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X8 E$D 0H  0޽h ? <#sO|Z'  (  .   A}  ?pppy2 ?Hv '<<P]pP8  $D 0   Lpppy2 ?Hv '<<P]vPy,$D 0 v(2) sv'Y\vcq_TisvR^ s'Y f~s^fW s\ f~a\ 0 ck`R^_Ny:Nؚe(Gauss)R^<( 2    3   3   >.`  c $A|  ??0P   H  0޽h ? 3333f*'  R(  P  Hxpppy2 ?@,$D 0 r4.hQck`R^(p38) Spem0 s21vck`R^y:NhQck`R^ \OX~N(0, 1)0 x, xccccc     c g3c$     ZA~  ?pppy2 ?08  $D 0H  0޽h ? ' TH ,$(    c $A  ??n8  $D0  H`pppy2 ?`  ,$D 0 nR^Qpeh:y:N2( 2ca   c $A ?? {:8 $D 0:  N4pppy2 ?pH,$D 0 vQ[^Qpeh:y:NJ  xcg3c H  0޽h ? 3333fT'  s|(    B( 1?i,$D 0 N,vis~YeyfNGWD ghQck`R^hOgF(x)v3}v#  &# 6 @ 8 B ck`R^h@ !0!0 8 0  V ck`R^h 2 H 8 0޽h ? &&:5(ffJff ' TH    (    6T&&,$D 0 :(p67)14 Ny5uP[CQNvO(u[}T8\e gNck`R^.(100,152),gNhV Nň g3*NُyCQN N*NCQN_cOWN&T/fvNrzv.BlO(uvgR90\eQeNCQN_cOWvis.F\x# + 5# T6  0,,$D 0 ,:Y:NO(uvgR90\eQ_cOWvCQNpe,. 2# $   c $Ay  ??P p@ 8  $D 0   0p2 p,$D 0 DEe 2    c $A  ?? 8  $D 0   6x6,$D 0 HRY~B(3,p) 2 #    B;`  ,$D 0 LvQ-N 2#    B ck`R^hp@ !0!0  0>P V ck`R^h 2 H  0޽h ? <#sO|B '  X(     pppy2 ?Hv '<<P]`P,$D 0 zN0yceW:gSϑQpevR^_&( 2g  c $( ; Pp`<$D 0     6  b ,$D 0 > (p55) XN*N:gSϑ R^_:N X^P{Xxk}pk, k1, 2, & yg(x)/fNCQUSO4 X~U(0,1),BlY=ax+bvis[^.(a`"0) 2 # < T ( BTO,$D0 &: Y=ax+bsQNx%NUS,SQpe:N6" #  " . ( c $A ??08 $D0 ( 0@ G,$D0 4Ee 2 ( c $A ?? l 8 $D0 ( 0\ @ G ,$D0 4  2 ( c $A ??` M 8 $D0  ( 0 pP ,$D0 4Ee 2  ( c $A "??` 8 "$D 0H ( 0޽h ? &&:5(ffJff '  @8(  ~  s * ;P     3 rgֳgֳA  ? ?=Ev8  $D 0`  c $A ??p` `  c $A ??@8 `  c $A ?? p H  0޽h ? *'  pR(    Npppy2 ?P@Z  t`N8( 2gcV  H pppy2 ?,$D 0 N0kXzz 1.:gSϑX gNSpe:N2,p vNyR^ :gSϑY gNSpe3,p vNyR^ RP{Ye"1}= X\}Zl +   ZA ?pppy2 ?0@Dn8 $D 0H  0޽h ? 33 ,2(  , , Hpppy2 ? 0A,$D 0 Nt2.:gSϑX gN0 2 NvGWSR^ R:gSϑY=X2(W0 4 Qv[^Qpe:N fY(y)= d;   RH , 0޽h ? &&:5(ffJff D<0(  0 0 HT%pppy2 ?,$D 0 N3.:gSϑX~N2 2 NP2<X<4 =0.3 RP(X<0)=L(  2  H 0 0޽h ? &&:5(ffJff RJ(    600[ DN.Ng'Yf[0Rkpfz-N g6*NN\,GP(WT*NN\/f&TG0R~opvNrz,v^NG0R~opvis/f1/3.NYh:y}lf(W,{N!k\PbkKNMR@bǏvN\pe,BlYvR^_.(GP[}lfS(WG0R~opb0Rkpfze\Pbk)ii#66H  0޽h ? &&:5(ffJff'  @8(    H:pppy2 ?Pq,$D 0 v N0g\Kb[v\Q USS}T-Nis:N0.6 sNTbN*NGWSvP[ TbQQp1\[vrz\QQS BlNp`}Y}T-N$NSvis0@<( 2c9c;H  0޽h ? 33 $Z(  $ $  xEpppy2 ?Hv '<<P] V.]w:gSϑXvis[^:N2( 2cc8` $ c $A ??@. " $ B4J`  BlY=1-X2vis[^F 2ckc,H $ 0޽h ? &&:5(ffJff^    ( x     c $dT;P    22.6 N~:gSϑvTTR^ N0 Y~:gSϑT!# !# ! t   ^pppy2 ?Hv '<<P] ,$D 0 \z1.[IN(p41)\n*N:gSϑX1 X2 ...,XngbN*Nn~Tϑ (X1,X2,...,Xn)y:N n~:gSϑ0.6( 2 c a# + # + # + # + # + # + #      ppppy2 ?Hv '<<P]``,$D 0 N~:gSϑX  R1 Nv:gpPWh N~:gSϑ(X,Y)  R2 Nv:gpPWh n~:gSϑ(X1,X2,& ,Xn)   Rn Nv:gpPWh Y~:gSϑvxvzel_NNN~{|H  0޽h ? &&:5(3q33 LD  D(  D D  Cpppy2 ?Hv '<<P] ,$0 ,O2.]wN~:gSϑ(X,Y)vR^Qpe:N$# . D  A ?pppy2 ?Hv '<<P]->8 $0, D 0H@@p,$0 <1)Bl8^peA B C0 2)BlP{0<X<2,0<Y<3}i"  D 0L  @ F: 2  D c $A ?? 8 $D 0  D c $A ??G 8 $D 0  D c $A ??P  8 $D 0  D c $A ??  8 $D 0  D c $A ?? p8 $D 0H D 0޽h ? &&:5(ffJff TH 0 (    6V P0 h N.TTR^_ " #  0|\ 00,$D 0 ~(P42)傌N~:gSϑ(X, Y)SSYSR*N  1?P  p  U... 2A  $ HB  1?P z @  U... 2A  $ HE  1?P P @  U... 2AjB  $ BD1?PpB  $ HD1?@ jB  $ BD1? $ 0I  P,$D 0 ZTTR^_v'`( (1) pij 0 , i, j1, 2, &  (2)vF       6 3 $ c $A ?? 58 $D 0D $ <T @08   x1 x2 xi 0 P2CKCKK$2CK $ <<^ ^Pd ,N~yceW:gSϑvR^__NSRhh:yY N:    $ 0(d P0  3P43 2Z $ B:޽h @ ? ̙33K TH   @(s (  ( (  pppy2 ?Hv '<<P]4 FO3.(P43)-N g$NS~t NS}vt s N>eVxdtN!k N$$#  (  A ?pppy2 ?Hv '<<P]P `   ( <P` ^ l,Bl(X,Y)vR^_0 B ( s *D  ,$D 0B ( s *D pp,$D 0B  ( s *D p ,$D 0  ( 0d   ,$D 0 5X 2"   ( 0 p ,$D 0 5Y 2"   ( 6X0  ,$D 0 P 1 0 2 "    ( 0tP 00 ,$D 0 S 1 0 2"   ( c $A ?? 0rp8 $D  0 ( c $A ??  p8 $D  0 ( c $A ??pB8 $D  0 ( c $A ??p 8 $D 0 ( c $A ?? 0W8 $D 0 ( c $A ??P  8 $D  0 ( c $A ?? P  8 $D  0 ( c $A ??} ~48 $D 0H ( 0޽h ? 3333f   P\<( x \ \ c $Y} 2 "   H c $A ??0 l8 $D  0B  H s *D@  ,$D 0B  H s *D`0`,$D 0B  H s *D `,$D  0B  H s *D  ,$D  0B H@ s *D `0 ,$D  0 H RW?G[SO Px,$D  0H H 0޽h ? &&:5(3q33\  TH   p d (  d d B 1? O ,$D 0 4Bl(1)8^peA(2) F(1,1) (3) (X, Y)=(W N҉b_:SWDx0, y0, 2X+3y6 Qvis0  2)c   c   c   c BCR B d c $A ??`8 $D 0 d B ' dO4. (CC B  d s *D ,$D 0B  d s *D 0 ,$D 0B  d s *D  ,$D 0B  d s *D  ,$D  0 d 0d P ,$D 0 p(1)1uR_N'`2 2"  "   dP c $A ?? C 8 $D 0 d c $A ??pp8 $D 0 d c $A ?? `m8 $D  0H d 0޽h ? <#sO| bZL(  L L # A ?pppy2 ?. `ZZS`TS`TZ 08 $D 0 L 6<[,$D 0 fr(3) (X, Y)=(W N҉b_:SWDx0, y0, 2X+3y6 Qvis0: 2c   c   c   c ># L BP,$D 0 F"   L c $A ??P@8 $D 0 L c $A ??1_ 8 $D 0 L c $A ??p `J 8 $D 0H L 0޽h ? &&:5(3q33  TH pp(  p p Bܿ 1?PP ,$D 0  3. $N*N8^(uvN~ޏ~WR^ (1)N~GWSR^(p45) 傌N~:gSϑ(X, Y)v[^Qpe:N Ry(X, Y)(W:SWD N(Q) gNGWSR^0 & 20 <2( 2A ;CCv    p c $A ??w(8 $D0 p c $A ??  >8 $D0 p 0 P ,$D 0 Ff X Y (W:SWD N(Q) gNGWSR^ [DQNa:SWG g $0 s2$Cl H p 0޽h ? <#sO|Z  t(  tj t  P pppy2 ?Hv '<<P] ,$D 0 RO5.(X,Y) gNYV:SWD NvGWSR^ (1)Bl(X,Y)vis[^ (2)BlP{Y<2X}  (3)BlF(0.5,0.5)8-D# c n   . t  A ?pppy2 ?Hv '<<P] 8 $D 0:  t 3 A ?pppy2 ?Hv '<<P] `  8 $D 0 t <A ?? 8 $D 0 t c $A ??pT8 $D0 t c $A ??@8 < 8 $D0 t c $A ?? J l8 $D0H t 0޽h ? 3333f   x6(  x x B 1?@@ ,$ 0 vQ-N m10m2:N[pe s1>00s2>00| r |<1 Ry(X, Y) gNSpe:Nm1, m2, s1, s2, rv N~ck`R^ S:N ^ xC    C  C  C C          CAA6! x s *A: )??A&8 )$D 0 x BA$ ??PW 8 $D 0~ x Bh2 1?,$ 0 |(2)N~ck`R^N(m1, m2, s1, s2, r) 傌N~:gSϑ(X, Y)v[^Qpe:N(P101)? 2 C         CACA6  x c $A! ??P8 $D 0H x 0޽h ? <#sO|  TH f ^ | (  | |  Kpppy2 ?Hv '<<P]Pr,$D 0 LR^Qpevi_Sc^0Rn~:gSϑv`b_0 N[ N [n~:gSϑ(X1, X2, & , Xn) F(x1, x2, & , xn)P(X1 x1, X2 x2, & , Xn xn) y:Nvn~:gSϑ(X1, X2, & , Xn)vR^Qpe b:gSϑX1, X2, & , XnvTTR^Qpe0j( 2#GOGOGOGOGOGOGO GOGO GOGO GO GOGOGOGOGOGOGC     | ZA% ?pppy2 ?` P 8 $D 0 | ZA& ?pppy2 ?@0 8 $D 0 | Nhpppy2 ?PA1 ,$D0 ^[IN2.4.6. n~:gSϑ(X1,X2,...Xn) YgX[(W^vnCQQpef(x1,x2,...xn)O[Nav nCQzeSO.C '/'/'/'/'/'/ '%   H | 0޽h ?    (   (    Hpppy2 ?Px ,$D 0 d[IN2.4.7. (X1,X2,...Xn)vhQSS '/'/'/ '/'/'/'/'/'/'/'/'/'/'/'/'/ '/'/'/ '     h  Hpppy2 ?&4,$D 0 zRy(X1,X2,...Xn):Nn~ޏ~W:gSϑ yf(x1,x2,...xn):N(X1,X2,...Xn)vis[^0>'/'/'/'/'/'/'/'/'/'    H  0޽h ? 3333f  q i P (  Pv P  pppy2 ?Hv '<<P]@,$D 0 XFBl1 P{X0},(2)P{X1},(3)P{Y y0} $( 2ccc  c  c ckc P c $A' ??`8 $D 0@ P Nľpppy2 ?P,$D 0 $EX::gSϑX Y vis[^:N"( 2c$B P 0D p ,$D 0B P 0D`` ,$D 0 P <L2 y ,$D 0 3x"  P <j ,$D 0 3y" B  P s *D`P ,$D 0  P < ,$D  0 3D" 2  P 0pP ,$D  0 T{: P{X0}=0R 2" c c B P 6DpP ,$D  0 P c $A ??P 8 $D  0 P c $A ?? 6 8 $D 0B P 6D  ,$D  0B P 6D  ,$D 0H P 0޽h ? &&:5(3q330     \X (  \F \ B  1?p f ,$D 0 FY(y)F (+, y) P{Yy} y:NN~:gSϑ(X, Y)sQNYvR^Qpe. I0 2CKC C CCAT. \ c $A* ??P 8 $D0 \ c $A+ ??p0 8 $D0d \ c $; @<$D 0   42.7.R^Nrz'` N0R^Qpe(p46)X $Bg '  \ <PW,$D 0 ZFX(x)F (x, +) P{Xx}x. 2CK C C CV \ <Py,$D 0 2y:NN~:gSϑ(X, Y)sQNXvR^Qpe 2CB J \ 0 p,$D 0 <R^[E N/fؚ~:gSϑvg*N (gN)NO~RϑvR^0@ 2CGCH \ 0޽h ? <#sO|4 TH `\(  ` ` Hpppy2 ?P $O1.]w(X,Y)vR^Qpe:N $ 2  ` ZA^ ?pppy2 ?B   ` Npppy2 ?W  BlFX(x)NFY(y)0X    ` ZA. ?pppy2 ? `8 $D 0 ` 0 ` @!0!0H ` 0޽h ? 3333f   ~vd(  d d s *X@;<$D 0    d B 1?PP8 ,$D 0 2傏:gSϑXNYvTTR^_:N (p47) (X, Y)^ P{Xxi, Y yj,} pij i, j1, 2, & Ry P{Xxi}pi. i1, 2, & :N(X, Y)sQNXvR^_ -x6!$   %   $3 d c $A ??0 $8 $D0 d c $AZ ?? P 8 $D0 d < Pk,$D 0 ~P{Y yj}p.j j1, 2, & :N(X, Y)sQNYvR^_0 R^_6q_NnR^_v'`(0f%,   ET!Z d B:޽h @ ? ̙33      hB (  h h Npppy2 ?{/W O2.]w(X,Y)vR^_:N x\y 1 0 1 1/10 3/10 0 3/10 3/10 BlX0YvR^_0 "IHF, h H| pppy2 ? ,$D0 l x\y 1 0 pi. 1 1/10 3/10 0 3/10 3/10 p.j d3n2n .  Y h ZA[ ?pppy2 ?p0  h ZA[ ?pppy2 ? 0`   h ZA\ ?pppy2 ?@   h ZA\ ?pppy2 ? p   h N*pppy2 ?` p,$D0 rEesQNXTYvR^_R+R:N X 1 0 Y 1 0 P 2/5 3/5 P 2/5 3/5:n:< )  h 0 P@ @!0!0  h B+p  ,$0 52/5  h BH3`  ,$0 53/5  h B6 p ,$0 52/5 h BX: r ,$0 53/5H h 0޽h ? 3333f   TH   p (  p p s */;` <$D 0   n p B 1? 7 ,$D 0 0:N(X, Y)sQNYv[^Qpe0 , 2CAH p c $A ??P4@8 $D0 p c $A] ??7p 8 $D0 p <80pMw,$D 0 D^(X, Y)^f (x, y), (x, y)R2, Ry (p48) 0 2C CK*Cc  C> R p 000 ,$D 0 <:N(X, Y)sQNXv[^Qpe Tt y 2C@R p 0< ,$D 0 fwN(m1, m2, s12, s22, r)v[^QpefX(x)/fN(m1, s12)v[^Qpe fX(x)/fN(m2, s22)v[^Qpe EeN~ck`R^vR^_N/fck`R^0H` C            CKC      CKC     CGC  H p 0޽h ? <#sO|     t (  t> t NApppy2 ?4 ,$0 O3.(X,Y)vis[^:N"( 2c( t c $A_ ??`@P 8 $0\ t H4Gpppy2 ?0w,$0 ,1 Bl8^pec;(2)BlsQNXvis[^"( 2c> t ZA` $?pppy2 ?@K8 $D 0  t 0 MPW ,$D 0 :(1)1uR_N'`8 2"  "    t c $A ?? [ 8 $D 0  t c $A ?? 0 8 $D 0 t c $A ??@ ^ 8 $D 0B t 6D00,$D 0 t c $A ?? 4 8 $D 0B t 6D,$D 0B t 6DP`,$D  0 t c $A ?? 8 $D  0 t 0 @p @!0!0H t 0޽h ? 3333f   =(  8   Zpppy2 ?Hv '<<P]@@ ,$D 0 R(X,Y) gNYV:SWD NvGWSR^ BlsQNXvTsQNYvis[^ F*x# cd .   A ?pppy2 ?Hv '<<P]@`8 $D 0  0aP`,$D0 7x=y 2  0e ,$D0 8x=-y 2  c $A ?? P 8 $D 0  c $A ?? `8 $D 0   d WfjJ?EXNSeLwiR,$D 0H  0޽h ? &&:5(3q33  *"0x(  x x s *n; <$D 0   jV0:gSϑvvNrz'` "   x  upppy2 ?Hv '<<P] ,$D 0 [IN2.4.1 y:gSϑXNYrz Yg[Na[pea<b,c<d g(p49) p{a<Xb,c<Yd}=p{a<Xb}p{c<Yd} sSNN{a<Xb}NNN{c<Yd}rz Ry:gSϑXNYrz0z # ' #  #  #  #  #   #  #   2  x  pppy2 ?Hv '<<P] A,$D 0 [t2.4.2:gSϑXNYrzvEQR_agN/f(p49) F(x,y)=FX(x)FY(y) . #  ' #    c4  3H x 0޽h ? ԥ<#sO|~ TH  |(  || |  pppy2 ?Hv '<<P] ,$D 0 jF[t2.4.3.(p50) (X,Y)/fN~ޏ~W:gSϑ XNYrzvEQR_agN/ff(x,y)=fX(x)fY(y) [t2.4.4. (p50)(X,Y)/fN~yceW:gSϑ vQR^_:NPi,j=P{X=xi,Y=yj},i,j=1,2,... 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