z- 1or,,^)m, lcolct-z-r- to n#1pi5lro- U'=:,sf,fiBl '^n-'"

    tFv(ut y'J

    '

    Pn11.l.*u-",ll,'wi.;,r':i) Xi o - r -n L- u!:,G-. *|1-* L-21"^ P .-".- {;-YL a*i1-11,wiC \*L{&i4,..\,.-^,^ l^,. io.l1t'*- '2Xt- i; I p Yzr\^ /vu'$}dr'! -q tr\,{:.l i- 6 IllL';{ -pT '*1i.ro: ,\ Ls (- .l.n:e f-:,\ byv,.+',

    -)- -^ '

    ""12''(r^-... '5i'I'"-cft,

    ),$5'

    i - jl r f j_rru?{!t 'uJr^ol,\rr\

    tcn Z.,Lr6,

  • ,JJ iirr,i 5 ut,'.':.,t1.,-,:, . :, -r'r-,J-ir\- arL.ri r :,yr -,1 :-,.-:. T ry,.L-.t-,-i: 1o .t{,_" >i :

    -.:.,. n- ..._,c..,:^- ),_{/--3.-.\{-rv,,,r.1",,3 i 5 c,a :,!, r)), :.;,,) ; QJi,,ts, jj,.n_t..,

    ' . r , . \ , . ' , . . t . . . . | , . t , - . . , 't

    l ' : l t ' ' t . , . I .J. . . r . , , I . . ' . ' , .

    ?(A.) :

    l ( l r r , . r ) 1," _.c.- . , . i !_ j { ,a.r1 ?; ,1_ _ i . ( ; , i . I

    Pk')YlA, lP(r, / , \ ,1 ' t P(. :r . ) i11u,11,, i -

    ,1i ; , t3n i ; .1;c, .rr .g 1) I i , i - r ;- . . i . , f , r . }

    s -i;r

    - ,-rr -t i'r i-",i-;,,,t -k cilq Pi i'' ,i-. , 3,':>

    -.':-:L:'*'l].t- '. ' 'rrf-. 1 -' ----,-,* ir)LL z-c-\itc,.,r:cr r i - t 'h; ! ' t , - , - j

    . i< i I j -Pt-11t

    ,rr c

    : ;

    ,*

    L l . r tL.rr-< r) , l , ,d i .L l r . -1, , . , , , , r I ,

    , . l l ' . , , , ( t { , . . ' - . {q}-1, 'c. {^. L- I , , .: - lc , .cdJrr \ L,( , r11 . , - , , , . ' ) ) \ , . , . .

    ' { r i , , i , " . ;J, 1. \ - , , . r ' iu, ' . , . t . . vI :r{r4-r-v.!L Lri" f\ )i I r.\.1."._1i},)1

    .11.i - y'">.-v*J g:r -".. ' \ i ' p t , , , . \ . , t , , . .J, . i i ) : . i . , , . r - , \/^1' > i> t, ;;*'Lti.i. pr :: *--: - 11 ;.rf, +..;r,1,

    ?(,i I I "tl1 ' t ,J ' q,1

    t ; -i - la l

    t -, I

    P( 1\,| ( l'.'l ) i l7, tn i - ,n5?tnl.-t ,)- t , j ) .r fq

    T'?: , ' . -^) = f : ) i? in l l , l = Clr

    ?(n)= ?(4,1[(k l / t . t ] 'T, , r i . ) l (Dl ' i ' ) - r , l r , ) i * , ) ,1 C.; t _,- ;2_?.:I

    - .:-: f\.yv:,\r,, D r\,i -\i i;rJ.,D l.t-

    -

    lo-d!-\,-tr tc{ r*1^o,x l ) : C, n- ) ) \ \ ( , . i , i . , r i

    tl,Ol !s f ,, .. .(.1-.- :r.):,,;,!1,i. ,ryvr.;,,-;:^i,'1 y-^.i.

    ., I ,4.t- -

    1t:-.il'c-wc " ir-:b 1f\ '-\

    '1 , ,1 a ". ) ' . . . t ! ' l i i , ; . ,) 1a.

    :

    : . )S^ ' ' , - l l l , r ( ly

    -1. ]+ f i l " ) i r1, I'r(i ' l ' i :,' '.1nft

    ,\It

    ^

    '

    l ] ] / \ : .

    ' ' :4 l t " 't r 4.r I r r i i 41)

    ' i

    lC. : -

    : l f'1 tl1'( 3l ' .-\

  • P(/.) *

    a

    r!t.trl.l6

    ItGlFGa=GGFFF5cFeFeeeee(t

    Ii

    II!

    i-i

    :

    I ' .

    - -

    t

    Az .rii.j.o"-q-.".>. tA3 z;cla-'t-noX

    f L ZI / -?(Ar) i3, 4o,b

    .:.13>ttt;e 2'"LLa'\1'

    ?(b)- ,?[ArnA,",Ai \ = "(A^)"PtA' \ \Ai)

    xb)" *hk=ff i -o, i l

    I * cri r 4!_k-c..,/,\t

    ?(r)- l -p i r ' ) , -?(4. 'n n A,=o)-- l -?(A;)P(A,. i ) = I tH)* N 0b)Ptzr Lc''

    ' ' u' lt^ ltr z">t

    ,to-d. OLLct tuE'1,:.'or-lT 'o'>c u{"trrcttt /-^d't-3L u , -^. ..,- ,0t{ic'o.-,.^er^.-od"'"oSc'uLC':t-c["t /ld'Lqc

    :z- . P,'*qu--'l't^ tt1'1']S

    -.,,t;i."L-;"nL 9d r>,ehta 't anrc'Mt l'^vzdtg: z ttaL" a1r'"c bt p

    d -{j- ?Co1-- ?Ca n D.) ' ? [ol)r[n.)= P'

    xp- *

    {,r-p.1(a p.)i,f-r-i]

    t

    ---

  • Z^l:n"t loi>:t'.^

    -i1nle-t-.uf.f2 [f(xi= .l

    .

    " .

    ?(X= L)

    T(.1. P(X< x )O

    '1,1g- x\(OI

    ?.rtlcO(x.( ,,{*-tt* ,4< "( 3$ .tt* "t 1*

    p,O /721}?L

    | (n l '

    &.&r* loit ogbt^Xb,.r,#- rr \I f \XlL, {-^*o- ?*"1*,{t f^t d.gb)

    t

    io "^ '< -,4't "w -:(xpg=o,,112,. . .

    S.= 'u'

    L'4f (/.

  • c( 'qT. \C.rr.)

    r

    o({(r . . ru J =,/ c"s] - (zt-*:{ j'

    sr l l l l !e 4 z

    VI\ l :i ce,- { rii:-I n .i.r-

    ay-"'ccz r'toQ c,sh ,1, I

    ' r r

    J g{" lo\x =-{- f

    +a

    -

    r - ! -: ( ) Ca,.a\ :g ioX l r . -

    o-

    C

    Fe=F

    -

    f.-ef-Ft=Fv

    FFF

    -tF7IFI

    -

    -Ff

    -

    i-i-i-I

    C

    -- 9.1.* : rl

    , l

    .-:

    "

    i1)',^,cca {-i-n.i.\L^,-al"J e

    I n.6 *.

  • t_,

    )III

    %t- do".,-. tyrrl;\L|)r

    tt \ |{ t , /= [a,

    -

    xz&. x)OoU.&.. . (O

    Xe

    LVr'^"rtL ro erbg,.

    C1.,"e". agat-Xo* fe fA r-..^,(,*7 Cs*4+cr, { r*1

  • CI O"lrp xF '.(-' it ( ( l= , l 1 'a-a-, , i lc - t
  • '7trFFFFp

    tP3tt?3ttI

    III

    f x= a-A'* . lEt"=o' . ! . , 4r .

    9 s 'x . #-8.DX= 5

    2d.

    'wrY^,

    +p>t |

    -oxFl:J xoo dX\,

    W"l p.edapo6ot,e,{sL,u 6v(x=e,l)'."{ - *

    ^A*) 's ' , i -2, t ,b.Y/ . . , '2, t t 9- j rg__Ai *J 3 ' i *3=; 6-,bea.-Q * lZ

    a6 ib- 3o

    r x=f, ytl"r^ # I i" =fryulor' I @ o arnf,o^,""'.c*,,^fl iPon,!4.o/a o"13 tA zArwV.a***a .rr"z j:l-"qx, ih,t=**l.*.

    ^^t

    p({=[i:t-' 1 v.t,Z,J. - (au,.,o *wlo"*{totlo.e

    zPd./j'y^.eo,--

    ?[x=k)= # u-' k4,t,2FX-:i

    Ld. LI{"",l'r- ry.^o,^rft T.l,Iod3_ ,*aa&r,,^ng

    l(^l= | :'-* d'6 v)oL O oUa_ x.(p

    - { ^=u u'.1 f' i u'o.

    * !'=i* l$ rr-.=rz td =lv I/ v l- o-u-* n-u-^ i

    7 Za"*tr-o-dT

    t&

    "

    -e,x | +. \' l^

    -OIe ol( :

    i

    eox

    b'qu-"^tuf*u"'\.-L'X'tux''-"^'t't|, I' ooI -Ox I

    - cLL tO -

    tO'. j,..oo-o-(ot,olt

    AzX = i' -ot. - ou,t0X- a

    " -a l " - | r . -^-o\

    -x-_e .l r- J -{. x rz _.

    L\,\'

    '.:

  • Ufr"l;i,li4.L%'\ttl'a. '9r 'rdus

    f] i:z-rL{ifl. ,P(r

  • , ,) Trx'.2\ = 4- t[x-c) -

    l t*. { } . /-(#, i I : ,1. i ,o,f l-.T,p- t

    J:"a?r;zrr*4ctL;L,,-; rl nt s"=,yriu-

    -

    1-() r)rr, ;'at, rjtjtJ...\..\:-y,, ," r ' . , '11t ir : .r . ,br.-.--rr. /c: i-{ .r lh 1:1.-r:( ' \V i t . t*: . p*Z q ' i\ , .1p i ; j 1,1 r

    ( t ' ' ) '= A, \ l-f

    , l -n= \ i ) '^=

    )-"1 )- lf ' / t l la

    at piA

    ,n= 2aoP'o,o '1 ?(x,)e,) ,4- [p6=o) rp6=.t i l . 1 L!"r . ] "*4,k ' - f#

    ?(,\ 'r J' ff e 'il : -n

    \=.n.oo1 )(x.7r/ t l r \ ) ,3.)o / . ?(x g1:, . , , r .

    I ' t r=O) < o,oJ

    1 11 c.) i ) ' . -

    ( . r ' r ) , r r ) -

    (- t:.. .,,non n&'--,,.,i-.ufac

    .,u,..-"-^a( ^-r, r

    /'*li-. ) \'+Le( ';CIqc:, ( )

    ^; ir.-t , \el-," p-cc.,,I ,t L_crir_f -r.,!a-,.5y ..r l .7^55f..t.

    a

    lu-4,".rlo.'nc)-{-

  • N ('.1+,c)O =\a

    rr'r= 35

    ?g>ss) = ?(Y7 ?") = r(Y23) -' l- -f tr) ' l- ' ' ' :, :r;rjrt -

    = a,OO4l. l - o l \7. J

    ilF-FFFFc

    -FFF

    trF

    f-f

    F

    r-FI

    a

    I

    r-

    C

    f

    t'

    t:

    i

    t

    :

    L.;z'*.nt- (tSt:rt':,- { ",.tt-'"

  • ))iItIttt?tt?til

    ;.,",.".",,!rr, rr:b, LJt- xn, Xr " x'ot t-Ly*\--?= o i6-nd-r''r-1\t --Je"'

    sL"nb.,'^{.r" ?. W P(x-r'l= # u' k'o"i', aoo

    l( e.h !io,r= E /''J t - r

    O LL . =,

    lYI \ A

    A--2 5 '= { . } 'l -_\

    N = (.rn .rr, r 5 r,m' 151= t rco;,,rt ,l lt, #' atrtffia)' (o'+1

  • fbur.;tt'.'.,4 tj.'t,',u-{u+n!-z,c i-Y - 5C

    6x:l ,w,r .po? iro' ! .1"]5

    i)rz-r-cLe. i:.[ ,u\^.,t:i.. .r|S, fn,3-\rQar')-. pu;t:t-,-L-'--P-^:-, it

    < "p 51al 1

    '3 c-,( , n07. rR = 61 ?JC

    u)^/tal -'.

    'r-irl- tvw ( f ,x."qf'

    ; ,:-*-E >r \ 'n/' \-il

    2R.. i

    ,:V,,"v-.-.lL^+ [t*l-Utg,). f-"t] Lt)---7

    . Xm -;Yt ' li : - -avn 5nt

    D-{rr{).;:rDrvn Xa.Tl\ r-'

    i l^i

    I i . , - r ' ,1 \ l l jt, .\.r1 - ri1-r

    ' * \ l tm1.< 5.'1 / a

    \\ rfi, \. \ i , rJ- , il t \ -n

    ( Z..' -.>- @rl ,

    ,I),

    0'17'J- -^-:'t-i t)jc\r,.

    ^ l - i , ' r r t\

    -^ - ---:=i : | = ,l -1----t( i

    p rart. ci J ctfrrose r

    .n=5' , - -

    - o, '4 j

    1)2,-111y-.- 61"'C>. -

    (ir-c- "rYv

  • r-r
  • rlt{"c li'.,:!i ')i '-'''"'L'i re f\>''-.-r,,\J- liinsl."-

    _1r=Lq, r '

    - j i/ r tT :j:),ii.+r 1.),.t..-

    'a c',-t .,: . -\* ; -.-'..' ,: ,v1.- ,..r't ;-v: 1 -. .

    : l . -\ - r z-q I

    \i L.r, l,, -:1,.r:' !f ltt h*j '^ 'n( r { t (2 ' t.1

    ; - i 0. . ( r ( ,1LI * : , ,

    ' , - i ' -

    - . /-

    :__ -::_l__ __l _

    .-:-- -1

    , I r l.1 ^

    ^.*r-5r-n1"/ l l\ ' ' . i - r { - \ rJ ' l \^) L=-1, i ' Vl-r . i . o

    i "n: " \

    J- ii { jI

    ul'[fO) A=(:,C] A(t,21 ..2'-t'.te.;."x3rutr-t--r5 ( ' ' . . i , rx-1*. i q|- -\O4t(a 9.^

    : i i / - ' ) r.J-

    , tiDl : :l ' )

    al ' =_,

    ' )^

    , ,1 - l= l - -1

    ,/ y(

    ^ i i.L)

    i.,JL

    drclul - - t :

  • z-{,.ccclD)= I : i -q ) , \ +r .1A-- { \ ( t . . , . ,11". ,1L

    ( : i )

    ,, =.,

    -S {.

    Li : \, i r''Yr L'fa\c.y\1,)er^ z) '",/ t 1, r, r

    r j ' i , .1 ' i , . , : . , , ' . , , . . : ,

    1, i '

    pzuJ=J

  • . \ / \I ( ) , |

    -

    ^ -

    t ?-"'.-iJ? - i:-!*-A. 1-r:ri \

  • o.t 0- S , , tht4rn l - - ( -4/

    rh--l

    Oi't*l-il,r.^ioso ;i

    *=/-+'5- ' { ' . . -l. O,oc6l

    m 7t lco oooa&, >dD'J- a

    A

    : Cfrrr"r,OClrrcex-ra E O".f3 /={

    , , ' \1 . - l F ^,

    , ,h ^

    t '

    f / : ' ; r ' - /or, =Z l(- , t i n. i x. 'dn. :,r.:9 0

    -n:c

    Ju'"dx=J(\o

    ^ /n:f)

    ot--!#.,+'.'( - t l "I I uz^ r latn l )q, t " lo '7 rtr /| -o ' ' t ^ '12n'11

    - { _.1 ,a . ,_ ) ,_ , . r , I=E Ji t - ' -u. . s r1n i r . f t : + t i+-

    . r . ' . i I orr z-

    * 'or | ; l * - ' lot f'\ ,t r.--O r\=o

    !4r ^ : - -d^, . , ,a/ . . , , ta, =J;ol=Lnl t - t l l " ' t - l l - r lnauz!4,-eL 3 ? rcz4111! q'i/t) +NfiL o 4-+ ' rcr2Qhca",ec a-q fezlCliiil/ ,t6 l6J R?S

    _,,1l

    ;s t.,n

    2'- !_ ' ,* ;vl rn+,l '

    .0"\r-61 lro-l.3gorI L-w\.L$:-

    ^i-)Ll3i )t

    _

    --\ 1

    , iU/.. \ - .1

    -

    l ' - ; - 2/,+ \_: l- y- . r:I

    . - - : . t a-

    e rr -- ,4 -

    ? l.,q,i.L

    : . i>q+f i t :n,_.1^ /\\ t

    < _ l .= lt_ - l ( Ie== o'(csf ."r . i ,1 {

    lFc-i-:A+--r-r+1]le r{ -- ,.,r,r " ' ,';' { q I

    'a

    U:l i l l * o. ( l r i .g.

    i,a

    - = / . 'n

    -z- - r . -4,r()

    *,qe R] . , - r . l - / . , , IJ

    -

    ^r {rq Io: -a '

    qu - )+al

    , l )--f t-

    "

    n 11- (,gl '

    i . ;, L,

    " f k iT, _ ,{ ?2 LIIJ1 tnl / t - : l r

    -

    i {1 *21f;=hi , c ' ' i i - )v\ ' t

    +-), Lnl , { \ ,n l4 l+ ' c . r1q1. ,:g ' I1lA:LI

    i " ; . ;o l r l *

    L'., [ /-, Il ' :eo

    I t 1+ALn < "]"il

    rt ,n -.{ r-*11. ' /L

    r 'l1j

    _. x -X- Jt;;;;---1 =l / , 1 l -

    - t

    1""i -f,,"-"-y.,u-vr5,: oL:.,>ie /Llc.1fq -9T rF

    z.1r

  • ca5 2 | 6tmz 'bL ltt^l*Xxr',t" ot4O .- | ^-a<

    +---\ - _

    \ r , j3_ / , t

    - '==

    --Z- i ; i .n2

    , . 12 ^tZ( {-

  • { (a) 'a= ':>p /:'L',L!-n?-:4, ]e;t l,6,e4-n ,.g,"i---r,-"--. . t i ' j - * + r5,rr . r ' l =,-" ,a. ,q f r , . ; - \ r l r l iq

    -

    =-r--C,r(. pJ 'r (x,3)

    9I. i ^,.5.i ; Y' = i\ rc-.=,ri ] '"- '-- ^-. C-R;pei' r"-';r"'-c;x

    -

    Z7 a

    2f = - oi"r:;i,r5 -g = - \5,n n ?'.'""-.'*

    q' li 5prt.,'''e'a-- , \

    .LX (

    Ii.)--ot :rt^-,r,-,t;r ,.,. C^R. o,3!" gnTo.,w{*l*."*."*.-.1 lr_ :.El:-/*

    - / i . '1 ' l= x-rna-

    i - \ . i ' t f . iL_ , \ L, L i

    -afi^i bp"tw.o- .c. L- R m^t 1art+.,ci[fqc.-'l-s-

    p,i4a. itLc;.1,'7rc"*L.- grr2"..1-;i (j ' r clzL

    A

    "l f \ - -

    , r - l . ' r-

    \ t t - z-4 ' \L l

    lcrtcC ii>1o.1c.'"'L.t.,-,'up.ly" p*,I,iA ,Mi , Y:: .

    z-- r p( , l rz; - i )*-=

    I* i ,1- ,1J-f C

  • -----------!

    u]!,kaR-y*"X-, , X-o l@) p,r fu

    "-"lar},:'* lx: l:5 ^z-

    ct : :c'"-r- 1

  • l-::---

    -

    \+ - -

    -

    . ^ . - - - i - -/ rL- { r r \ ' " - !

    r,--r-tlI

    \o;1- L(fjr" &r'a

    : - - -

    zz +)- . . .

    ,(]0

    -lii

    a, ! \ \

    i f . : - . r l f in. , ' \ - - ) -a! , iJ | : . . " . " - ,

    - - '^ . - * . . . ct : i . t . , r r i i

    ; ' - l -+- . * , - - ; . - t 'e1:- l :1 L\* : r ' \ \ i ) \ ! !

    ^l2 Ll)

    t^ t v _-=-- l a ^o)1 r >-n-

    -2- _-

    Zi-l., nrJ