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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 (