Abraham de Moivre ( 1 667-1 754) . r b

Reverend Thomas eaves ( 1 702-1 761)

Joseph Lagrange (1 736-181 3) 8:

n J 4 diut r ~ u ~ r i ' u ~ ~ w u i n ~ w j n a i u ~ i ~ : ~ ~ u I u a ~ a ~ ~ m a a a w w d 18 do~iIu~ma3~wd 10 ~im 6lrnon 4~~fj~~~fnjnu~di~~d~~aidnic11 (1748-1827) I d i n ~ m i ~ t i ~ u ~ q 4 vi~wum rilunalwjnaiud~anilu~1.a"n'uw"a 7 l d

~~ii~~iluiio~lnw1nqwjna1u~i~:r.ilrur~ai:~~udau~d~"~1o~~^aada:41a"u r ~ i : , sir aqn1adu%?nd~:~1Wa:n~u6au "n-nuldr~duou" rflutiau'b~d~bu do~mv~iiaaiuui

viau nioomra1auiil1u~~uwi~'ba~~i~:~o~rdduw~u~i n?oni? jn~ur io :%dd~~a~ i i~n~u n ~ ~ o a ~ q G a A Pr'nfinwi~~onfuunoufia~mof ~wa~:niaii+~~r~uwdGuu ~ : $ a ~ ~ ~ ~ v i m u l 6

h u h nnio~rfi~rj,dni3~inuud~:?"111 l i n ~ n w ~ k ~ w ~ ~ ~ u n a ~ u ~ d ~ ~ d u o u ~ i ~ : ~ i ~ o ~ o u ~ i u

nfold

8: iiii rnqn~sni nu iu6~ uaWnniu (outcomesl n~pd I 3uhldmnni.rn3:ii -

Ba. B nisnnaoJ ~ d u nisnnao~luu~niuy i Ku ~ra:nsiu~ilun'ouo:~ilu~nqniamoPanu~ usriiiln'

r ia rio:b8u~n~ni3niiin~und~ n ~ o n i r n ~ i u ~ v i a i n i i f i i 1.u I;~MOUIRIRUIW$II ~ ~ i l u 6-d a rwqni-rzii~uwd~ sintlqnimm~du~d'b6M"~nue, 52 6% nisn~:~i~dol&i in~n~nia6 i iun i i

"7Wl"RQu (experiment) L L ~ E U ~ ~ F I ( I ~ U # J ~ U ~ ~ I ~ ~ I ~ M ~ ~ O J ~ ~ ~ ~ ~ I sample space Ldu ~ ~ ~ ~ Y ~ R R O J ~ U U L R ~ U ~ 1 sample space ;El

'ni3nEiul~ 1 l u a:!8sample space d~ 52 ad14 nis1uugn~diarJ sample space 6 ad13

t.~qn1~5$naiuO'Wa:~iUnji rnqni~d~~fiwai?~' (mutually exclusivei t.40

rnui=inLfin$u'!.6rk3ia~: I mqni3ni ku;o fii!o'ulnbicvdJbfin$Wbb6a ~ngnisddt.~~oa:!.d

ifin bdu inqni.rru"i699"a i~a:~nqni~mT6n"ou~~nnia1uu~n4~~~4u~ I n f ~ a:~ilu~n~ni3niC(

ldiwaiaun'w do ~dobn iuyn~ iu~8u~a~~62 iiouarlJJ1oniatAn iwrir luudu~nfa.~ua w .a n~owani.riiotuda:?a3 a:hmn 3 o d i ~ Go G, P, F LLR:$J 3 3uu ~ilu~n~ni~nid1aifiwaiau

a. B n"pd ~wai:~a"n~nwi~~d~:rkulJ~iuianorl6~nae,uinnii I .ace, msuu aswe, ~wonaaawouii A da.

aqn i~dn~u~u~uanwm: '"l.diiwaiauni" n9ob.i l o n isniuni~ot i i ingni3&~nhifu

aiui3n~n'slw~ounitk~~~d 2 ~ u $ u l ~ l i ' I n ~ 6inoui i l6 n u ~ u ~ ~ a i u i i ~ i l u ~ n g n i ~ d d

fi uaiaun'u (W!d mutually exclusive) 6-d a: d 8: ' . r i u d a u o ~ ~ n ~ n i ~ m n ~ ~ ~ ' b ~ l 6 M " ~ ~ u ~ a i n ~ i u ~ e , a o ~ n d ~ r:biunsiu.aouuiiG

$nwm: Collect~ve exhaustive L Y ~ ~ ~ I ~ ~ U W L ~ ? U Q I 3 1 ~ d 0 H LLQ: T L.?h.4 collective exhaust~ve

5.4 0Jnl3lLIdo Collective exhaust~ve. ~ O J ~ I S ~ U U ~ ~ L ~ I 2 qn

5.5 L~OMSUIY~UI 1 1~ aindi9u 52 1u t.nlni~dlo!dWd dlm6 6LWdwaia~ii'u"

d 2. dulYi"Uan~iu6e, ~m:iit.bms 4. ~i lu Ace ~ ~ a t ~ a u n

-

' ;

5.6 L ! ! O T . U U ~ ~ L ~ I 2 BnwiOUfiLwqn?S&d~md\ad~era5aun"u ~rnutual ly exclusive) d A'

I . ~ ~ M ~ J T I U L R T I 5 LLR: W B J ? U ~ & 5 8:

2. n~ 2 9 n ~ ~ ~ ~ ~ ~ i L L R : W ~ T ~ U T G ~ 7

3. $3 2 ~ ~ L ~ U L P Y j L L R L W A ~ ~ U I G Y B A a"

4. BnMUJTIULBV 2 L L R ~ W B S ~ U ? . & 9 d A'

5. ~ n n u J u w L a u 4 U B : W P ~ ~ ~ T X 1 0 a. d &

5.7 OJMI sample space ~ ~ ~ n a ~ ~ n - i a n ~ g n u d ~ 2 nu L L R : I , L ~ R 3 nu ( ~ ~ L L W ~ ~ I U L W R )

5.8 &~uu~nb& 2 gn o~win7iuriis:~8u~o:I6~6~fa~~b3~ I , 2, 5, 6, 7. lo, 1 1 0, w

5.9 n . PJMI " ~ ~ q n i 3 d " U O J ~ [ S U ~ ~ L ~ ~ O T - T R J

TI. ~ n q n i 3 d l u u ' o (n) d A ~ m k , ~ o l ~ e c t l v e exhaustive MU? n. ~vlqnisdlu% (n) rgu mutually exclusive MU? J. 8 1 ~ i d i n . i i u h l ~ q a b ~ u ~ ~ u ~ ~ ~ n a ~ ~ u d i u o : l h ~ i ~ ~ ~ i o : ~ ~ u n ' ~ l ~ ~ q n i a d u $ ~

(n) o d i ~ l a

3. n i ~ w ~ ~ a i u t i ~ ~ = L f l p d 3 55 I Lid

1 . 15flBlfVEfl (classical approach) 21- - A

2. % ~ & ~ ~ I % . J ~ ~ R U W ' Y I ~ (relative frequency approach) PdLi 8.-

3. lF9GlaRfJ (subiect~ve aowroach)

wuqu~wq ~ I T V E Z R ~ I ~ ~ ~ R

ii dm12 +t~ 618 1 ) mutually exclusive ~ u l u ? l d

I-I LLB': T ~:~fimw$aun"odIodn1~fuu~4u~

I w&'bail~ ~ : L ~ ~ A L ~ u s H V?Q T 6pdb

6U~urnd~l'iliu 2) equally likely Hu1f.I

? l ~ n a ~ u ~ ~ ~ ~ n ~ n ~ l ' i ~ ~ ~ u u n " u " u ~ ~ P,

~ ~ o ] n i s 6 f i d u % m Z u sample space dl ~ r a ~ ~ o a w u ~ u i i d ~ ~ ~ u ~ d a u ~ ~ ~ a q : ~ f i

5.11 6iVlZLlld 1 ~ i n d i f L I d $ 52 !U 0 9 9 1 1 ~ 7 7 % J d l ~ f 1 ~ ~ " 1 1 ~ 9

n. !&iu ({3) ~ . l r w " t r r a ~ (.s)

V. ~ ~ $ I ~ v ~ R I N K ~ (-25) 9. 16,pI~tXlnu IJ, Q, K I (g) n. rn#i!w#aa~ UR: Ace (h) a. 2bSf nisvina~udiortQur~~l~~lm? (uuu

n a i ~ 6 n ) d ~ o . 2

5.12 ~ ~ ~ n i s ~ i u ~ o ~ ~ C n ~ i u 225 nu ~ I Q ~ E ~ ~ G w H ~ ~ u ~ ~ u

21) goun-ii ao,ooo UIW 9) 12,000 - I c i , ~ ~ uin

5.13 ~ ~ ~ n l ~ d ~ ~ ~ l ~ ~ h i l ~ ~ ~ l ~ ~ ~ R 9 6 9 1 ~ 9 b ~ f ~ 9 ~ ~ b R 2 I 5 ( 7 ~ 7 ~ 200, 250, 300, d

350 ka: 400 r n s 0 ~ 6 ~ u ~ m s i d 7 u ~ h 6

"ailJt.t.dloii !dad6 300 uar 350 ~ld-~urviiifu~l?olJ adf6niiTonind~tuiu

16 350 Y I ~ ~ U LEJU 2 LY~IVQJ 400 vdau T o n i ~ d a t ~ i u 300 wiau IOU 4 rimo~ 200

P (A M ~ Q B) = P ( A ) + P(BI Oq pl

LL~:~!Uu~fulU~mUbbe~u6)1~ Venn gild {John Venn L B U ~ S L S U I $ )

P ( A M?O B ) = P(A) + P(B)

h F I $ i J @rnunq'~vdd:~l j 5 nu l o n 11 n d s 7 d ~ i n a i w d i ~ : ~ f l ~ d TI d o A ?z l%fub~an$d

P (11 w j o A) = P(Y) + P(A) 1 1 = 5 + 5 = i = 0 . 4

6 nJJfi~Flu (law of complement)

P(K) = P(not A ) = 1 - P(A)

u'u1rr

A 11Pt. B ~rl i l jwai2ufi~id0 P (AB) = 0

s i n h o u ' i r r l u n a i u r i i o r r f l u d II a r l d i u d a n $ d ~ o .

nqn~ss?~hus'uac1ni~d~f iw~r !au~u 81 A LLR: B ~ i l u b ~ ~ n ~ ~ s ; d d G ~ ~ a ' a ~ ~ n " u (not mutually exclusive) na~uri~~z~fiuuor

r ~ q n ~ s n i A ~ 4 0 B 6~

f i f l h s ~ I H & J ' ~ w 1 a l l ~anltTn"8:'6~ Ace Hf~'bWbbfl9 50

fimuii~:tduuuuijh~uIu 61 A LLR: B LaubwBlni~tid!dLfl~~~atfi"pd n 2 1 ~ ~ 1 l t ~ i l p d 1 1 0 ~ ~ y n i x i i B L u n ~ i u

* a Y ;I A T w ~ n w ~ o a

P(BA) P(BIA) = P(A)

n a w q m ~ U $ Q 81 A LbRt B VbJba~E613~5pd

P(BA) = P(A) P(BIA) ' d l

~ a t i i n m ii p l a n ) I i ~ ~ v i i i ~ u p i s ) . pin] i w u o u 5 u n s G . d 'A LLsr B ~ ~ v G a ~ r 5 o a

nioti1.r qna~ii? 60 Qn P t R ~ i d m i T i d n i ~ ~ l n L L l d j 2 U < u ~ ~ i J d

Zvi A f l o p n a i i ? l h , - A = gn~~ i i ? i r~u~

B "nogn!~ii?JUnaid 8 = gnr~ i i? !gd id l~

A A

- - v

PC- 6

%

3n-

In-

e,

e,

te

2

e5) I)

zk .

ST

s

e 3'

c!

c!

5.29 ~ ~ m n i a ~ i u ^ ~ u ~ i i ~ ~ ~ ~ n d ~ ~ v ~ i ~ i ~ ~ ~ i i V ~ d ~ L ~ ~ d ~ i ~ i ! ~ d i n ~ l LLREI+'~UIPIUNIW L ~ U 2 hwuin 1riiwRiil~u6iuod~"ui"uiu'b~~mRd hulonin 2 lu l o aoiiii@,Jmr

aimBuh ~: i i~$~ iuau~iu~ol$~d6au 'bonin 5 lu l o ~ ~ ~ : i i i $ ~ i ~ l d j v ~ ~ w m i ~ E ~

2 ~IWUIYI ~:iilK4iuau~iu~m~~&auloni~ 7 1% 10 ~ i ~ : 6 i ~ ~ d . & ~ m r n i ~~s:l+'Gu

Iwamiriiw 2 hwvin Iomadiiuauuile~:6~~6~~~~u 8 1u 10 iiiLViL&d$LLid$uii Y

b n i n 60% ~TIL~~JUIWW~IL~~U 2 ~ i v q i n ~~s:i;bn(lnl~ 30% d ~ : ~ ~ ~ l u ~ i m i i n ~ i v o ~

LVI aa:nuqFil$d-~lwunnr~s:~ifi~~D'~bgna:n'u ~ ~ ~ i n a i u l i i ~ : ~ S u " u n ~

n) i iuZi iuo~duidi iainlXini i ~r~r l$~~uIwumv, f iu 2 Aiuvin (918)

U) ~ U ~ V O J ~ L L ~ J i j ~ i n i d i n i i ~ i o l i Y ~ ~ u I ~ 1 ~ m ~ u i n n 4 1 2 [iiu ~~d)Ldld 2 a d i d

w f o u h kufo 8 ~ a i n i i i n d i qe1a~miAin+ii 2 n"iu ~rciiiiiainilJ61niii1:

I o l ¶ ? 4 N l ~ d ' (.54)

n) a i n i u o ~ ~ ~ ~ d ~ l i d i n i i ~ 4 o I u r t n r ~ ~ r i ~ ~ (-28)

7. M(IY ~UIIPLUIIC A d u i n n n w n ~ h q l r a~\ruaai ryn i~nf im~inmi 4 a Thomas Bayes (1 702-1 761 )

a4a a' ~ ~ u ~ ~ ~ a ~ a i ~ ~ u ~ i u ~ a i u d i ~ t ~ D u ~ ~ ~ l ~ n " ~ ~ o u l ~ ~ o ~ ~ n ~ n i a d d ~ ~ i l u ~ n ~ : : n i r i i o

d r- nqu~uo~luuR'i~rinman-~i~ 7 i io m ~ l i l l h a ~ i ~ s u ~ u ~ ~ u 8 5 7 ~ a " v d ~ d n a i d i ~ ~ i ~ i ' b a "

rioru~k n a i u r i i r r ~ ~ u ~ d i u d ~ ~ ~ n d ~ u ~ ~ u n i i n~~a~rii4r~flunBjnmao.l w i n postenor-

probability

R i o r i l ~ nuyR+i dan~6idldnuqsljO~ 2 ai(m 2i7uiiuau~Yii 7 nic ~d~~ ign ih#dnum

IRinrjo~ ido~~iuui~uuMsiu 7 n?d w ~ r n s n m ~ o ~ u o r ~ n ~ 6 i a ~ m ~ ~ ~ n i ~ r i i ~ d t a n u 40% It: d d It: It:

uorndnun Riau~rii~utuotatmn 2 ndiu 70% ~ o ~ i i u a u n a ~ n ~ ~ ~ m ZUW~ PIA = .4. A d a..a

P(AJ = .7, A = M~~IMUJM~Q A C ~ KIYI~U~~LUU[~U 1 ~~LLK-JGIU w~nlmno~riiilll6dgn oLnnnSiv 2 41 1onind~:L8u~n~dia~mwd I ~rii!~? j%pnu ~ s i o i o ~ & d 6 ~ w a i ~ ~ a i ~ a i v ~ i ~ u ~ d o ~ ~ ~ n

It: d d U P ~6-183 2 rirnidit-7~ &uu ~ o n i ~ n o : ~ i l u a ~ a r i a n ~ i a t ~ ~ u ? L L ~ A I ~ B U W L L M ~ ~ J ~~J~~BISNI

~ 7 n m i ~ i ~ ciiok~d

ad a A' do16 1 MUYURI elementary event go $odd 2 PIE,) ~ i l u n m u d i ~ t ~ i l u dtniui3nnil6douni3nnaoc n3da la'nimirLuu

naia'm 'lo d;n~h~wdu~ 2 aSn 6 ~ u i i u ~ u ~ r i i 5 u k$u P I E ~ I = PIE*) = 1 L L R ~ - 8: m q n - ~ ~ d " s ~ ~ l r i d e ~ a i a u n " u LLR: 2 O i ( 3 2 u n i ~ B u n ~ ~ w ~ n m ~ ~ ~ KJUU W B T ~ U V O ~

~ O J ~ ~ Q P L ~ ~ U M ~ J L R ~ J Q

$odd 3 ~on2iuiiclt~iluuufl~d~oa!*u ii ii i r~ua~m~d~TonisdrX Ace = .4 hilwa$m d Y naod Toniadorl6 A c e \= 0.7 W R ~ ~ U V Q J ~ O J U otI.riI,ti~itd

$odd 4 ~ Q ~ ? I U ~ ~ O ~ ~ ~ U ~ ~ B J ~ " ~ " U Q ~ ~ ~ ~ ~ ~ P ~ S ~ " I Ace ~~at~Bugn~6iaGncii~ 7 dd!a'nnguWB

d 16 Ace u19;j~13minaiu0di~:~iludouni~~m~o %dkYdiaJB?9fi80 n a i u i i ~ t ~ ~ u ~ ~ y ~ l

PIA E ) P(A2/E) = - a -636

P(E) ' .5%' d w wda~~nniiwa3?uuoddo4~&0db~u~6d w n ~ ~ ~ n ? i u i i ? r ~ i l u " ~ o ~ b ~ ~ n 1 ~ 6 M " d ~ u n

d 1nstflu4!iu 81w~rnrn~nsmm~iu~'~n"~u4d A C ~ L n i ~ n ~ n i l u q n ~ i i ~ ~ n n ~ ~ u ~ ~ ~ IY

BJUU ~ ~ T i : ~ n ~ 6 i ~ ~ ~ ~ L ~ n d ? ~ A i u $ a & ~ n j l Y A d lfi E ~owania'buul~nuioun'bdld Ace

..

i

B n ~ d l g ~ ~ # 1 = A ,

Hn~6irGnd 2 - P(A,IE) .30/.45 = .67

.15/.45 - .33 7

! 1 .OO

p ( n i )

.5

.6 - I .o

m~di~rl7u posterior p robab~ l~ ty ~ d ~ ~ X d l ? ~ l ~ l d ~ ~ ~ l l ~ ~

Nuy ~ i i ~ a u u ~ L i n p n L ~ ~ ~ d ~ ~ n n ? J ua:wai;on$i Ace gn a~~i~onlado:if lu~ntdi ~~da:.nbm

n'ou'ou&~~in~iudi~:~~r~u~~lds'J~ul"u~ou

Ifl E ?IO ~ I T M ~ Y ~ U R G I M ~ J 2 nfJ

P ( 2 AcelA, ) = (.4) (.4) = .16

PI2 Ace/A21 = (.7) (.7) = .A9

P(CIA,)

.6

.3

P(EilE) 80 PiA, IE) = 3x = .246

245 P(A21EI = r5 = 2 1 .OOO

E.

A 7

~ ( n , n i ) .5 x .6 = .30

.5 x .3 = .15 - P(EI .45

.P(E.)

b5

.5

1 .O

oinwclnisLu 2 $3 d ~ ~ f l ~ ~ e i ~ ~ u i n ~ u i i ~ ~ u n ~ ~ n d 2 (.754 L ~ ~ U U ~ U L R U .50)

fiiwani3Iou 3 n f ~ ~ i l u E E E , F ~ O ~ ~ ~ 3 I~JI~ Ace % d i ~ d ~ ~ f l a i ~ ~ i U : b ~ u ! ~ u

diwoc~tiu2nir ~ n u n ~ s m n ~ i u 6 n ~ w u 2 ~ ~ ~ d a u ! " u r i o u

P(EIE,

.16

.49

.b

~ ( E E ~ I A , ) = A x A x A E

P ( E E ~ ~ A ~ ) = .7 x .7 x .3 =

P(E-flE)

.5 x ,I6 = .080

;5 x .49, = ,245 - ,325

I

ST 206 45

I

f

I

~ ~ ~ Y ~ B M ~ A I I U ~ ~ S Z L ~ ~ M V ~ ~ M ~ W ~ ~ U ~ ~ ~ ~ I ~ ~ ~ ~ ~ ~ # ~ ~ & ~

M ( tree diagram) ~~inn?msu?nJi~ubdu "

d d 014

5.33 I~LSOJM~JUMUJRQGUWI 2 a& l o A LLR: B 20% uocriirinciuqsRo~r~~~wvrui

luasJu A En 10% ~ o s 6 i C n ~ i u ~ u u ~ ~ l w w m i l u B LLa: 70% " ~ o ~ 6 i ~ n d i u d ~ u u a d 8: ws 2 a4J'uwYourYu ~inds:~unis& wu41 75% U Q ~ ~ ~ ' W . ~ I ~ U A a4J'u~ftua 0tYb6iimou

d uinn41 I $u 65% ~ o d 6 w w m i ~ a d l u ~ ~ u B ~ 4 J ' ~ b ~ ~ a P E V b 6 ~ 7 ~ 0 ~ ~ i n n ~ i I $u LLP:

d It: 90% U O J ~ ~ W N I Y I P J ~ J 2 acu ~:!66imouuinn-h 1 o'w ~ i ~ i ~ n i i u ~ ~ d ! 6 f l d ' b w w m i

d It: a~:!MFiimou~EiutKu~?iua PJMIR~IU JIP:L~~~~LUIJ::R,IIOIW~IYIJ 2 a& (.45)

iinwninuo.suywo' (.oo~, .0025, .0014) W d 2 .

U) - a a l n n a i u ~ i - a c r i 3 ~ 1 1 0 ~ n i a r f i ~ . r ~ ~ a a ~ ~ ~ (.0022) d d w Y

5.35 aui%nC~uaiacluaunau

,tdiwrwnaiu mq 30 s t u ~ d 5 20% 4 d y'diwrwnaiu o iqh in i i 30 11 u 40%

d 4 ~ ~ i w t a ~ ~ n a i q d i n i i 30 11 u 70%

n) -a~ '~~ i rdo f t~~dl i~ul%ndbf lpbvi~ . (-60)

Y) naiudi-atri3u~~:rium 1 T'IU t in:r i l~aiuoi~hini i 30 o (-67) n w c B w

5.36 1yOri~uu~v~1clua-aiA~7n5 12 nu wrinaiuviu 25 nu ~d.r :ni~un:~wvm~ i 8 d d*

nu rinirn.ri:vi 5 nu Iu.r:~11~1) uaqan.r 3 nu, ~ r i n i n ~ i u ~ i u 5 nu, (dxn in 6 Y

nu rrscinirn.ri:d 2 nu 'b6~uniardou~u ii7rjuwrinaiunduuui 1 nu d.ringiniilu(

1.~uni.rt8outus:nii.sg

-aa*in2iuliirtai3wdwrinaiuZ~-atrilu n I 3 Y r i n d I n) wrinaiuviu (32) J) 3nan.r (.is)

I

X n) elu-a:mn 00% voaaaiau5'uu

9; d , X V) 4u~:an 00% " u o ~ w u ~ w u i n s 6 ~ 1 n ~ ~ a u u

3 zit: n) - a i no% 51 Knwmrgiioi ni~13ut..d.~u -azfiil%4unn 00% u o ~ i i w ~ u n ~ ~ n ~ ~ u m

5.39 R ~ ~ ~ i l l g n ~ f l ~ ~ i b C l n l ~ ~ ~ l n ' ~ 6 ~ ~ b f i ~ ~ ~ ~ ~ d b l ~ a " ~ ~ ~ J ~ d ~ l ~ B

~ J ~ i ~ ~ i ~ d i ~ ~ t ~ O a 6 b ~ n ~ ~ M ~ J ~ : b ~ ~

n) -5iG~n1a (J)

TI) ~u6~~6u i~~au tTnw3 s c $ )

n) ~ r n i i ~ i u y n i i ~ ~ n i (3) J) naiurii-a:~Bulut (n)-(n) tBun21uri1~-~d~%~~1bm~?<lm? (UUURRIR~R)

A' B 5.40 [ i i ~ n ~ i u a 0 ~ 1 u d f i u ~ ~ ~ 4 ~ ~ u ~ 1 < ~ ~ : u i m ~ i n i ~ i u G i u u o ~ u i u i i ~ i ~ ~ i ~ i n i ~ ~ ~ u ~ n

0diJGo~ 15% - f l l U l ~ a 6 ~6ouGi~~Gi6ae~na iud i~ :~~u .60 d 2 ~ ~ l ~ V ~ J ~ l ~ b b R J 6 ' i l ' Z ~

bomn .80 6~ :11 iu~u3 in i~~n i i~ f iu 15% 1u 6 L~'~IW$IJMGI ~ ~ ~ ~ ~ I U Y I ~ L ~ ~ U ~ ~ ~ I V O J 3 d A' ~iCnaiuOa ~ ~ a z i i C n ~ ~ ~ % < d ~ : u i m n i ~ i i uiuviaibonin .70 n~:aoGiuuo~uiu

d 2 41 b b ~ ~ ~ ~ ~ n l ~ .3 ~91~%0~1Oa~ble~bb~J 6 l d 0 ~ ~ l g f l 6 b & ~ b ui8n 6 b&W 3 7 ~ ? ~ 1 ~ 6 ~ i U A' wa' d

ui~ao~nuwaintfiu I 5% -a~~ ina iur i i -a :~~~nuiu~ ia~~4os~" iu"uo~ (n) u i u i i (.64)

(V) UlUbbRJ (.36)

lcd w u ru 5.41 w ~ n n J i u 6 G l n i 3 1 d ~ ~ ~ d n u ~ ~ ~ WU~I R ~ L M ~ A J 7 ~ O ~ M U I U ~ U ~ J ~ ~ U ~ O

I. %dia~nvYo~6

2 . 1 d i i d o ~ u o ~ ~ d ~ ~ m ~ u i u

3.1dd4onuu

4. Wm~asm~i%d~w6duin~fiu%d A 6 W 5.W~ma~m371d~wauuoer~fiu1d

3 n) niraq#d 5. oliitu rUu " ~ n ~ n i s n i " lun~iurruiuuo~nqw~naiudi~:~~u~9?o1d? d 6 6 A

u) gn37uni.I "1diwaiaurYu" ~501J n?o is iun is laGi tn uwai2unicV

5.42 t.Viqni36do1d<~l:~i~6 6 b ~ d i ~ ~ i a u r Y ~ " \

n) ~ G s n a a i n ~ ~ n u i u ~ o RGIT. nminjuifuijoiI(3:n j1~ 18-49

1) I ~ ~ J ~ R L ~ O L ~ U ~ J ~ J I P ~ ~ ~ ' ~ M J I M ~ V ~ ~ , ~ I ~ I Y ~ J ~ I J ~ ' R ~ ~ ~ ~ w A ~ ~ ~ ~ I ~ w ~ ~ P ~ u

ni-iGimu

n) -a:dou~ul~wCn~iugn~u~ -a:~n~.u~~aw~:~~inu~bw' i i fu ~~d1r i i in i3~8owh

48 ST 206

d an n~nmni~1Rn$u?~vlquuwid~aad%~danow6 bbazanu33qmi l u .so7 uar .863 miu

i16u k n) o ~ ~ i n ~ i u r i i ~ r ~ i l u u ~ ~ n i ~ ~ i i a q ~ l ? ~ ~ q w ~ 2 wiialu~~~~t.fulu~~da~a"u ( 2 0 )

Y) ~ ~ ~ i n ~ i u r i i ~ ~ ~ i l u ~ ~ ~ n i ~ ~ i i a ~ ~ ) 3 ~ ~ ~ # ~ 2 ~ ~ S I U U ~ I J I I ~ ~ J ~ U U ~ ~ (.34) %:

n) ~ ~ ~ i n ~ i u ~ i o ~ ~ i l ~ d ~ ~ ' b d ~ i i ~ ~ u ~ ~ ~ ~ w ~ ~ l u w i ~ ~ ~ a ~ ~ ~ a : I u ~ i i o ~ l u ~ ~ d n u (.44)

5.44 ~ ~ ? ~ l f l l R 1 ~ ~ W 1 ~ ~ 1 ~ d Y Q d ' b 3 d d l ~ 6 ~ d d 6 0 15, 12. 18. 16, 11 LLRL 19 H ~ ? U ~ D w w

hu (pprn) ii7np~ui~Tii~ua~id7uim~~5~01r1'b~~~iu6~~!~i~4w'bd~n^u 18 1 .442~

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5.45 1~nl3ddLb~E1R0~~lBJWld'bd~~~ejs~~J~~~~ndl0d~ddL0~b2~lHRlU~3d8L32~~?~~R~~~b6 -

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52% Y O ~ ~ I U ~ O J ' b l ~ d ~ g l ~ d ' b i "

n) d i ~ d o i 4 u 6 ~ o ~ ~ n q n i a 6 d i ~ 7 ~ i l u n ~ ~ u r i i o : ~ i l u ~ ~ u u ~ ~ i ~ ~ n , nm&hw'nf d a POI

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1

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d d II: o ~ n i n a i u i ~ ~ : ~ i l w n n u n w ~ o : ~ u ~ ~ ~ ~ ~ a ~ u ~ ~ a : i ; ~ ~ i (.0031)

(Y) 81 50% ~ o d n a ~ u f l i a d d ~ 0 ~ a ~ ~ a ~ w ' ~ - ~ ~ d o , ~ ~ a u n ' ~ ~ o d ~ i o 9 ~ d d daiu~&uimdiu II:

n a i 3 na:d 95% ~ ~ ~ n a ~ u n i a l u $ ~ ~ u u 40-~~d-gnotij~un'u OJVIIA~I~J~IL~~U A d~~nnunu~o.-aisin~aoun~ad~'o-~~do~6au~u~~~:~a+~u'b~a:~u~ipbnai (.475)

(n) 81 30% "~1d~nfin~iaiu61b~~d~~upa'nfinwinm:~~~1ina L L ~ : 10% s r o d c n ~ n w i I

d A n m : ~ ~ ~ i ~ r i o i k o ~ n o w ' n ~ $ i u ~ i ^ a ~ u i $ u o~n~naiurii~:~ilu~~iununu~o:

~ ~ u l i n f i n w i n t u : G A ~ 1 i a ~ a " ~ ~ ~ ~ o ~ ~ o w ' n ~ 9 a " i u ~ i 3 ~ u i K ~ (-03)

w d n o r 5.55 u ? l j n n ~ ~ w ~ j i 72% ~0~ji~mnuawn(i~w~n~iu"~1iu\d~mdo~to1na~uou"~7e1~W~~tuk

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anasuau~ iuGu6 i~o~u5~n (. 1 44) d

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~ Q ~ W ~ I ~ ~ I ? R I ~ ~ L ! ~ L ~ ~ L ~ ~ ~ ~ M ~ Q ! ~ ?

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n"9 (n) LLR: (TI) 4 > (.60)

5.68 n a i u ~ i o : r f l u d w r ~ n ~ i ~ ~ i u a n ~ ~ 4 ~ ~ ~ : ~ i u a n I v 1 Fdnd m' o, I, 2.3.4 ua: 5

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ST 206 :-; 53

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(n) ~ G L L ~ J R ~ q nit 3 an (.027)

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(3) 1K Ace 3 %U k h % % d " o 2 %Y (f35

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d LB3R (125)

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ddn c3

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ui?io1dzn 15 S buauyfti i ni~ua~muurn~uo~ni i~~a:na~~i~~uEw~:n'u (.595)

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n?iudi~lotb~uuodmnnisdio\ad6

% I (n) ~3u$iu9l'aoeiis$oer 2 FITJ (.648)

ST: 206

(n) a ~ ~ i ~ o n i ~ d ~ r f l r n w ~ ~ ~ ~ 1 1 ~ ~ n i a b f i w ~ $ i u b ~ u a

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(n) LWR U P ~ ~ R ~ I U ~ I Y I R U ~ ~ ~ ~ U ~ U ~ L ~ ' M H " ~ Q ' ~ ~ ? LWSI:LII(I~?

(Y) PJHI P(MIF), P(MIF') I (-60)

(n) P J H ~ P(FIM), P(FIM') UR (-70)

(4) WHI P(M'IFO, P(M 'IF) L (-40)

(P) PJHI P(F'IM), P(F'IM'I L (030) I

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(n) ~ ~ a r w u i i ~ u d ? u u u ~ i ~ n o ~ a i n ~ i u r i i a : ~ ~ u d o r ~ i n A (-40) W i d w

(u) ~ ~ ~ : ~ u i i ~ i l u i i u ~ i w ~ n u i ~ a ~ i u ~ r l a i ~ ~ i u r i i a : ~ ~ u n d a : ~ ~ ~ ~ i n c (8145)

5.92 n ~ i ~ G i ~ l a . ~ i l f i ~ ~ ~ i ~ o : " u ~ u i i ~ ~ u u ~ n K n ~ ~ ~ 206 = 0.75 hmo~i~~uuflnKm ~uoa:; '

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5.93 o i n h 5.92 i i iqui l iaovIi i iu a ~ n i n ~ i u ~ i a : ~ ~ u d a ~ o ' b i u e ~ ' u ~ i ~ ~ u u ~ n ~ n (34)

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d d 20% LLBLWSI~~I dCninl$uuw~~u6iniaGiuo~ 60% iiCna?uu~u~u~a~uciiu?ai~ni

d a ~ ~ i n ~ i u ~ i a : a ~ u ~ ~ ~ ~ i a : ~ i n i a G i u T ~ u ~ d i ~ a u ~ ., . (617)

5.95 L ~ J , ii LLRSYI? Li/uw~n~iu~lu~bbps"~~doii 1ua~d~r~uu1Ja: jnL$ 20 $2 '

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