I LeC. +v. -r'~ ~J

Ibe. Sa YYlF1e. T~,-k} ,~J. '~:~~~_ J1e. Ce,,+r41 Li (Yt ~ t 1k~ fc W\

_ - • I U.Z& iI »

. . j. I

I· .S±O+1 Stt cs I o~J S?lm~)'~" 1?L-\1Y' k~~p\s ,

I. i

Sup pose.. 'we. have a ral1-doWl

Sa rt'lpJe. m~, So~~ fOf"" IQ+,OVl ,wi4h'le.c~ fXC'v-J Vc-riu!\Ct. 6)(

X . . '(1. "1.- '- -,' - ",-:;:.. Xl ))(2.) .. J Xn

I X)~ ·X

W:= h(XI) YJ-J ~~-/ X~ ) . ,-~, CG ItQJ a ~+O+'l J+t ~ II

I

- -

1+.~ ror'~ IC+'wJI\ rC~~Wl2 VaVic:;~~ >< i'J JI"i'U(.-k:. ~

)('J'xZ-J--jX", v:11 01/ ~ ~JC4rc+:e Or.l Si",ce- i W ~IS 0- (A .... ~;~"'~... tlf

d\.scf't.-k rCI- ~ 1'1- VC v~ c·~ /.r, j ;=-1- ,~o'

lVI/I' be cA{!Crt+e,

~ 4tC4-J 0 ~IO ~ ue&+V\).:" r

l-tovJ I~ W rAts1Y' bv.-kJ ? , 1\1\, 0 '1£1"" t)jU'.J!' /) -' { I I - ) f_ l f" , 1.1 ­• f ,- \" "'" Jf' Lj J W t\.",.,.f .. ~

p~~ fVv()(I) ~+. vy ; .' .' '. Tk d(siYJ ~ v-h.Q 1A f~/><:) 6~ VV ~

, ,(l 1 , I l .Il' . I . •

I S' C2 .r· ,(}.; $'0 W'11 I r- \ d1~1Y1 b",~"" J ...J ;

. S;rn',\ofb \f'-{h. f O p\A1 Gc-lw"l YOj,>~_ vaV((thk

X IS ~11/A~' IN~. l.J 17"'-+ -h (.() .... rl#-+e. ~ peLf ~., (>0) t>F W (I'l<)vJlr,J ~IAIJ.AI$)

I

WQ, \N; II JIA'f?\f ~ 35-5 3 Tr c... h (')<'I}---- XOOO\) i.J"'.Y'}"--o~+ ~ rn W'~V\

() I l11\-(Lor --Fut'c.:koV\ .

Ro ro<;'(-}wV\ L " (r~ 21q)

5(.4 pr{)S~ VV::::. Gl1X} +. -+~~ x... oS

nc.v I

(i) E Cwi::- E (a,X+·· - t-o~ k~ ) - aE(X,)+" t~ .. ECxYl) . . I , . .

e\ i'l I.+X Xz. .' -))(1-- Crt , .. dP~f)f'.Jo-~ ~. I ) i) . I. \ '.

X+-. L{)i...•.. X.).. ..~ 0(~v.CX4)+·"fa,.~V(X).VIIfOt I If!1/< /It ': . ..J- .j 1\

(~~ ~ / ( c. 'X) ~ c. ~ V(X) )

I

No VJ s~ p~o~~ XIXi -... x-II .)). .) n

Q n::. _ arC"~ ~ W'I S 01'1"1 rIt. .f;.o w.. ct..

fotv- )o.~t'\ orE- YM.o'" r C\Ad vav 1~""C.e...

iu So

= 'x +_.f-)( . II ~

I . . .

,. ...... ;;: x, I

-1- . -+ XV) L . ... ... _"

111

5 ,~Y.s Q r"l I rn Y'l1 e d;ate C<i;1.S~lV e.."e <2...

of fh 'Arrvtovr 1~resltt,'~()~ W··~ 1 .Ir

h a v--e,0'· lLDros,~ B1 S~ () pr.-Q Se.. X,) X'"J,.J~ ~. ~ X!I'l 1.5

a . V' 0 1/1 JoWl .fa 1M fIe.. ~W'1 a FQ frvt Ic..1u V\

(l . ¥YI('Q(,1 fAx Ol'lt~ ·VCy·/ C'" C( 0;. Th~

(\ )E (To);:- n r-X

(\ i) V(T 0 ')..; h 6 ~

:1 i'l) E ex) =- rX o.~

(\VI V(x)~ ~(;

-

Pr-d~f, (-t~'I.s '~l~ ~~rU!l~+C~+ ) , " , .',

i) E(T~ ) := E ( X, t· --+Xn ) , ~~ PY>f' ',' '. ' , ~ E()( 1") 1-"' -1- E.('K~ )

W~~ :! I I· !

. ri::::..i , rA .1. + ~ r +)If x·'. ,I J' X' ' I,'

I

I

I

II

" 'v\ ~fle j

, b~rX ' in V(11) ~ V( XIt· - t- XV-) ,

~~ ~ PINf ",', "\ , -.:-: veX',) +.. -t-V(X~J :2. - II,.

-=- 6", t··· tov..x ~.

~ . ·....(. 'X' ~).... =.' ,.' /d-\'. ( - '. ,,7" .,". v t" 'X ,,,.,E (, ' n'/\ I ' - - .,;. .' 'Vi!J

n .. :.~

8 ,

- rEemark

I +~IS'1 mfo~v+ 10 V'A~I!I.h .t'.,··>tet;1.J..",~"

+k- Sj~ bu Is .-- Ix o",d ICTJ( arc. -fk : ;-ncol"!. 0 ...,1 Va r'c'" ce

of fr-c fJ ~Jvr~ '''\1 to E~ tc: ~ · \.j. .

J" . ~c+ *J ore u..lItcL ~. M",lc~V\fr\cN' cr,J 1K..' -f0r,,-/o~/Il

Va. 'It(j"~. Gillet"· a ~+(jr:hc J

w;:~ (XI) · ') XV\) we wo~}J. . .

I,b Jow""f~k E(w )~ '~W

o~J \f (w )~. 6~ I~ ie~lr!

of 1t.t fo{) r\A l, .'''''. ~(fAf' f X Q" j ,

· I I

I '2- - 1-.

C'trC· .A _ = j 6 \J X V\X

:JD

cr:r""p"lo-bs",. s-k.Jcwl-de-vl C.~tAl1 - >( ==- "_.- --.­-

'In 'fY\

G __ :: vex)X

- 2 IV-X I Y}

/1 d· Samr)lrlj- -FroVrl ~WorWtol VI s+r, b\A~Vl

su pro~~ k]) ~ 2-) - :j Xn

a v-e-I"ckpe". Jp ,..+,­ 0" c1

X\N I\J(fA I ) 6\1-) ) . X,. 'V N!~~) ~ t. )-'J

·Le+- W' ~ a \/ +.. +°OA )(n· ~ - "t A ­ IP

.. \WN J\j ( ~lrl +... + ~'"' f~ )o.l~Oj ~-- +(1~1.6;J . . '

.RO() A+ ~I} '~~3G

WI[ Cvr '+ P~vt: WiS'. ~"wcl

(ve- CovlJ rt- we. ~-€~ ~~ t

4

ae Y\cr'""Q.4-1t.Aj'. fu ~ C1~ ""~ 0 ,r,-" ) . 1 I "',\.:, (/")'J. ' . - , "", lC It!} ~ J · "'­

13 II-+ IN€. C~ ~ C-()Wf ~ te '~ . Y1'I c Cc~ .O)\J VC'no~ce.. 6f \1V II Sf':)

~\'l\~ '\' ' . ,,",\<:J ";. t~"" L!'." -.

' i

E(IN)~ E (q: X,t- -+'Q~ Kv- J = G\ \~ eX ) i ~ . +c~ ET ~ }

I

~ (A Ir \+~ -- ~"~ r~

c~J . ~\I . _. I'f.) '( X .,,",,~~1)( )1,..

VI

, ('W' '/ 4- \'. f~: at i ,--- \1 OJ.. , fr...V,

!

. ' , !

== O~V(XIJ +.-- +av.~ V(x,J . ~ ~. ~ ~-

==- 0, ~ +. -- +- 0 QI 11\ ~

D

. 13 COY'lNow- we.

+he.oH$N'l w~ 1'\{~ d · I I

TIear-em ill.. _,..-.,......,..... I ­

. .SLt pros,e-!

x,)YL) • --0

.

)(V1 15

.. 0 'fO~~M sa~f'c ~1M,N(~J6'~

Or" _.­

qt'dX/]AJN tr ).~ ~. ) Ei()(Jf' lk- "'arJ r')Gr-f 1.1 -+t-elt ·~D-a~d

, ' I' .

'XOlfc-1\,OVV't'cl (-tltL~ IS Tht-ortJ- LCtJ)

ljoVv r~'..) + vr..(l~O~ -vF ,X- /4 ,IS f US';-J e-I~Fh~sduV1 M' Gr 'Th-~rt#- LeN o"cl ~ PGtme.

~

~I/ Q~~w li"J -f-k.-... Vat" CG~ c~ of")<

IS ~n' 0

~Yt1ov-k 1+. "i~ VUtl\... '1M j'Ul ,~~..+ 1:r

. -.J \

S~+()+t(Sik-t4. JGWr~ VCYlOllCe..

S1-~ I ~ (X._iX) 2

V\~\ L j

,~ (

}h\s: -(~ O!f..c ft:P~ol"\ -He1-- ~' I,

L r r~ .. \. cL..s dYl 1n t". +~V') LS ~/) 0C lilt - ~1 v Clft:'<.:::

Ilt"fl<lt~M -t­

I

~:n,e. [erlkl L;m..!-fThl!6rt~_(d 5-<+) ) 5

IJI\ Theort i"\ !\Iyve s ow -/-t, cJ. If I ... I I

\AI e.. S Q fhf I~ cl. n +rf'Jll~ ~ ItI1 a' IVJ ym c/ d..t jd-v, l,{,-~~ lA.Ii-lt i ~;. t4w-. o"c-I Vcy/onU? 01'2.. ~. . (

Ci) To ~ N (;,{/ A6~)

,/) Xrv Nrfj S;;t.) ~ J I,'--r- I V ("-,}I ~M""~eJ)~ f()~-#I lo_C"'~, fa tJR ... -r ,r~><, "

rAe, Ce~rkl Li~(rf lhe-Orfl4- J:O~

~J if We.- s.ol'V-f 4- . n fltfNJ 'w(~ .I r_ d t J

n IC'J C!..~ '"jll1 "1"f\) ~ 0 It~ t 5~1YJ '1". .. "'I Lv;~ (W\~. t Okl. Va Yt G rce,. (J t --I--te-.

TohvJ cprrox i ~-kj Nlr.f ) 11 tf"Lj cIt~Jy,6~" arJ X he-) C/ t ~ >r; ;;+-.~ty

AJ rt'/ if~ JtJ'f-r1 t, 'U-~.

x ~ N(~)o1,)

:., I

ReWlc~k .Thl ~ . rCJV 1+' W ovJJ. rt<l-t ~.~ sc/i1~-h fj

-1_ r.- ,I . ~ ., I . }r

. <II) f~~l>st~',w.e~~Ctov.J' .I?c CC(,~

±~ (,) n& ,e.sh' ~ «k ~..+t~'t'(f'Jc. (~(/01~ It-~ ... ~er~Xi~c~n

\--\()VJ tVU" on' evrJr e~+Il"\'\"'~ II \~ ik ~ l,./ V'l - ::)0"" "" C?~'t ~ -h.kt. Q",.

YfLro ~C\cl V 6' '" C t ~ ~v r5""e. •

Y1 ~ I, h~ "'f-M d(' c', ~ c I r\cc..c'.s YLo l,J yY\ OIl:J)' i

So +k (C0trC\ L'~I+ T~~ Sa~s ~+ f>y -tk rv:rr~H s e;.f

S a i'V'l'''j it' 117 '3 0 ~-tH-. . 3 CJ no. r~ WI. <'-.Q*'l. h.e- kQ res (;' S' I~ R ~a j/lrTlt. lvei't cit'" w'" ~~ ~_.N9~f1.,~_~_1arlA/~kfl, w;¥(~

S 0: l'r'- ~~ G .. J va ...~e-~ '" IIf f4.,

(] ~C? I· 'f!'\) rIt-l c~ t'\

Exam ~k r::;- 2/ /8

A (evh \'", ta'Y'l svrn~ o\r3°I't12-Q kV1 re Y0lf't +k YI v IN\ hDl""d 1-'>1 oJ()Y' de ~e:h'

~V" e..-cc ~ Yle.v.J cu.1-'l> ~ ~; l{. -if 0+ 1+ ir'~s, I

SVfr>\:C-. 4-i ~+ -}?t' MV WI t-,4r Q+ sV c/h '

dQ~-h ~V"o cer~-'V1 ~cl~) Ts a.­

rc .. d..o ~v Ci r' ¢~ k- w,~ r'fL0-.~ '3~ ~ o ~ J s+CII J.l jrd dRv I Q -kil\, ;;}? 4 . A~ "-.j

I 00 rc .. ~I'\-~ se fecit ~ CPlrS o-f~; ~.k\ wket IJ -k f~iJ c~ (it}..-t\ -+J..('j

. . . --J .1J t1 r I ~ "

TH..,. 0 VW() j e.. r. v ~ "c.v 01""" ~fee;Ts

e<t'ceks 4~

·Solu~V\

LdI

X:;:: if of Jc ~~t fn r +k I

;~ -ft. 60~r

x ~ XI + X~+ p~ + Xl()O

. \tlO

...x -=- OVWc jl2.. t1 V ytr- h(.v ,.+ J~~c-f.s

S'6 W~ ·1.JJC'tr~·

pex >4-) . I

:

. I '. 20IVour' E(X )=: )1 :; 54 ;2

i . V(X)= *~= _C?'~lL ,i V~· l~() I

\

L~+ Y~N( 3-~(~;:)) .'<

..' . . V!<f -=: .,~q

. '. ." V; . (' .. '+ v ..

f,J ·.V \,. =".' rl" 0(.' Y'> .) \ Ctiy~..'..\C·.. '. ..' 1\ / . J '1, . I "- - '" \ ~iI'"' '. iI

. - . . \ ,~_1. ,,,,vc~..... "i . ­

. ~ .~ .. /

. .' . •.... == PC y~ -2 ~ ~-h) . .' - .. ~~ . ~ 2-~; /

...- .' "..... •.•~. Tc7 2 .{f ~ f 3<IT o 00 • o. • ,. 2<1-' _

-"- . '- ­

~. I-p(3<11) =- J-, rr1' == .. 000'1­

I

t10vJ +l-i.. CeVl-+rc\ L ;~l+ 'J-\.' I '

Th~.t:~~_Ge.+s U$='dw~~,~ ;.'."C::'- ~~'''''.ii' &!i!IlY!!l"_-$r;I~,~.~ •. . _4'~ I

Tk CLT' \~ YY\lAC~ ~n c4e-~1 I ~ . .

+i-Ol\ , 'O'~ Q. ~ OV Ie! e!'c:f n +. 7k+ Ts h-e e..a v .:i<- V)1 0 iIj wd1- k VtJ:l \.1.11/\

J 1_'I . I .

ot{SdYIVv~~S' CC/r<- be ~111.-\'d. .

O~ SGW'l4. ~Is 6f- a .. s o ""'11 l.t. J ro w'" ~Wl a .....~, ~S1Y1 h""~"I ,

1· ·w" \\ ~~+e.. ~'J a..s -. .

Ge~(wd t?~~c1k SUf ~St;,.. at Y.' C f" ~t'<- V () YI (j ~ W ,c d ~ be... N.-o tI '2:.€ cd () oS Q..

S 0 ~f~ +rtu\ "W= ~=. )(\+~~.+ XI'\ -],1

~~ ~b l"ot. X" 0 "d n'7 "'S () .' .

~ " W r-s \(iH-VOX' ,~oh~ ltvi'~Q\

I' . ~.()..

E>\ a Wc~lr.cs'.. ( h,/t.)-... (' \ f j 'J"" . ! '. ' , t . It h I ~ fA "/,. 0 If ({(....Q ti J "

I, \1\ / Q . JI 11· V V 1\.)1 LJ \tIl (~) p) ~ 1fJ\ r1 lPD e..­

. • i I

,2.' W rv G0 ~ tt' Q. Cd) F)~f~oK L°tJ~. I

r

3. ''N "-J 1<Jl.H~'" (Ai) ,Jt;\ Lp"J('··I

. I

HY~ef O-tTl'Qx,~LiA. ~

bl~Il'i(cl ..l~.

"-Q(' N-c I c'Y f ("o)<='

'f'"f'r.. 1n I ~ W \". \".-...11 tlJ . 11';--" .V \,.

--------i

23

-

) -~ ~()HM (sv~ ~ b,~",{c(j ~s b/~~LO~

Sur ~~C X OLd Y a~ I"~~~+'> ' X,v Bl'i(Wf l i')

o "d . Y,v g1" r11 / f) - ll~

cW~ x+YA- B1~ ( ~~ ) \1)

<f,; Ir 5 , ~ f.,.

1,C-j ~ IN t r.v ,,/ J l .

OSS.VIArt 'P::c~ ,\ ~

Sur~.Ie.- .Fred [

~.(J e)' <1v

-1-0 t~ Q) i~ W1 ,.,. I (Nt.) o...L 'f/-vv'l I .

• I .Je- c Cc. to .He; a. ~ IV e.vr... V\ +11,...."..).

Lt \ ­

x~ if qf . ~- ~octs' FKJ ahJe;vc.)

y...- ~~ JeCk­ I I

~o x~

w~ h

~..-~,,-t ,. wk W-O~( i~"'j ~ _ I·

-hSS"lr~) IX -+ \{ <iSJIAJ+ .+k..

'rfu1z l. J1 v ".. he.r 01 I J-vu,j s ''I VZtt 171 +Js~ · of <:;'. rfa:1 V CA,.-.}-Q

- ,i I D· ­. .".-1 .~ i

I,

- I

- 'X 8'v-(J)0 ~·V ~.v . N . I . '\ 1)' ) '. 1\11\

. I ,;t 01)1~ (lJfl.' ]<7P;~::"l.1' J('1\ J

t) \ ­

-rh X'- ­

tTb := X t+~'- +-- +' Xi'\ 'V 1S,,, (~ J p)

'No\!J I~· ~ '/ 30 wt k~ vV

T() IS 6 Fr\A) Xi f ....-.c-h~ \W-) f' ~\.-~A' J 'ol

. .

w~ I\) {f4r)~ri

So· we ~c+ -t~M~vy-ll clr-y-,xH'V'~ iv 1k b'~WLG I (tv (-Ie- : h ~ :5 0

.

r'-/r (0 C i'J "'if 2- 10 ~cl ~ .? I(j)\1\

Ke~cvl

1+ r~l ~ ;~ f~~J

r, 'Tv'-",