CES 124 Ducua -

no acheal daussin, due t Labor Da4: N 23 diussia, he lk KRcegh%,

O5 hee notes nstaaed. Also Pazzn!

thks he lalbnck, ll adbkesr at te sttt fnest eek

n't be at OH à w2- but diek TAs /l2ecks l1'l ces lesa

phac eeks nd annaunte o be stat diun hea that kagen alse Aakng his n Mlanty, Bekmbx b do sd-giales

LCluatens Cceiaial wTGFLC)/NE) 22] d) T)())

TC) knid ewk i hay do IAnan ho ay tiuge

te s it ba athes tb te kes tuo veticea n ta gla..

TO) I e eda ik eit.

bebvaeni nehbXS

Eanp

T) :o TO) 0-1-9 T)-2 (-2-3,14 and Ns = o ad #NG

(1-3) and Ns 2

(2-3,2-4) -ahbnuk nekos

(NC Max Vale at T be & 2 ox

eue tkat Cu)= e S

Ditbitn Cu)2

Fx Nc)k, Ci) & te avega poplin ehb corebaa o4)< mkes sese.) that ate made (

Cel idependent evy cber e, dl te ponbilty eh Cnebas psi

E CCuNc) =k psbe p)- (ubsch pi

a4 seen abey4

Thstue any k 22, So ural answe,

E CCIN 22P

2. Saning ilheut Replacmenk

IU daua dagkaon sist PCx=1) 7N

X3 Px-2) P(X-3) 3 4

N N

x kam Cad te ot e ME ka X) X«2,-. X8_d Copde kam

dekotions E and vbt bat a kt ak.

Tdeas ha Lostea?

Synmekey sitat doesnt Aaly have it.

ina e epectain sens gosal, kt has

ndicala VoLatles ol chate Ttsa equente eent, so Can ok

dach e seaately.

Sa ad ien pe good ik 1

8 t Xkoa t be at least1 hen ne ind tata.

each bad en seee 7

ECI EDX] I+ BECX1 Dstatia oall idhobs the Same

k is deaug.a autae - 8 BGGBRB Cach X just a Queziay abast Aelabie side d twe ens, ch e lato h ihe in tHe dha Bsdocan lt mallea)

Fa FLX: consda bd iea B; ad k Ggocd ileak

veiogdDE all adehaA- ats P6juut pbe daraa j ht PR iArt) ELx. J

E 1B NL G CrAI

Not as eas Knot_iadepesnt -B

VasX) o no iae20k y valiame

OR (2X)

e ) E[E)*]- E[x-1 spltup

EC 1z E) +Z ED Hexents ak idetial, so

E -8E1E(-) ED

E _FX]-&Gt&o diat RU 0-0 nd )

EC he Sane heasaung s tli gt H2 spaces fa gol nd e 2 bd ies, whal PE, B, lo hid hn)2

G G2 bae G choida deasgeament

E ] 2 G+DG+1)

ElE B + 28(8-1) G)+)

Now, pu all togelhea

28(8-1) Cc+1) CC-D

X

G

asatplitl bu wde a mon denomuatz

VveX

CH) CG+2

=8Gw Ctl G+2),

3 Tack Makoy Baucd

i ad th ne H hes bok He dkn, ad it kooka kng tme

dnt tomuuh u pnd it kad.)

ECX/a Mako baund hguesal PCX 2a) /a Xzo X2o DescRe aasieR5

Nako general doesn't havre a hcos, so e kot piuk ona

&at depends n o s LA

e abowad t gtsid e E1, ht haw? ekov don

eea wak Jo oukX aa itk not honneantie.

Let's rabe RV at i ronegatie an haa sonehing td do ath

Fst atept XX E Vag X+E1 - va X =

Sne we s sbl dealia h be event X2a, e Natbou w kza2.

(2o onpliea Kzd Q x 2 )

Greod a but be question has a tihea baund.

endig X2X_ered tp nRk hel, et's sone he funetin Seud tbat estiea nonegpie

whod should

aybe )X*2 lds y t

PX2a) s E*

4 00atS ECX*LNo cda lalso no Sa e foal ansue

Cantgo b highe _pavels 4 hea_mese b do h ,Xx3R

e a haen t ued a geneial quedkad yet: mue ) Ax+ BX+C

A,BC. Sut Senemba x) 20 Se co't _e ay A, 8,C.

st aad to uie nonnegabinie Hu4

PX) CXt

Lsa ee poaretea e can val o gie le tightest_bnd

PX2d) =P(X= (+) sElx EC]+2cEC] +c (d+c)

PX2 +e (

Tha laks_dosex Hay do he pik te esi c

to Manue t S taka dotiahve (o+)

=o 2 -) >o_

Plug thiin to get

PX) (

PX) s to =

Pa)