{VERSION 3 0 "IBM INTEL NT" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 
0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "
" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 }{CSTYLE "" -1 256 "" 0 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 
0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 259 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 1 18 0 
0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 1 0 0 0 0 0 
0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 263 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 1 18 0 0 0 0 0 0 0 0 0 0 
0 0 0 }{CSTYLE "" -1 266 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 267 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 
0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 
0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Ou
tput" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 
-1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 
-1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }
{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }
3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "
" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {SECT 1 {PARA 3 "" 0 "" {TEXT -1 43 "Probability Distribution \+
Function and Shape" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
256 "" 0 "" {TEXT 260 21 "The Beta Distribution" }{TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 17 "A \+
random variable" }{TEXT 261 2 " X" }{TEXT -1 12 " has a Beta(" }
{XPPEDIT 18 0 "alpha,beta;" "6$%&alphaG%%betaG" }{TEXT -1 68 ") distri
bution if its probability density function (PDF) is given by" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 18 "               \+
   " }{XPPEDIT 18 0 "Gamma(alpha+beta)*x^(alpha-1)*(1-x)^(beta-1)/(Gam
ma(alpha)*Gamma(beta));" "6#**-%&GammaG6#,&%&alphaG\"\"\"%%betaGF)F))%
\"xG,&F(F)\"\"\"!\"\"F)),&\"\"\"F)F,F/,&F*F)\"\"\"F/F)*&-F%6#F(F)-F%6#
F*F)F/" }{TEXT -1 5 " for " }{TEXT 262 1 " " }{TEXT -1 10 "0 < x < 1 \+
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 263 1 "f" }{TEXT -1 2 "( " }
{TEXT 264 1 "x" }{TEXT -1 5 " ) = " }}{PARA 0 "" 0 "" {TEXT -1 60 "   \+
                               0                elsewhere" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 6 "where " }{XPPEDIT 
18 0 "alpha,beta;" "6$%&alphaG%%betaG" }{TEXT -1 70 " > 0.  The follow
ing code will draw the density function for the Beta(" }{XPPEDIT 18 0 
"2,3;" "6$\"\"#\"\"$" }{TEXT -1 62 ") distribution, but you are encour
aged to try other values of " }{XPPEDIT 18 0 "alpha" "6#%&alphaG" }
{TEXT -1 5 " and " }{XPPEDIT 18 0 "beta" "6#%%betaG" }{TEXT -1 1 "." }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots
):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "f:=(alpha,beta,x)->GA
MMA(alpha+beta)/(GAMMA(alpha)*GAMMA(beta))*x^(alpha-1)*(1-x)^(beta-1);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6%%&alphaG%%betaG%\"xG6\"6$
%)operatorG%&arrowGF**&*(-%&GAMMAG6#,&9$\"\"\"9%F5F5)9&,&F4F5!\"\"F5F5
),&F5F5F8F:,&F6F5F:F5F5\"\"\"*&-F16#F4\"\"\"-F16#F6\"\"\"!\"\"F*F*F*" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "alpha:=2; beta:=3;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&alphaG\"\"#" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%betaG\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 29 "plot(f(alpha,beta,x),x=0..1);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 
300 300 {PLOTDATA 2 "6%-%'CURVESG6$7X7$\"\"!F(7$$\"1LLL3x&)*3\"!#<$\"1
'fTojx%z7!#;7$$\"1nmm;arz@F,$\"1sk(yTtG]#F/7$$\"1++D\"y%*z7$F,$\"10#fI
&>WANF/7$$\"1LL$e9ui2%F,$\"1\\Z*H[s3]%F/7$$\"1++voMrU^F,$\"1i+k\\v$Gb&
F/7$$\"1nmm\"z_\"4iF,$\"1*e+dnBWb'F/7$$\"1nmmm6m#G(F,$\"1RgG1>l7vF/7$$
\"1mmmT&phN)F,$\"197u*p1;U)F/7$$\"1++v=ddC%*F,$\"1JASs;?y#*F/7$$\"1LLe
*=)H\\5F/$\"1f#*\\&3v(35!#:7$$\"1nm\"z/3uC\"F/$\"15V=@_tY6Fgn7$$\"1++D
J$RDX\"F/$\"1Ti:9VXt7Fgn7$$\"1nm\"zR'ok;F/$\"1Crb[!)*yQ\"Fgn7$$\"1++D1
J:w=F/$\"1Xy.0K%e[\"Fgn7$$\"1LLL3En$4#F/$\"1$ef\">g]q:Fgn7$$\"1nm;/RE&
G#F/$\"1GN$z\")[@j\"Fgn7$$\"1+++D.&4]#F/$\"1ewm(o8xo\"Fgn7$$\"1+++vB_<
FF/$\"1fFDW'o%H<Fgn7$$\"1+++v'Hi#HF/$\"1[l6B,3d<Fgn7$$\"1nm\"z*ev:JF/$
\"1sbp$Qt>x\"Fgn7$$\"1LLL347TLF/$\"11j)e]qxx\"Fgn7$$\"1LLLLY.KNF/$\"1m
D(\\0MJx\"Fgn7$$\"1++D\"o7Tv$F/$\"1@@)4;Duv\"Fgn7$$\"1LLL$Q*o]RF/$\"1V
!\\C'e'[t\"Fgn7$$\"1++D\"=lj;%F/$\"1mglS;W,<Fgn7$$\"1++vV&R<P%F/$\"1u=
b(o>=m\"Fgn7$$\"1LL$e9Ege%F/$\"1\"GA6OeIh\"Fgn7$$\"1LLeR\"3Gy%F/$\"1J
\\euU?i:Fgn7$$\"1nm;/T1&*\\F/$\"1(*G_0$z9]\"Fgn7$$\"1mm\"zRQb@&F/$\"1p
)f7BrEV\"Fgn7$$\"1***\\(=>Y2aF/$\"1BU*))p6'o8Fgn7$$\"1mm;zXu9cF/$\"18<
]'z*o&H\"Fgn7$$\"1+++]y))GeF/$\"1zQ5SU%p@\"Fgn7$$\"1****\\i_QQgF/$\"1o
Thv`AP6Fgn7$$\"1***\\7y%3TiF/$\"1LGmmm>e5Fgn7$$\"1****\\P![hY'F/$\"1LD
\"z\"f***o*F/7$$\"1LLL$Qx$omF/$\"10I#G-Y?)))F/7$$\"1+++v.I%)oF/$\"1Gq;
F5f>!)F/7$$\"1mm\"zpe*zqF/$\"1DQM3@>WsF/7$$\"1+++D\\'QH(F/$\"1U[=\\Hq4
kF/7$$\"1KLe9S8&\\(F/$\"1=3$[`aKk&F/7$$\"1***\\i?=bq(F/$\"11(p7s>!o[F/
7$$\"1LLL3s?6zF/$\"1e8%*pT/UTF/7$$\"1++DJXaE\")F/$\"1X#3Y.SFU$F/7$$\"1
nmmm*RRL)F/$\"1npg)4efx#F/7$$\"1mm;a<.Y&)F/$\"1`#z\"*f\")z;#F/7$$\"1LL
e9tOc()F/$\"1\\@q3^8D;F/7$$\"1+++]Qk\\*)F/$\"1!QCjCT[=\"F/7$$\"1LL$3dg
6<*F/$\"1t.XJuUgvF,7$$\"1mmmmxGp$*F/$\"1.O!p$)*\\sWF,7$$\"1++D\"oK0e*F
/$\"1#=XIAmG-#F,7$$\"1++v=5s#y*F/$\"1')3w)QD@a&!#=7$$\"\"\"F(F(-%'COLO
URG6&%$RGBG$\"#5!\"\"F(F(-%+AXESLABELSG6$Q\"x6\"%!G-%%VIEWG6$;F(F\\\\l
%(DEFAULTG" 1 2 0 1 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 }}}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 77 "The Beta distribution can
 take on a variety of shapes.  To see the effect of " }{XPPEDIT 18 0 "
alpha;" "6#%&alphaG" }{TEXT -1 26 " on the shape of the Beta(" }
{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT -1 1 "," }{XPPEDIT 18 0 "be
ta;" "6#%%betaG" }{TEXT -1 92 ") distribution, the following animation
 will draw a series of probability density curves as " }{XPPEDIT 18 0 
"alpha;" "6#%&alphaG" }{TEXT -1 58 " varies from 0.1 to 2 by increment
s of 0.1, while holding " }{XPPEDIT 18 0 "beta;" "6#%%betaG" }{TEXT 
-1 16 " constant at 3. " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "alpha[0]:=0.1; alpha_step:=0
.1; beta:=3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&alphaG6#\"\"!$\"\"
\"!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+alpha_stepG$\"\"\"!\"\"
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%betaG\"\"$" }}}{EXCHG {PARA 13 
"" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "for
 n from 0 to 19 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "  density[n]:
=plot(f(alpha[0]+n*alpha_step,beta,x),x=0..1):" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 52 "  num:=convert(evalf(alpha[0]+n*alpha_step),string):
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "  tracker[n]:=textplot([0.8,1,`
alpha is `.num],color=blue):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "  P
[n]:=display(\{density[n],tracker[n]\}):" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 3 "od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "display([seq
(P[n], n=0..19)], insequence=true, title=\"Varying Alpha While Beta is
 Fixed at 3\");" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 13 "" 
1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6$-%(ANIMATEG667&-%%TEXTG6%7$$
\"\")!\"\"$\"\"\"\"\"!%,alpha~is~.1G-%'COLOURG6&%$RGBGF0F0$\"*++++\"!
\")-%'CURVESG6$7en7$$\"1+++;arz@!#<$\"1MN%)R\"Q%eM!#:7$$\"1+++e_y;CF@$
\"1-K1&o-j8$FC7$$\"1+++*4bQl#F@$\"1^I-jk**oGFC7$$\"1+++T\\#4*GF@$\"1g<
\"=3MMk#FC7$$\"1+++\"y%*z7$F@$\"1PZX(>7/X#FC7$$\"1+++kW8-OF@$\"1nG^\"=
Tq8#FC7$$\"1+++XTFwSF@$\"1]HErA?$*=FC7$$\"1+++3Q\\4YF@$\"1n`F%=<hn\"FC
7$$\"1+++pMrU^F@$\"143,X?$>]\"FC7$$\"1+++JJ$fn&F@$\"18K&Hq=*e8FC7$$\"1
+++\"z_\"4iF@$\"1qdm4CHR7FC7$$\"1+++m6m#G(F@$\"12Dt8E;\\5FC7$$\"1+++S&
phN)F@$\"1Qd.0#\\p0*!#;7$$\"1+++*=)H\\5Fjp$\"1q/=8PhQqFjp7$$\"1+++[!3u
C\"Fjp$\"1j0yLRLgdFjp7$$\"1+++J$RDX\"Fjp$\"1Kc<p:1!z%Fjp7$$\"1+++)R'ok
;Fjp$\"1,(=]\"HFHSFjp7$$\"1+++1J:w=Fjp$\"1\"oE9/xoV$Fjp7$$\"1+++3En$4#
Fjp$\"19%GU>k#\\HFjp7$$\"1+++/RE&G#Fjp$\"1!z#o-KE&f#Fjp7$$\"1+++D.&4]#
Fjp$\"1LJ-zk*4E#Fjp7$$\"1+++vB_<FFjp$\"1=KT^1sy>Fjp7$$\"1+++v'Hi#HFjp$
\"1=1Gb<lY<Fjp7$$\"1+++(*ev:JFjp$\"1l_ROBYj:Fjp7$$\"1+++347TLFjp$\"1`@
S#QmOP\"Fjp7$$\"1+++LY.KNFjp$\"1#R3'\\k!GB\"Fjp7$$\"1+++\"o7Tv$Fjp$\"1
4BmvC@)3\"Fjp7$$\"1+++$Q*o]RFjp$\"1!yOu^I'\\(*F@7$$\"1+++\"=lj;%Fjp$\"
1,E+#e&GV')F@7$$\"1+++V&R<P%Fjp$\"16<02wW/xF@7$$\"1+++Xh-'e%Fjp$\"1?I9
g(Q%GoF@7$$\"1+++R\"3Gy%Fjp$\"1^h(R(px0hF@7$$\"1+++.T1&*\\Fjp$\"1:r.s.
r.aF@7$$\"1+++(RQb@&Fjp$\"1Apr3\"R)\\ZF@7$$\"1,++=>Y2aFjp$\"1(e6:AljB%
F@7$$\"1+++yXu9cFjp$\"1PDC7R+MPF@7$$\"1+++\\y))GeFjp$\"1t\">!R*=jE$F@7
$$\"1+++i_QQgFjp$\"1\\IQhvGaGF@7$$\"1+++!y%3TiFjp$\"102Nz%RW\\#F@7$$\"
1+++O![hY'Fjp$\"1f?*pL!\\N@F@7$$\"1+++#Qx$omFjp$\"1KOGAf=Y=F@7$$\"1+++
u.I%)oFjp$\"1LBx.p)*o:F@7$$\"1*****ppe*zqFjp$\"1aG%e$GzV8F@7$$\"1+++C
\\'QH(Fjp$\"1xIHd(=O7\"F@7$$\"1+++8S8&\\(Fjp$\"1$=\"3[u(RR*!#=7$$\"1++
+0#=bq(Fjp$\"1&*f^ijG)o(F[[l7$$\"1*****p?27\"zFjp$\"1*)z![#pMAiF[[l7$$
\"1,++IXaE\")Fjp$\"12'fuO**f)[F[[l7$$\"1+++l*RRL)Fjp$\"1t*QjBVux$F[[l7
$$\"1+++`<.Y&)Fjp$\"1\")f$o#Gd7GF[[l7$$\"1+++8tOc()Fjp$\"1//R#>VJ,#F[[
l7$$\"1+++\\Qk\\*)Fjp$\"1Vbbo&)339F[[l7$$\"1+++p0;r\"*Fjp$\"1_Ll3*3rd)
!#>7$$\"1*****\\w(Gp$*Fjp$\"1X!*=SX,s[Fd]l7$$\"1+++!oK0e*Fjp$\"1#p4'4O
;7@Fd]l7$$\"1+++<5s#y*Fjp$\"13BQj3lhb!#?7$F.F0-F36&F5$\"#5F-F0F0-%+AXE
SLABELSG6$Q\"x6\"%!G-%%VIEWG6$;F0F.%(DEFAULTG7&-F:6$7fn7$F>$\"18ph08!>
R&FC7$FE$\"1:B$oE=/%\\FC7$FJ$\"1\\c(R3O=c%FC7$FO$\"1***3=f*HRUFC7$FT$
\"1^;*ecV3'RFC7$FY$\"1,_2w)3M]$FC7$Fhn$\"19&)p9IGUJFC7$F]o$\"1*fH1b#Q;
GFC7$Fbo$\"1$3W8$eZ^DFC7$Fgo$\"14W-METJBFC7$F\\p$\"1idQ8SNX@FC7$Fap$\"
1Lc%4y8a%=FC7$Ffp$\"1sZ#4F>^h\"FC7$$\"1+++:ddC%*F@$\"1c^Siy*GV\"FC7$F
\\q$\"1jnpb.5%G\"FC7$Faq$\"1s\\!4LG#p5FC7$Ffq$\"1Jro!=tw-*Fjp7$F[r$\"1
.>)QDq!)p(Fjp7$F`r$\"1%G!*=0s_k'Fjp7$Fer$\"1bxQ%*3OldFjp7$Fjr$\"1R?X$=
hz6&Fjp7$F_s$\"1zX9'Hp\"*\\%Fjp7$Fds$\"1\\'4H#QIqRFjp7$Fis$\"18iB/hoIN
Fjp7$F^t$\"1g2[oDG!=$Fjp7$Fct$\"1>b!)e[z8GFjp7$Fht$\"1mV6C6LRDFjp7$F]u
$\"16r61o?bAFjp7$Fbu$\"1FaWby%3.#Fjp7$Fgu$\"1sa!Q^\"**4=Fjp7$F\\v$\"1+
YG)=r6i\"Fjp7$Fav$\"1QsYMMtV9Fjp7$Ffv$\"1x`NwlP'H\"Fjp7$F[w$\"1i\\donI
_6Fjp7$F`w$\"1vlTirD<5Fjp7$Few$\"1ewO=#Gd5*F@7$Fjw$\"1!z%R8->c!)F@7$F_
x$\"1X*\\QExN2(F@7$Fdx$\"1ZlYxB9.iF@7$Fix$\"1tS,QL-RaF@7$F^y$\"1\"y/I]
uGn%F@7$Fcy$\"1(Qj&>&zA0%F@7$Fhy$\"1FyLcW$[X$F@7$F]z$\"13Cc\\=FnHF@7$F
bz$\"1p)H]b%\\)[#F@7$Fgz$\"17Rkg&oh3#F@7$F][l$\"1!oX$e+67<F@7$Fb[l$\"1
Z)R#*39$*Q\"F@7$Fg[l$\"1#)4[x0(Q4\"F@7$F\\\\l$\"1Bg3tZAy%)F[[l7$Fa\\l$
\"1\"4)>#=?&GjF[[l7$Ff\\l$\"1xy.%zk2a%F[[l7$F[]l$\"1P)o\"*fpH=$F[[l7$F
`]l$\"1&yZ*oGfV>F[[l7$Ff]l$\"1_v5+?P16F[[l7$F[^l$\"1hVM[(er![Fd]l7$F`^
l$\"1wbFt\\Wo7Fd]lFe^lFf^l-F(6%F*%,alpha~is~.2GF2Fj^lF`_l7&-F(6%F*%,al
pha~is~.3GF2-F:6$7fn7$F>$\"1&pf4c\"*zC'FC7$FE$\"1Y9J`lB%y&FC7$FJ$\"1G/
W$)e?\"R&FC7$FO$\"1dZ`)f\"3`]FC7$FT$\"1;aa6+`eZFC7$FY$\"1%)3C'Q&zoUFC7
$Fhn$\"1E/jISTwQFC7$F]o$\"1'Q(*p@\\t^$FC7$Fbo$\"1z\"QR;#e@KFC7$Fgo$\"1
kE4wu!H(HFC7$F\\p$\"1%zp+?G.w#FC7$Fap$\"1a<Y&fxDT#FC7$Ffp$\"1!*pl/'R29
#FC7$Fabl$\"1^tXLg?A>FC7$F\\q$\"1Pdnq[>T<FC7$Faq$\"1$\\DnUG^Z\"FC7$Ffq
$\"1!=;pT#ek7FC7$F[r$\"1;_K#eMJ4\"FC7$F`r$\"18(4lP%))\\&*Fjp7$Fer$\"1U
9G$ecnP)Fjp7$Fjr$\"1))zj,y^,vFjp7$F_s$\"1Z7#*fWGamFjp7$Fds$\"1jS?X:1@f
Fjp7$Fis$\"1!y#4`!\\XI&Fjp7$F^t$\"14nU'Qy\"3[Fjp7$Fct$\"1\\KUb$3RG%Fjp
7$Fht$\"1M<pi!*e()QFjp7$F]u$\"1E'Q:_EPZ$Fjp7$Fbu$\"1c%Q1d\\T9$Fjp7$Fgu
$\"1%4!*RKbr\"GFjp7$F\\v$\"1A'4*3qVNDFjp7$Fav$\"1![DXHj(oAFjp7$Ffv$\"1
!)Hf(evd/#Fjp7$F[w$\"1))\\4`iLE=Fjp7$F`w$\"1Hw@3(p#>;Fjp7$Few$\"1Uz\\E
qpa9Fjp7$Fjw$\"1[7R(>x=H\"Fjp7$F_x$\"1z(zyqg&Q6Fjp7$Fdx$\"1j2-6w)>+\"F
jp7$Fix$\"1HDs!odY\"))F@7$F^y$\"175\")z\")))*f(F@7$Fcy$\"1$HS'=+*3h'F@
7$Fhy$\"1=O.@v?acF@7$F]z$\"1:*\\%3v))p[F@7$Fbz$\"1kUD^FH'4%F@7$Fgz$\"1
f-UprQVMF@7$F][l$\"1nv$Qv2Q$GF@7$Fb[l$\"1uBLShf0BF@7$Fg[l$\"1d))H)*H=?
=F@7$F\\\\l$\"1ya#ygAVT\"F@7$Fa\\l$\"1Gmtr!p$e5F@7$Ff\\l$\"1uG)ehqBh(F
[[l7$F[]l$\"1o`\\MgvZ`F[[l7$F`]l$\"1!ong.aMF$F[[l7$Ff]l$\"1,6P,*pt'=F[
[l7$F[^l$\"1T!pa<'yJ\")Fd]l7$F`^l$\"1&e@?W'=]@Fd]lFe^lFf^lFj^lF`_l7&-F
:6$7Z7$F>$\"1(*o2KsQ&Q'FC7$FE$\"1-#\\2>#ysfFC7$FJ$\"1$y%3$Hx#>cFC7$FO$
\"1%pkM02@J&FC7$FT$\"1.3\\h%R?/&FC7$FY$\"1\"zh,L;ue%FC7$Fhn$\"1-yG?*zv
@%FC7$Fbo$\"1M%yFwFve$FC7$F\\p$\"1Ox1/ONKJFC7$Fap$\"1<nk&yV<y#FC7$Ffp$
\"1>M\"e[%[-DFC7$Fabl$\"1<R(4XAUF#FC7$F\\q$\"1=!Qh#QI#3#FC7$Faq$\"1\"p
>Kl))[z\"FC7$Ffq$\"1a#*)GN3Bc\"FC7$F[r$\"1U[!\\KK!p8FC7$F`r$\"1rF8[zS5
7FC7$Fer$\"1;J-y'HM2\"FC7$Fjr$\"1FP\"pjssp*Fjp7$F_s$\"1](H;Sz*z')Fjp7$
Fds$\"1\"z^z-gzy(Fjp7$Fis$\"140DB,))GqFjp7$F^t$\"1\"*\\kw^E6kFjp7$Fct$
\"1nBl]'HAv&Fjp7$Fht$\"1j\\xI$e\"\\_Fjp7$F]u$\"1p;h0[.>ZFjp7$Fbu$\"1LR
y[B;$H%Fjp7$Fgu$\"1eY-z2<nQFjp7$F\\v$\"1f1_;rB(\\$Fjp7$Fav$\"11X-(f8W9
$Fjp7$Ffv$\"15^M[#*HZGFjp7$F[w$\"1K*QjDYHb#Fjp7$F`w$\"1-U&yq&HtAFjp7$F
ew$\"1Z01g`k\\?Fjp7$Fjw$\"1ju4/Z4F=Fjp7$F_x$\"1&))fic)H;;Fjp7$Fdx$\"10
&=Z;^uU\"Fjp7$Fix$\"1w$f$3k!*f7Fjp7$F^y$\"1HgNb28!4\"Fjp7$Fcy$\"13X#*H
G$>^*F@7$Fhy$\"1atbxyRh\")F@7$F]z$\"1Bb_u8-\\qF@7$Fbz$\"1yIov.%p%fF@7$
Fgz$\"1(QZ#3uo7]F@7$F][l$\"1k8[(3Kn8%F@7$Fb[l$\"1`z,<\"QXP$F@7$Fg[l$\"
1fh@/tBrEF@7$F\\\\l$\"1D4]Xz%33#F@7$Fa\\l$\"1q\"=)[H1h:F@7$Ff\\l$\"1'3
D#p``D6F@7$F[]l$\"1Te*=%\\ECzF[[l7$F`]l$\"1$))4P'RXi[F[[l7$Ff]l$\"1dDA
NMwzFF[[l7$F[^l$\"1vb_c\")>87F[[l7$F`^l$\"1')G*4f9Y@$Fd]lFe^lFf^l-F(6%
F*%,alpha~is~.4GF2Fj^lF`_l7&-F(6%F*%,alpha~is~.5GF2-F:6$7Y7$F>$\"1p+#
\\Hgh2'FC7$FE$\"1%H'y9'>Du&FC7$FJ$\"1jH\\%eNMX&FC7$FO$\"1A^#=vI'*>&FC7
$FT$\"19MP\"*GLu\\FC7$FY$\"1)o]OKU,f%FC7$Fhn$\"1x;NeVfsUFC7$Fbo$\"1t;
\"4ft(>PFC7$F\\p$\"1b&Hx!Rg4LFC7$Fap$\"1_n\\B6S')HFC7$Ffp$\"1$QZw8$zBF
FC7$F\\q$\"1()4M\\Ul=BFC7$Faq$\"1$3rQ<#[L?FC7$Ffq$\"1dk***\\Qrz\"FC7$F
[r$\"1uTLwlU'f\"FC7$F`r$\"1@*p!y`VG9FC7$Fer$\"1TEENiv!G\"FC7$Fjr$\"1)R
T&4**>n6FC7$F_s$\"1+Dw'))>U0\"FC7$Fds$\"1Xbj4ioP&*Fjp7$Fis$\"1d\"zLC%*
>n)Fjp7$F^t$\"1#*)zOs)zfzFjp7$Fct$\"1/PW9<j\">(Fjp7$Fht$\"1Ae;tPC*f'Fj
p7$F]u$\"1&*zK'ef!pfFjp7$Fbu$\"10?y!Hk\"eaFjp7$Fgu$\"1&*[73yxU\\Fjp7$F
\\v$\"1fD7T9^\"\\%Fjp7$Fav$\"1[$f#G.vdSFjp7$Ffv$\"1(QP3)\\!)*o$Fjp7$F[
w$\"1IX?%)3vALFjp7$F`w$\"1S)4k*GerHFjp7$Few$\"1xdqvN$*)o#Fjp7$Fjw$\"1+
'p_V-gS#Fjp7$F_x$\"1m%Q8*zRO@Fjp7$Fdx$\"1`iz`lX$*=Fjp7$Fix$\"1D5x1Auw;
Fjp7$F^y$\"1=<NRc%fX\"Fjp7$Fcy$\"1!R3GE.VF\"Fjp7$Fhy$\"1O**fuL'o4\"Fjp
7$F]z$\"19\"paED-]*F@7$Fbz$\"1NCE1D!)Q!)F@7$Fgz$\"1xEiy9R%z'F@7$F][l$
\"1ARd45jAcF@7$Fb[l$\"1BbAY'e()f%F@7$Fg[l$\"1*y$f^D5]OF@7$F\\\\l$\"1[J
@=;a]GF@7$Fa\\l$\"16:%e3sQ9#F@7$Ff\\l$\"17#yu,2&\\:F@7$F[]l$\"1+)GNe0L
4\"F@7$F`]l$\"1]%\\MT=^s'F[[l7$Ff]l$\"1G\"QgyNG&QF[[l7$F[^l$\"1'3;')\\
#G&o\"F[[l7$F`^l$\"1kgl6N$[Z%Fd]lFe^lFf^lFj^lF`_l7&-F:6$7W7$F>$\"1QaPE
57<bFC7$FJ$\"1pMQ6W6]]FC7$FT$\"19/m,3z#o%FC7$FY$\"1Z\"Q-gNDQ%FC7$Fhn$
\"1)f)Hlq5ITFC7$Fbo$\"1i=#ejk-o$FC7$F\\p$\"1ZXN6:uOLFC7$Fap$\"1x8qz')G
fIFC7$Ffp$\"1h;(3k.*GGFC7$F\\q$\"1Lvs>VfjCFC7$Faq$\"1T5:9xG)>#FC7$Ffq$
\"1SLjCPfs>FC7$F[r$\"1)[d*ovLw<FC7$F`r$\"1l7J7e`3;FC7$Fer$\"1\"y$oQ[9e
9FC7$Fjr$\"1V'HyWZ0M\"FC7$F_s$\"1Q`k<vv@7FC7$Fds$\"1[H$3^gX6\"FC7$Fis$
\"1.+)eLB4-\"FC7$F^t$\"1'HC=%QyH%*Fjp7$Fct$\"1'4YMEg%z&)Fjp7$Fht$\"1%=
_c@Bm\"zFjp7$F]u$\"17pqMaV/sFjp7$Fbu$\"1mc%*pC^@mFjp7$Fgu$\"176H#RM#Gg
Fjp7$F\\v$\"1w#H0C*G/bFjp7$Fav$\"1lPfKNd'*\\Fjp7$Ffv$\"1]LSTviiXFjp7$F
[w$\"1!zPG$oiETFjp7$F`w$\"1sv3()\\Z1PFjp7$Few$\"1+t$pzmgO$Fjp7$Fjw$\"1
`'3%Q#QK-$Fjp7$F_x$\"1>&)Q2j`%p#Fjp7$Fdx$\"1)emKStlR#Fjp7$Fix$\"1)))H#
=RHH@Fjp7$F^y$\"11#e%RhYb=Fjp7$Fcy$\"18!R]))))*G;Fjp7$Fhy$\"1\"G-YJOmS
\"Fjp7$F]z$\"11g3'>W<A\"Fjp7$Fbz$\"13N.PY)o.\"Fjp7$Fgz$\"1#z]w1Jwy)F@7
$F][l$\"1b`gicF#H(F@7$Fb[l$\"18>lQm4!)fF@7$Fg[l$\"1p]*o\"\\DfZF@7$F\\
\\l$\"1A$4d^5hs$F@7$Fa\\l$\"1,bWsEV4GF@7$Ff\\l$\"18O698\\N?F@7$F[]l$\"
1`*eA\"oMR9F@7$F`]l$\"16BA(z``())F[[l7$Ff]l$\"1^M1t)*e&4&F[[l7$F[^l$\"
1\"Q%zH]&QB#F[[l7$F`^l$\"1UiQhp#Q%fFd]lFe^lFf^l-F(6%F*%,alpha~is~.6GF2
Fj^lF`_l7&-F:6$7W7$F>$\"1Qs\\Q<;W[FC7$FJ$\"1v]$HObA_%FC7$FT$\"1l&4/*\\
#GE%FC7$FY$\"1$y[&oA?YSFC7$Fhn$\"1t9X#*4fgQFC7$Fbo$\"1PoHMq)4_$FC7$F\\
p$\"1:/)f-fID$FC7$Fap$\"1du0b#40.$FC7$Ffp$\"1%4&))3-4TGFC7$F\\q$\"1t76
EG>JDFC7$Faq$\"1O:Xuz+)H#FC7$Ffq$\"1n-ei-r$4#FC7$F[r$\"1KcjBDG6>FC7$F`
r$\"1!>*=3Zb^<FC7$Fer$\"1Y?\"RZ0`g\"FC7$Fjr$\"1MFqL#>))[\"FC7$F_s$\"1`
x(\\a$=p8FC7$Fds$\"1fRn<zYf7FC7$Fis$\"1d2NTZAi6FC7$F^t$\"1x&H[()\\-3\"
FC7$Fct$\"1!)G07!os*)*Fjp7$Fht$\"1F6+W\"3N=*Fjp7$F]u$\"1?Ah'3n%3%)Fjp7
$Fbu$\"14v]IwmnxFjp7$Fgu$\"18dn&e%Q4rFjp7$F\\v$\"1)>EWL\"yAlFjp7$Fav$
\"1*z;c2A&\\fFjp7$Ffv$\"1@m<\\robaFjp7$F[w$\"1BbIV\">e&\\Fjp7$F`w$\"1i
L\\S1^qWFjp7$Few$\"1rD'QSIY2%Fjp7$Fjw$\"1+gxsyUtOFjp7$F_x$\"1'o&**4<J'
G$Fjp7$Fdx$\"1\\nF0#\\K$HFjp7$Fix$\"1x/q=bt9EFjp7$F^y$\"1LpY.gc'G#Fjp7
$Fcy$\"1))z<Y1m8?Fjp7$Fhy$\"1'po0H^Vu\"Fjp7$F]z$\"1!4XI'3K>:Fjp7$Fbz$
\"1o%R\")QzKH\"Fjp7$Fgz$\"1l9#p2Y!*4\"Fjp7$F][l$\"1#)4!y7Tb9*F@7$Fb[l$
\"1/97Usm>vF@7$Fg[l$\"1v'zs<91+'F@7$F\\\\l$\"1&R7_B[)4ZF@7$Fa\\l$\"1)e
j#>?4gNF@7$Ff\\l$\"1$ewnVQce#F@7$F[]l$\"1@sfpdOK=F@7$F`]l$\"1LA9QhkK6F
@7$Ff]l$\"1,ZJ9Jv;lF[[l7$F[^l$\"1cXtYaDjGF[[l7$F`^l$\"1TGNL!fWj(Fd]lFe
^lFf^l-F(6%F*%,alpha~is~.7GF2Fj^lF`_l7&-F:6$7U7$F>$\"1H[\"oUtj9%FC7$FT
$\"1,+wg(yHy$FC7$Fhn$\"1)G92;_z^$FC7$Fbo$\"1\"35LrERG$FC7$F\\p$\"1#eB'
=Vv\"4$FC7$Fap$\"1,Fs?(Rl#HFC7$Ffp$\"1VN2fbg\"y#FC7$F\\q$\"1****>3TFND
FC7$Faq$\"10O5mn'=M#FC7$Ffq$\"1p1p2ESm@FC7$F[r$\"1[!G#zby/?FC7$F`r$\"1
HX$o]Y$f=FC7$Fer$\"1=Tc=K*Gs\"FC7$Fjr$\"14P'*Gr#>h\"FC7$F_s$\"1I=J#4He
\\\"FC7$Fds$\"1w/QG+W(Q\"FC7$Fis$\"13?!f*[#)*G\"FC7$F^t$\"1UkzBtR17FC7
$Fct$\"1uxUk\"\\I6\"FC7$Fht$\"1>!QIXM&Q5FC7$F]u$\"1&3,!p[.n&*Fjp7$Fbu$
\"1NT%>$[;$)))Fjp7$Fgu$\"1L&4cFyO<)Fjp7$F\\v$\"1J[a+,VNvFjp7$Fav$\"11F
dHC91pFjp7$Ffv$\"1Jw9sqcfjFjp7$F[w$\"1m>Ci<--eFjp7$F`w$\"1i\"Q#R@]c_Fj
p7$Few$\"14.,DVO3[Fjp7$Fjw$\"1%p\\_z_7N%Fjp7$F_x$\"18/%>G.t!RFjp7$Fdx$
\"17PXj8')*\\$Fjp7$Fix$\"13==J'Q,8$Fjp7$F^y$\"1![')*)['*pu#Fjp7$Fcy$\"
1yDWk%*fECFjp7$Fhy$\"1&pgA]s(3@Fjp7$F]z$\"1(=M%4W)=%=Fjp7$Fbz$\"1M.cGj
_s:Fjp7$Fgz$\"1%Q$G@k**R8Fjp7$F][l$\"1^lGa#[\"=6Fjp7$Fb[l$\"1jQ\"o%\\
\"z@*F@7$Fg[l$\"1-hKm&ybP(F@7$F\\\\l$\"1>+XQrl.eF@7$Fa\\l$\"1z*=P[@zR%
F@7$Ff\\l$\"1N+]6k\">?$F@7$F[]l$\"1\\R=oK1uAF@7$F`]l$\"1n](Q7:\"49F@7$
Ff]l$\"1y3@F@yC\")F[[l7$F[^l$\"1>TH!oSxd$F[[l7$F`^l$\"1$)RWB[Zf&*Fd]lF
e^lFf^l-F(6%F*%,alpha~is~.8GF2Fj^lF`_l7&-F(6%F*%,alpha~is~.9GF2-F:6$7S
7$F>$\"1:>%3m>%yMFC7$FT$\"1jktO$*G!H$FC7$Fhn$\"1d!oW(=)=9$FC7$F\\p$\"1
+fv(4H*zGFC7$Ffp$\"1lYi)yI\"pEFC7$F\\q$\"1D#\\L$3z)[#FC7$Faq$\"1;)=PZM
!RBFC7$Ffq$\"1o%fY<xp>#FC7$F[r$\"1lC%Hl%)41#FC7$F`r$\"1/M#QTkW$>FC7$Fe
r$\"1)45knpA\"=FC7$Fjr$\"1'>k4$)e/r\"FC7$F_s$\"1=;G!GW;g\"FC7$Fds$\"1&
)Gb0p(z\\\"FC7$Fis$\"1OTZ[t#HS\"FC7$F^t$\"1f$=z#\\W?8FC7$Fct$\"1\\Mph&
4oA\"FC7$Fht$\"1(Hl2Ud5:\"FC7$F]u$\"1@9E]e%o1\"FC7$Fbu$\"1;pYsMac**Fjp
7$Fgu$\"1<?4vK:5#*Fjp7$F\\v$\"1=61!eD>`)Fjp7$Fav$\"1v@A7z#p&yFjp7$Ffv$
\"1c:nycclsFjp7$F[w$\"1;Wu)oOul'Fjp7$F`w$\"1Z2.alfdgFjp7$Few$\"1'Q?q%G
AhbFjp7$Fjw$\"1_f\"4K1:0&Fjp7$F_x$\"1\\e9$*=7`XFjp7$Fdx$\"1v*zt;iF4%Fj
p7$Fix$\"1N?S6:^sOFjp7$F^y$\"18Fd2)=WB$Fjp7$Fcy$\"1Fx<!f$)f'GFjp7$Fhy$
\"1!*zZ)>d&)\\#Fjp7$F]z$\"1f./(4i%)=#Fjp7$Fbz$\"1/qZc+*R(=Fjp7$Fgz$\"1
Z.^H`B,;Fjp7$F][l$\"1dvx\"oS)R8Fjp7$Fb[l$\"1C$foRmu5\"Fjp7$Fg[l$\"1C8i
p!e])))F@7$F\\\\l$\"1FM;_&p!4qF@7$Fa\\l$\"1f@]o*GZK&F@7$Ff\\l$\"197t)*
y6')QF@7$F[]l$\"1T#Hy$)Ggw#F@7$F`]l$\"1B='efb\"=<F@7$Ff]l$\"1+)p1Pny#*
*F[[l7$F[^l$\"1MZu7e[\"Q%F[[l7$F`^l$\"1Qs*)4,:t6F[[lFe^lFf^lFj^lF`_l7&
-F:6$7S7$F0$\"\"$F07$$\"1nmm;arz@F@$\"1(H*yACkqGFC7$$\"1LL$e9ui2%F@$\"
1(fBXN3/w#FC7$$\"1nmm\"z_\"4iF@$\"1zq,1p,REFC7$$\"1mmmT&phN)F@$\"1BFK)
\\x&>DFC7$$\"1LLe*=)H\\5Fjp$\"1'))pp)=X.CFC7$$\"1nm\"z/3uC\"Fjp$\"1=-R
wfB)H#FC7$$\"1++DJ$RDX\"Fjp$\"1Y[^;Dx\">#FC7$$\"1nm\"zR'ok;Fjp$\"1jAN&
eBV3#FC7$$\"1++D1J:w=Fjp$\"1YFf]m!*z>FC7$$\"1LLL3En$4#Fjp$\"1fls%Q+`(=
FC7$$\"1nm;/RE&G#Fjp$\"171&3f9by\"FC7$F_s$\"1GN%3Qsqo\"FC7$Fds$\"1p(e2
TM5f\"FC7$Fis$\"1=bK)zY6]\"FC7$$\"1nm\"z*ev:JFjp$\"1v?r0Xy@9FC7$$\"1LL
L347TLFjp$\"1lIsA,AI8FC7$$\"1LLLLY.KNFjp$\"1%)>`zs.b7FC7$$\"1++D\"o7Tv
$Fjp$\"1ic&>DL.<\"FC7$$\"1LLL$Q*o]RFjp$\"1#[2\"oZ#y4\"FC7$$\"1++D\"=lj
;%Fjp$\"1qf&f&)Q4-\"FC7$$\"1++vV&R<P%Fjp$\"1Si,HZ>.&*Fjp7$$\"1LL$e9Ege
%Fjp$\"1$3!3oQL$z)Fjp7$$\"1LLeR\"3Gy%Fjp$\"1w$>DFFd;)Fjp7$$\"1nm;/T1&*
\\Fjp$\"10.U'*\\\"[^(Fjp7$$\"1mm\"zRQb@&Fjp$\"1[HaY=KnoFjp7$$\"1***\\(
=>Y2aFjp$\"1J%>$3=UFjFjp7$$\"1mm;zXu9cFjp$\"1UWyJ&R\"pdFjp7$$\"1+++]y)
)GeFjp$\"1(Gj.(HX>_Fjp7$$\"1****\\i_QQgFjp$\"1hJ^)R<$3ZFjp7$$\"1***\\7
y%3TiFjp$\"14^_'3L)QUFjp7$$\"1****\\P![hY'Fjp$\"1L&fy!HVYPFjp7$$\"1LLL
$Qx$omFjp$\"1ca'zx7*HLFjp7$$\"1+++v.I%)oFjp$\"1Vv'fCvA\"HFjp7$$\"1mm\"
zpe*zqFjp$\"1f<whB*zb#Fjp7$$\"1+++D\\'QH(Fjp$\"1xNC8,&p>#Fjp7$$\"1KLe9
S8&\\(Fjp$\"1C#p931B)=Fjp7$$\"1***\\i?=bq(Fjp$\"1m]b5SRz:Fjp7$$\"1LLL3
s?6zFjp$\"1*ebzf;*38Fjp7$$\"1++DJXaE\")Fjp$\"1&y;!=1&H0\"Fjp7$$\"1nmmm
*RRL)Fjp$\"1,?,/\"osK)F@7$$\"1mm;a<.Y&)Fjp$\"1%)\\nz42UjF@7$$\"1LLe9tO
c()Fjp$\"15+ron')RYF@7$$\"1+++]Qk\\*)Fjp$\"1p%Gb7W(4LF@7$$\"1LL$3dg6<*
Fjp$\"1yR-)RC41#F@7$$\"1mmmmxGp$*Fjp$\"1l*GQw$R$>\"F@7$$\"1++D\"oK0e*F
jp$\"1<%z\\%\\ey_F[[l7$$\"1++v=5s#y*Fjp$\"1L6zqYI;9F[[lFe^lFf^l-F(6%F*
%-alpha~is~1.0GF2Fj^lF`_l7&-F(6%F*%-alpha~is~1.1GF2-F:6$7]o7$F0F07$$\"
1LL3x1h6oFd]l$\"1p;mXSbC<FC7$$\"1nmTN@Ki8F[[l$\"1i/n!Q7e%=FC7$$\"1+]7.
K[V?F[[l$\"1pFB-.d>>FC7$$\"1LL$3FWYs#F[[l$\"1)3J4\"*)*G(>FC7$$\"1++D1k
'p3%F[[l$\"1#4Q/iF*[?FC7$$\"1mmmT&)G\\aF[[l$\"1o-JvC'H5#FC7$$\"1++]7G$
R<)F[[l$\"1*Q*eE(**z<#FC7$$\"1LLL3x&)*3\"F@$\"1j]s]\"o#HAFC7$$\"1++]il
yM;F@$\"1,!\\!o^+'H#FC7$Fbcq$\"13k$zQ2pL#FC7$$\"1L$e*)4bQl#F@$\"1)QWmF
4.O#FC7$$\"1++D\"y%*z7$F@$\"1Ys8N<6wBFC7$$\"1n;ajW8-OF@$\"15f</?N'Q#FC
7$Fgcq$\"1=ZebbL#R#FC7$$\"1n;H2Q\\4YF@$\"1sEa_g2&R#FC7$$\"1++voMrU^F@$
\"1?\\z3>W%R#FC7$$\"1L$3-8Lfn&F@$\"1r$>M#32\"R#FC7$F\\dq$\"19v`OjV&Q#F
C7$$\"1nmmm6m#G(F@$\"1V2Q0dhoBFC7$Fadq$\"17t?&\\BhM#FC7$Ffdq$\"19_uKu`
*G#FC7$F[eq$\"1,)e:%4]FAFC7$F`eq$\"1(4CjP.p:#FC7$Feeq$\"1:U#G]<$z?FC7$
Fjeq$\"1j&HhL8*)*>FC7$F_fq$\"1\\XgLg=9>FC7$Fdfq$\"1)zf'3qcQ=FC7$F_s$\"
1'R,DOQHv\"FC7$Fds$\"1)*ympu$pm\"FC7$Fis$\"1C)R9IUWe\"FC7$Fbgq$\"1iT*y
wB,^\"FC7$Fggq$\"1B&Qe\\rFU\"FC7$F\\hq$\"1=CPtw$)\\8FC7$Fahq$\"1)*R!))
RMkE\"FC7$Ffhq$\"1.U&[h]S>\"FC7$F[iq$\"1g\"epgVj6\"FC7$F`iq$\"1[>#e)p8
W5FC7$Feiq$\"1jv3*etxq*Fjp7$Fjiq$\"18@'z`bG0*Fjp7$F_jq$\"1$eHSq#[n$)Fj
p7$Fdjq$\"1E(G]:?'zwFjp7$Fijq$\"1N(ec\"\\Z,rFjp7$F^[r$\"1\"=I]C)H*\\'F
jp7$Fc[r$\"1s&*R(4#4-fFjp7$Fh[r$\"1=oQh#RHM&Fjp7$F]\\r$\"195MgD3E[Fjp7
$Fb\\r$\"1(>\"[dHg!G%Fjp7$Fg\\r$\"1C(Hc(*Hk\"QFjp7$F\\]r$\"1^fr2pU[LFj
p7$Fa]r$\"1[\\Y3$R$\\HFjp7$Ff]r$\"1\"Q0^E71a#Fjp7$F[^r$\"1k#HQr#o#=#Fj
p7$F`^r$\"19!4X94l$=Fjp7$Fe^r$\"1yL**[X,E:Fjp7$Fj^r$\"1qf!G.&*3B\"Fjp7
$F__r$\"1%e^!y`5f(*F@7$Fd_r$\"1P6tgVE^uF@7$Fi_r$\"18t^sXikaF@7$F^`r$\"
1f`\\jie1RF@7$Fc`r$\"1O>&GKB&QCF@7$Fh`r$\"1cwV&[m]T\"F@7$F]ar$\"1\"G!y
LA0tiF[[l7$Fbar$\"1vUO:/l'o\"F[[lFe^lFf^lFj^lF`_l7&-F:6$7[oF`br7$Fbbr$
\"1HcQdJb7)*Fjp7$Fgbr$\"1NgM!GIc7\"FC7$F\\cr$\"1W72d&\\!>7FC7$Facr$\"1
K&4.E%[*G\"FC7$Ffcr$\"197q68f%R\"FC7$F[dr$\"1,hI6e9t9FC7$F`dr$\"1,t!ej
V))e\"FC7$Fedr$\"1(fy\"[tqt;FC7$Fjdr$\"1zs![hV^z\"FC7$Fbcq$\"1*)Rnj'\\
/)=FC7$Fger$\"1'4;/o>B)>FC7$Fgcq$\"1)H-:74%\\?FC7$Fifr$\"1W'z(f9W*4#FC
7$F\\dq$\"1H!*fPHLJ@FC7$Ffgr$\"1%[RWsB.:#FC7$Fadq$\"1rX$Gn$Rf@FC7$$\"1
++v=ddC%*F@$\"1y)oLq72;#FC7$Ffdq$\"1*o@VoYe:#FC7$$\"1++v=JN[6Fjp$\"17K
@B\"yn9#FC7$F[eq$\"1t[?SC-M@FC7$F`eq$\"1)RFz0)3)4#FC7$Feeq$\"1o\"=[lz.
0#FC7$Fjeq$\"1>%*)zk2[*>FC7$F_fq$\"1!*)o'3XKJ>FC7$Fdfq$\"15]o7FMr=FC7$
F_s$\"1\\w9E=N+=FC7$Fds$\"1,)))eJ-js\"FC7$Fis$\"1%=7AvbIl\"FC7$Fbgq$\"
15.PmuV&e\"FC7$Fggq$\"1->D8m>/:FC7$F\\hq$\"1bM)e(3/N9FC7$Fahq$\"1#3p\\
23YN\"FC7$Ffhq$\"1T'R'\\)>PG\"FC7$F[iq$\"1+]F*ptl?\"FC7$F`iq$\"1jS55T(
R8\"FC7$Feiq$\"1kF,%))f$f5FC7$Fjiq$\"1%*e)Hq70#**Fjp7$F_jq$\"1*3,n(QN4
#*Fjp7$Fdjq$\"1\\mPh+())[)Fjp7$Fijq$\"1fB))p0AyyFjp7$F^[r$\"1$3\\w/_tB
(Fjp7$Fc[r$\"1**z,nT(pf'Fjp7$Fh[r$\"1>b@gT6$*fFjp7$F]\\r$\"1:kF?\\EJaF
jp7$Fb\\r$\"1qF`A(zW$[Fjp7$Fg\\r$\"1@+s^1aBVFjp7$F\\]r$\"1Bx/+*ea!QFjp
7$Fa]r$\"1$G/+%fIhLFjp7$Ff]r$\"1&)Gp,*=T!HFjp7$F[^r$\"1)Ggm1y<]#Fjp7$F
`^r$\"1')f`L7$36#Fjp7$Fe^r$\"1?r]fUee<Fjp7$Fj^r$\"1`(=92-BU\"Fjp7$F__r
$\"1k@3eA^I6Fjp7$Fd_r$\"1d)*f%\\(R`')F@7$Fi_r$\"1jn*4p'phjF@7$F^`r$\"1
wSey5$yb%F@7$Fc`r$\"1X&)f_.+_GF@7$Fh`r$\"1PpN9oae;F@7$F]ar$\"16$3TfA)o
tF[[l7$Fbar$\"1#oCf*[T&)>F[[lFe^lFf^l-F(6%F*%-alpha~is~1.2GF2Fj^lF`_l7
&-F:6$7]oF`br7$Fbbr$\"1nc921iFbFjp7$Fgbr$\"1T]Fi]-'z'Fjp7$F\\cr$\"1#[b
lY.Ym(Fjp7$Facr$\"1LD(e'f2W$)Fjp7$Ffcr$\"1`8=k(GwR*Fjp7$F[dr$\"1#\\n,q
q;-\"FC7$F`dr$\"1V\\3#Q2v9\"FC7$Fedr$\"1!f:9LySC\"FC7$Fjdr$\"1!HLf^d&*
Q\"FC7$Fbcq$\"1Hy!yys!)\\\"FC7$Fger$\"1g)yXF7tj\"FC7$Fgcq$\"1Zvz\"*e9Q
<FC7$Fifr$\"1$GS%QTWA=FC7$F\\dq$\"1dKE]HK&)=FC7$Ffgr$\"1\"p7\"o$)pK>FC
7$Fadq$\"1s=dQ@sn>FC7$Fccs$\"19#4LRdF*>FC7$Ffdq$\"1y*=q)et4?FC7$F[ds$
\"1!4\"pMmT>?FC7$F[eq$\"1K?Yyd4C?FC7$$\"1LLe*ot*\\8Fjp$\"1L%HLAfV-#FC7
$F`eq$\"1.Tjn7a??FC7$$\"1LLekGhe:Fjp$\"1\"o$*py;G,#FC7$Feeq$\"1$=Gu*))
p,?FC7$Fjeq$\"1Q(*zv\\(3(>FC7$F_fq$\"1wC=Q/?H>FC7$Fdfq$\"1@CEkUs&)=FC7
$F_s$\"1u]4PQiI=FC7$Fds$\"1`Gh&*y'*p<FC7$Fis$\"1d=othX2<FC7$Fbgq$\"1eO
X<@#zk\"FC7$Fggq$\"1_\"e]8OWd\"FC7$F\\hq$\"1&***z74U5:FC7$Fahq$\"1$eXi
o$[M9FC7$Ffhq$\"1%R&)eTrjO\"FC7$F[iq$\"1.,cjF5\"H\"FC7$F`iq$\"1Wx5D(p#
>7FC7$Feiq$\"1\"=;h&o]W6FC7$Fjiq$\"1$\\)>M2Iw5FC7$F_jq$\"1J^'>L$\\.5FC
7$Fdjq$\"1=*o!p'**)*G*Fjp7$Fijq$\"1#)3&ykSGl)Fjp7$F^[r$\"1(o&pMl\"*yzF
jp7$Fc[r$\"1ub$*Rp>+tFjp7$Fh[r$\"1a\"*)Q%fUbmFjp7$F]\\r$\"15jYWGV^gFjp
7$Fb\\r$\"1*pM)=-i0aFjp7$Fg\\r$\"1g/oQ+B\\[Fjp7$F\\]r$\"1ey7A*y<G%Fjp7
$Fa]r$\"1+4%QEYEz$Fjp7$Ff]r$\"1\">b&f'elG$Fjp7$F[^r$\"1`.()38&*QGFjp7$
F`^r$\"10I`$Hb>S#Fjp7$Fe^r$\"1M6ul`S1?Fjp7$Fj^r$\"1N0j)z(4F;Fjp7$F__r$
\"10t+lnb'H\"Fjp7$Fd_r$\"1I0CZ7M\\**F@7$Fi_r$\"1rqhP%QAL(F@7$F^`r$\"15
,;*HcYE&F@7$Fc`r$\"1v3Rp4N-LF@7$Fh`r$\"1'R#fY=bC>F@7$F]ar$\"1$4a8q_(p&
)F[[l7$Fbar$\"1PT]8T\"QJ#F[[lFe^lFf^l-F(6%F*%-alpha~is~1.3GF2Fj^lF`_l7
&-F:6$7\\oF`br7$Fbbr$\"1l&G><8n3$Fjp7$Fgbr$\"1wzA**=RnSFjp7$F\\cr$\"1U
GUb30xZFjp7$Facr$\"1InF\"yABN&Fjp7$Ffcr$\"1fBZm%ovF'Fjp7$F[dr$\"1]D(3f
%*Q-(Fjp7$F`dr$\"1n.%zuba@)Fjp7$Fedr$\"1*>a)Q.!o;*Fjp7$Fjdr$\"16w0*yTi
1\"FC7$Fbcq$\"1aS,%zdI=\"FC7$Fger$\"1xFL:_dS8FC7$Fgcq$\"1N]p=5Kh9FC7$F
ifr$\"1+ARC$=#o:FC7$F\\dq$\"1m1^!G(=`;FC7$Ffgr$\"1R]c#Gs>s\"FC7$Fadq$
\"1sY-%p]ux\"FC7$Ffdq$\"1[\"G)))R@d=FC7$F[eq$\"1*)>eoZ6.>FC7$Fa`t$\"19
CL%*=Y=>FC7$F`eq$\"13KG!=<*G>FC7$Fi`t$\"1D\")z>W8N>FC7$Feeq$\"1SwBm!er
$>FC7$$\"1LL3_(>/x\"Fjp$\"1PEjP[TN>FC7$Fjeq$\"15!)oOSFI>FC7$F_fq$\"1Y
\"Gkw)H5>FC7$Fdfq$\"1fja0.n$)=FC7$F_s$\"1Mu'4x'>X=FC7$Fds$\"1#*HoGi$*)
z\"FC7$Fis$\"1Is)e***G[<FC7$Fbgq$\"1SMmoY&zp\"FC7$Fggq$\"1u;%R01Oj\"FC
7$F\\hq$\"1d3Ymx\"fd\"FC7$Fahq$\"1r[T9?%e]\"FC7$Ffhq$\"1P3JF3oT9FC7$F[
iq$\"1_d%H)Q_p8FC7$F`iq$\"1'y$>Kec*H\"FC7$Feiq$\"1Eo(=&3tD7FC7$Fjiq$\"
1xcU6t`d6FC7$F_jq$\"17(fn1JR3\"FC7$Fdjq$\"1L)3\"*=*z25FC7$Fijq$\"1K&))
GMs3U*Fjp7$F^[r$\"17-\"pcp)>()Fjp7$Fc[r$\"1!*Q&*3'R!3!)Fjp7$Fh[r$\"1#4
lB1vlK(Fjp7$F]\\r$\"1o46*H0Po'Fjp7$Fb\\r$\"1)z)y6[g\"*fFjp7$Fg\\r$\"1>
/?/%y9R&Fjp7$F\\]r$\"1)\\#QE(odx%Fjp7$Fa]r$\"1^(eLJw?C%Fjp7$Ff]r$\"1+!
R9Gvpo$Fjp7$F[^r$\"1$R!*o#\\^$>$Fjp7$F`^r$\"1(z8?ZJ%4FFjp7$Fe^r$\"12hM
qp@pAFjp7$Fj^r$\"1+')RaR<X=Fjp7$F__r$\"19rwa7/u9Fjp7$Fd_r$\"1D)4#[f(R8
\"Fjp7$Fi_r$\"1(fw%G4Ex$)F@7$F^`r$\"1;LP`Y9GgF@7$Fc`r$\"1`9o)R>0z$F@7$
Fh`r$\"1%yJ'*GuP@#F@7$F]ar$\"1CjlR=iz)*F[[l7$Fbar$\"1`gSjD0tEF[[lFe^lF
f^l-F(6%F*%-alpha~is~1.4GF2Fj^lF`_l7&-F:6$7\\oF`br7$Fbbr$\"1EK6e%=/r\"
Fjp7$Fgbr$\"1*\\w:a+cT#Fjp7$F\\cr$\"1s'f/$)fW&HFjp7$Facr$\"1s:EX3'oS$F
jp7$Ffcr$\"1\"3(H*RV6;%Fjp7$F[dr$\"1vu,;#Q<z%Fjp7$F`dr$\"1#[>NiXl$eFjp
7$Fedr$\"1e?[%H&[-nFjp7$Fjdr$\"1[rdaKj=\")Fjp7$Fbcq$\"1s%Qn=55F*Fjp7$F
ger$\"1#**fE6y\"*3\"FC7$Fgcq$\"1i\\:9'Q\">7FC7$Fifr$\"1ZtI#3\"3R8FC7$F
\\dq$\"1=;\"Ra)[Q9FC7$Ffgr$\"1*)4ACjUA:FC7$Fadq$\"1Weg2MB$f\"FC7$Ffdq$
\"1kod$zrIq\"FC7$F[eq$\"1G/Q?ugv<FC7$F`eq$\"1(z*>[+HF=FC7$Fi`t$\"117xe
h9Y=FC7$Feeq$\"1\"36\\s%Gg=FC7$F_]u$\"1U!>UH\"4q=FC7$Fjeq$\"1W)4*HW(f(
=FC7$$\"1n;HdG\"\\)>Fjp$\"1$*z&Hdj#y=FC7$F_fq$\"1lt4t*Qq(=FC7$Fdfq$\"1
GjSv=:n=FC7$F_s$\"1(4%*y4'eX=FC7$Fds$\"1[*GwH@V\"=FC7$Fis$\"1o$[FGPjx
\"FC7$Fbgq$\"1f(\\mGbgt\"FC7$Fggq$\"1r*ydxn>o\"FC7$F\\hq$\"12!***GIhJ;
FC7$Fahq$\"1cT**flfo:FC7$Ffhq$\"1%o&*)>eW4:FC7$F[iq$\"1qI#\\@R:W\"FC7$
F`iq$\"1]5+s-]u8FC7$Feiq$\"1BpQOki-8FC7$Fjiq$\"19hN]SLN7FC7$F_jq$\"1Vr
8cZ\"=;\"FC7$Fdjq$\"10iSG$))[3\"FC7$Fijq$\"1'Q%[89#y,\"FC7$F^[r$\"14-h
&QijX*Fjp7$Fc[r$\"1-m?,q(pr)Fjp7$Fh[r$\"1ZvQ-TR.!)Fjp7$F]\\r$\"1:__#=$
GDtFjp7$Fb\\r$\"1#oh1-_+f'Fjp7$Fg\\r$\"1.ypMXF[fFjp7$F\\]r$\"1h0)\\&ez
&G&Fjp7$Fa]r$\"1H*o<<%G3ZFjp7$Ff]r$\"1K`WrdP/TFjp7$F[^r$\"16VqA7ukNFjp
7$F`^r$\"1L/C*)*pF.$Fjp7$Fe^r$\"1IC8v7sYDFjp7$Fj^r$\"1S/6i/Rw?Fjp7$F__
r$\"1fP\"o)p$Hm\"Fjp7$Fd_r$\"1&RFC#>^#G\"Fjp7$Fi_r$\"1Z?0'zOw\\*F@7$F^
`r$\"1O\\$3!pG\\oF@7$Fc`r$\"15=SQ)*R<VF@7$Fh`r$\"1xx@!*G)o_#F@7$F]ar$
\"1q$\\qF8-8\"F@7$Fbar$\"1Gn&)*HBV1$F[[lFe^lFf^l-F(6%F*%-alpha~is~1.5G
F2Fj^lF`_l7&-F(6%F*%-alpha~is~1.6GF2-F:6$7gnF`br7$Fgbr$\"1*yHR$fyC9Fjp
7$Facr$\"1mMHrNo`@Fjp7$Ffcr$\"1Ik?`7ORFFjp7$F[dr$\"1)**3%>6cYKFjp7$F`d
r$\"1^P<Lp3=TFjp7$Fedr$\"1@S\"3\"**3n[Fjp7$Fjdr$\"1x#=*4YRRhFjp7$Fbcq$
\"1HF5`AX:sFjp7$Fger$\"1O7C8rk)y)Fjp7$Fgcq$\"1jy))=p755FC7$Fifr$\"1#R+
2z#fN6FC7$F\\dq$\"1pn9s-5V7FC7$Ffgr$\"1x)[=x&yO8FC7$Fadq$\"1e\\C1zK=9F
C7$Ffdq$\"1gw=Nq-^:FC7$F[eq$\"1+j$=2(HX;FC7$F`eq$\"1%>X:)>;><FC7$Feeq$
\"1P@c$*pAu<FC7$Fjeq$\"1J8Ewcr5=FC7$F_fq$\"16)pVuE<$=FC7$Fdfq$\"1dcZ;G
5Q=FC7$F_s$\"1!y&\\;HLL=FC7$Fds$\"1!)z)e(eI<=FC7$Fis$\"1L7\"optCz\"FC7
$Fbgq$\"1\"o(fwU&Gw\"FC7$Fggq$\"1eS'Q%3!*><FC7$F\\hq$\"1'znBC2xn\"FC7$
Fahq$\"1qwUXdxA;FC7$Ffhq$\"1q9xSBdp:FC7$F[iq$\"1(*>U_&\\p]\"FC7$F`iq$
\"1-(*\\N\"*zV9FC7$Feiq$\"1_+36]'[P\"FC7$Fjiq$\"1$*z@G.L48FC7$F_jq$\"1
3y9LfwO7FC7$Fdjq$\"1'QQkvv)f6FC7$Fijq$\"1Vr!3o7@4\"FC7$F^[r$\"1\"\\6+j
#[=5FC7$Fc[r$\"1Xs%4'**oB%*Fjp7$Fh[r$\"1H8z3,'Go)Fjp7$F]\\r$\"1==y9BYt
zFjp7$Fb\\r$\"1;T+N7j)>(Fjp7$Fg\\r$\"1r#zudFw^'Fjp7$F\\]r$\"1CezSTA5eF
jp7$Fa]r$\"1Kx4l!R**=&Fjp7$Ff]r$\"19bf()ytPXFjp7$F[^r$\"1>c.Y$o=&RFjp7
$F`^r$\"1n(*4pdWrLFjp7$Fe^r$\"1=(QU,(eQGFjp7$Fj^r$\"1nO#y\"yd?BFjp7$F_
_r$\"1G%[p(3>j=Fjp7$Fd_r$\"1eUSZ+dS9Fjp7$Fi_r$\"1q4#Rd5%p5Fjp7$F^`r$\"
1Nzu#z%)*GxF@7$Fc`r$\"1b4%emPQ)[F@7$Fh`r$\"1@dNcG_kGF@7$F]ar$\"1jqOf74
%G\"F@7$Fbar$\"1w%p.+3))[$F[[lFe^lFf^lFj^lF`_l7&-F:6$7fnF`br7$Facr$\"1
W\"R6'[5`8Fjp7$F[dr$\"1Lrq%zIh=#Fjp7$F`dr$\"1CT#y0Mx)GFjp7$Fedr$\"16V;
6&pD^$Fjp7$Fjdr$\"1Cq\"yJMTh%Fjp7$Fbcq$\"1ae(opH6e&Fjp7$Fger$\"1p9,&G@
![qFjp7$Fgcq$\"1xy9gs.=$)Fjp7$Fifr$\"1&>@Bzo5d*Fjp7$F\\dq$\"1Nw\"QrZw1
\"FC7$Ffgr$\"1i*zxBml;\"FC7$Fadq$\"1JX$*[>'[D\"FC7$Fccs$\"1Z0p<f[L8FC7
$Ffdq$\"1tJaaI(QS\"FC7$F[eq$\"1#[FMNy^^\"FC7$F`eq$\"1dn%3e*[2;FC7$Feeq
$\"1'pUZK[<o\"FC7$Fjeq$\"1%4kvR$)pt\"FC7$F_fq$\"1M2Cm,_w<FC7$Fdfq$\"1s
n<!G#Q)z\"FC7$F_s$\"1go!o,m*4=FC7$Fds$\"1RY?;c54=FC7$Fis$\"1,;kyyj(z\"
FC7$Fbgq$\"1(fPy-j!z<FC7$Fggq$\"1=@)fOyyu\"FC7$F\\hq$\"1%f!)f1*\\9<FC7
$Fahq$\"1!4Z%oh]o;FC7$Ffhq$\"1#*e4z51A;FC7$F[iq$\"1LCeESkl:FC7$F`iq$\"
10kRd!ps]\"FC7$Feiq$\"1>bWr$*=U9FC7$Fjiq$\"1(z+g6G#z8FC7$F_jq$\"1b,PT#
f%38FC7$Fdjq$\"1v:4![BCB\"FC7$Fijq$\"1#))pI.BY;\"FC7$F^[r$\"1&[\\*ev>!
4\"FC7$Fc[r$\"1OS[Ss]75FC7$Fh[r$\"1dm!G1/@O*Fjp7$F]\\r$\"1\\8?]SkD')Fj
p7$Fb\\r$\"1$Rr'QN2:yFjp7$Fg\\r$\"1&)y'4Qxv4(Fjp7$F\\]r$\"1-&ot1BuM'Fj
p7$Fa]r$\"1*z^*)e*p&o&Fjp7$Ff]r$\"19::8q,')\\Fjp7$F[^r$\"1b<'o)e5aVFjp
7$F`^r$\"1zMEvF!\\s$Fjp7$Fe^r$\"1<6f'p_W9$Fjp7$Fj^r$\"1W'G^ORvd#Fjp7$F
__r$\"1Iq#\\-FZ2#Fjp7$Fd_r$\"1u\\)zcg\"3;Fjp7$Fi_r$\"1NUM\"*zs'>\"Fjp7
$F^`r$\"1>p#>'R0o')F@7$Fc`r$\"1QYfA1j!\\&F@7$Fh`r$\"1JLitiJFKF@7$F]ar$
\"1Za2g8&*\\9F@7$Fbar$\"1vF#)HqnZRF[[lFe^lFf^l-F(6%F*%-alpha~is~1.7GF2
Fj^lF`_l7&-F(6%F*%-alpha~is~1.8GF2-F:6$7ZF`br7$F[dr$\"1&4\")\\s%*QY\"F
jp7$Fedr$\"1X8!3!\\$4_#Fjp7$Fjdr$\"1X[K2ja[MFjp7$Fbcq$\"1)Qz%)=4IH%Fjp
7$Fger$\"1b'o\\YS2i&Fjp7$Fgcq$\"1ss7$Gl:\"oFjp7$Fifr$\"1@46;(R>-)Fjp7$
F\\dq$\"1sL-0\"e'=\"*Fjp7$Ffgr$\"11c'eOnB,\"FC7$Fadq$\"1)puKYpS5\"FC7$
Fccs$\"1e/[#GZu=\"FC7$Ffdq$\"1$)[J-Gij7FC7$F[eq$\"19%e$R,g(Q\"FC7$F`eq
$\"15H[sGs%\\\"FC7$Feeq$\"1nd<ghB&e\"FC7$Fjeq$\"1$QSR*))*pl\"FC7$F_fq$
\"1mms5yS8<FC7$Fdfq$\"1nNypuu\\<FC7$F_s$\"1>o\"4Fspx\"FC7$Fds$\"1D*>vn
R4z\"FC7$Fis$\"1lD#e%Q!Gz\"FC7$Fbgq$\"1WIU)z[ay\"FC7$Fggq$\"1zBa@^Wm<F
C7$F\\hq$\"11mSOjOU<FC7$Fahq$\"14arGq*fq\"FC7$Ffhq$\"1Tj!po%*pm\"FC7$F
[iq$\"1,$Gp5!f<;FC7$F`iq$\"1z2kU&*yk:FC7$Feiq$\"1'\\`D63W]\"FC7$Fjiq$
\"1JTf%)zyW9FC7$F_jq$\"1<>^a)>mP\"FC7$Fdjq$\"1&z')[rNAI\"FC7$Fijq$\"1%
Rj5t\\]B\"FC7$F^[r$\"1?\"e*=2[g6FC7$Fc[r$\"1?m>\\N#=3\"FC7$Fh[r$\"11*G
ayTQ+\"FC7$F]\\r$\"1*pNiwV$z#*Fjp7$Fb\\r$\"1S'y;#3=P%)Fjp7$Fg\\r$\"14>
TiM?'o(Fjp7$F\\]r$\"19@Awgx&*oFjp7$Fa]r$\"1hw))H6A%>'Fjp7$Ff]r$\"1\"e)
zXC:[aFjp7$F[^r$\"1iL9`+kqZFjp7$F`^r$\"1Rm[n!eD4%Fjp7$Fe^r$\"1v-=m'HRY
$Fjp7$Fj^r$\"1m[5gM0ZGFjp7$F__r$\"1)37)y\"[uH#Fjp7$Fd_r$\"1ha1))oF&y\"
Fjp7$Fi_r$\"1')3_;\\wJ8Fjp7$F^`r$\"1*z<TuEsm*F@7$Fc`r$\"1wj#z(*H&QhF@7
$Fh`r$\"1#e[e^ieh$F@7$F]ar$\"1r@5799G;F@7$Fbar$\"13ND/&*3UWF[[lFe^lFf^
lFj^lF`_l7&-F:6$7ZF`br7$F[dr$\"1!=NwNsJv*F@7$Fedr$\"1]0B%z;,!=Fjp7$Fjd
r$\"1\\^H\")4RkDFjp7$Fbcq$\"1m[-[\"=bG$Fjp7$Fger$\"1^a#p2q)fWFjp7$Fgcq
$\"1TjonWx\\bFjp7$Fifr$\"1I!pBY3'*o'Fjp7$F\\dq$\"1,Dx3>$)[xFjp7$Ffgr$
\"1:fOII;T()Fjp7$Fadq$\"1`T'\\tS\\m*Fjp7$Fccs$\"1S@ZX]1_5FC7$Ffdq$\"1f
mzUHkJ6FC7$F[eq$\"1ko;^)\\VE\"FC7$F`eq$\"1Bli$\\^GQ\"FC7$Feeq$\"100g].
s'[\"FC7$Fjeq$\"1L([u%*=Fd\"FC7$F_fq$\"115N(R'>W;FC7$Fdfq$\"19k\"Q#\\$
Qp\"FC7$F_s$\"1a')R0UxN<FC7$Fds$\"1&H?6;2Sw\"FC7$Fis$\"1.8<wz&*y<FC7$F
bgq$\"1>fj'48Gy\"FC7$Fggq$\"1+*QeE)>w<FC7$F\\hq$\"1@s'\\-\\<w\"FC7$Fah
q$\"12_#yzDbt\"FC7$Ffhq$\"1.JS\"zDXq\"FC7$F[iq$\"1)p!o:S#Gm\"FC7$F`iq$
\"1P$RZW0jh\"FC7$Feiq$\"1[w)[***Qh:FC7$Fjiq$\"1c9fa\\#e]\"FC7$F_jq$\"1
)4MLm?5W\"FC7$Fdjq$\"10nQ(=d!p8FC7$Fijq$\"1q$)flV7.8FC7$F^[r$\"1)*4@n(
f!H7FC7$Fc[r$\"1t6aI40]6FC7$Fh[r$\"1qRJ0f#42\"FC7$F]\\r$\"1=GRgu>K**Fj
p7$Fb\\r$\"1+!efMLG1*Fjp7$Fg\\r$\"1Pa:BFj\"G)Fjp7$F\\]r$\"1$4#4/zo`uFj
p7$Fa]r$\"13sbQD;9nFjp7$Ff]r$\"1j:nTJ2BfFjp7$F[^r$\"1X(HuXQ1?&Fjp7$F`^
r$\"1;NC#f0QZ%Fjp7$Fe^r$\"1;nM))\\g'z$Fjp7$Fj^r$\"1KsoIb()GJFjp7$F__r$
\"1[uAQrBJDFjp7$Fd_r$\"1`Js_k*=(>Fjp7$Fi_r$\"1xoT6'eXZ\"Fjp7$F^`r$\"1(
=+K\\:F2\"Fjp7$Fc`r$\"1ck(3nT#GoF@7$Fh`r$\"1U8A]'Q2.%F@7$F]ar$\"1()p*f
$>+>=F@7$Fbar$\"1?kOaL>t\\F[[lFe^lFf^l-F(6%F*%-alpha~is~1.9GF2Fj^lF`_l
7&-F(6%F*%-alpha~is~2.0GF2-F:6$7XF`br7$Fedr$\"1'fTojx%z7Fjp7$Fbcq$\"1s
k(yTtG]#Fjp7$Fger$\"10#fI&>WANFjp7$Fgcq$\"1\\Z*H[s3]%Fjp7$Fifr$\"1i+k
\\v$Gb&Fjp7$F\\dq$\"1*e+dnBWb'Fjp7$Ffgr$\"1RgG1>l7vFjp7$Fadq$\"197u*p1
;U)Fjp7$Fccs$\"1JASs;?y#*Fjp7$Ffdq$\"1f#*\\&3v(35FC7$F[eq$\"15V=@_tY6F
C7$F`eq$\"1Ti:9VXt7FC7$Feeq$\"1Crb[!)*yQ\"FC7$Fjeq$\"1Xy.0K%e[\"FC7$F_
fq$\"1$ef\">g]q:FC7$Fdfq$\"1GN$z\")[@j\"FC7$F_s$\"1ewm(o8xo\"FC7$Fds$
\"1fFDW'o%H<FC7$Fis$\"1[l6B,3d<FC7$Fbgq$\"1sbp$Qt>x\"FC7$Fggq$\"11j)e]
qxx\"FC7$F\\hq$\"1mD(\\0MJx\"FC7$Fahq$\"1@@)4;Duv\"FC7$Ffhq$\"1V!\\C'e
'[t\"FC7$F[iq$\"1mglS;W,<FC7$F`iq$\"1u=b(o>=m\"FC7$Feiq$\"1\"GA6OeIh\"
FC7$Fjiq$\"1J\\euU?i:FC7$F_jq$\"1(*G_0$z9]\"FC7$Fdjq$\"1p)f7BrEV\"FC7$
Fijq$\"1BU*))p6'o8FC7$F^[r$\"18<]'z*o&H\"FC7$Fc[r$\"1zQ5SU%p@\"FC7$Fh[
r$\"1oThv`AP6FC7$F]\\r$\"1LGmmm>e5FC7$Fb\\r$\"1LD\"z\"f***o*Fjp7$Fg\\r
$\"10I#G-Y?)))Fjp7$F\\]r$\"1Gq;F5f>!)Fjp7$Fa]r$\"1DQM3@>WsFjp7$Ff]r$\"
1U[=\\Hq4kFjp7$F[^r$\"1=3$[`aKk&Fjp7$F`^r$\"11(p7s>!o[Fjp7$Fe^r$\"1e8%
*pT/UTFjp7$Fj^r$\"1X#3Y.SFU$Fjp7$F__r$\"1npg)4efx#Fjp7$Fd_r$\"1`#z\"*f
\")z;#Fjp7$Fi_r$\"1\\@q3^8D;Fjp7$F^`r$\"1!QCjCT[=\"Fjp7$Fc`r$\"1t.XJuU
gvF@7$Fh`r$\"1.O!p$)*\\sWF@7$F]ar$\"1#=XIAmG-#F@7$Fbar$\"1')3w)QD@a&F[
[lFe^lFf^lFj^lF`_l-%&TITLEG6#QGVarying~Alpha~While~Beta~is~Fixed~at~3F
^_l" 1 2 0 1 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 44 "This next
 section of code will animate Beta(" }{XPPEDIT 18 0 "alpha;" "6#%&alph
aG" }{TEXT -1 1 "," }{XPPEDIT 18 0 "beta;" "6#%%betaG" }{TEXT -1 30 ")
 distributions while holding " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }
{TEXT -1 27 " constant at 2 and varying " }{XPPEDIT 18 0 "beta;" "6#%%
betaG" }{TEXT -1 33 " from 1 to 4 with steps of 0.1.  " }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "alpha:
=2; beta[0]:=1.0; beta_step:=0.1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%&alphaG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%%betaG6#\"\"!$\"#5
!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*beta_stepG$\"\"\"!\"\"" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "for n from 0 to 30 do" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "  density[n]:=plot(f(alpha,beta[0]+
n*beta_step,x),x=0..1):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "  num:=c
onvert(evalf(beta[0]+n*beta_step),string):" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 60 "  tracker[n]:=textplot([0.3,0.4,`beta is `.num],color
=blue):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "  P[n]:=display(\{densit
y[n],tracker[n]\});" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 93 "display([seq(P[n], n=0..30)], insequence=
true,title=\"Alpha is Fixed at 2 While Beta Varies\");" }}{PARA 13 "" 
1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6$-%(ANIMATEG6A7&-%%TEXTG6%7$$
\"\"$!\"\"$\"\"%F-%,beta~is~1.0G-%'COLOURG6&%$RGBG\"\"!F5$\"*++++\"!\"
)-%'CURVESG6$7S7$F5F57$$\"1nmm;arz@!#<$\"1LLLL3VfVFA7$$\"1LL$e9ui2%FA$
\"1nmm\"H[D:)FA7$$\"1nmm\"z_\"4iFA$\"1LLLe0$=C\"!#;7$$\"1mmmT&phN)FA$
\"1LLL3RBr;FN7$$\"1LLe*=)H\\5FN$\"1mm;zjf)4#FN7$$\"1nm\"z/3uC\"FN$\"1L
L$e4;[\\#FN7$$\"1++DJ$RDX\"FN$\"1++]i'y]!HFN7$$\"1nm\"zR'ok;FN$\"1LL$e
zs$HLFN7$$\"1++D1J:w=FN$\"1++]7iI_PFN7$$\"1LLL3En$4#FN$\"1nmm;_M(=%FN7
$$\"1nm;/RE&G#FN$\"1LLL3y_qXFN7$$\"1+++D.&4]#FN$\"1+++]1!>+&FN7$$\"1++
+vB_<FFN$\"1+++]Z/NaFN7$$\"1+++v'Hi#HFN$\"1+++]$fC&eFN7$$\"1nm\"z*ev:J
FN$\"1LL$ez6:B'FN7$$\"1LLL347TLFN$\"1mmm;=C#o'FN7$$\"1LLLLY.KNFN$\"1mm
mm#pS1(FN7$$\"1++D\"o7Tv$FN$\"1++]i`A3vFN7$$\"1LLL$Q*o]RFN$\"1mmmm(y8!
zFN7$$\"1++D\"=lj;%FN$\"1++]i.tK$)FN7$$\"1++vV&R<P%FN$\"1++](3zMu)FN7$
$\"1LL$e9Ege%FN$\"1nmm\"H_?<*FN7$$\"1LLeR\"3Gy%FN$\"1nm;zihl&*FN7$$\"1
nm;/T1&*\\FN$\"1LLL3#G,***FN7$$\"1mm\"zRQb@&FN$\"1LLezw5V5!#:7$$\"1***
\\(=>Y2aFN$\"1++v$Q#\\\"3\"Fgt7$$\"1mm;zXu9cFN$\"1LL$e\"*[H7\"Fgt7$$\"
1+++]y))GeFN$\"1+++qvxl6Fgt7$$\"1****\\i_QQgFN$\"1++]_qn27Fgt7$$\"1***
\\7y%3TiFN$\"1++Dcp@[7Fgt7$$\"1****\\P![hY'FN$\"1++]2'HKH\"Fgt7$$\"1LL
L$Qx$omFN$\"1nmmwanL8Fgt7$$\"1+++v.I%)oFN$\"1+++v+'oP\"Fgt7$$\"1mm\"zp
e*zqFN$\"1LLeR<*fT\"Fgt7$$\"1+++D\\'QH(FN$\"1+++&)Hxe9Fgt7$$\"1KLe9S8&
\\(FN$\"1mm\"H!o-*\\\"Fgt7$$\"1***\\i?=bq(FN$\"1++DTO5T:Fgt7$$\"1LLL3s
?6zFN$\"1nmmT9C#e\"Fgt7$$\"1++DJXaE\")FN$\"1++D1*3`i\"Fgt7$$\"1nmmm*RR
L)FN$\"1LLL$*zym;Fgt7$$\"1mm;a<.Y&)FN$\"1LL$3N1#4<Fgt7$$\"1LLe9tOc()FN
$\"1nm\"HYt7v\"Fgt7$$\"1+++]Qk\\*)FN$\"1+++q(G**y\"Fgt7$$\"1LL$3dg6<*F
N$\"1nm;9@BM=Fgt7$$\"1mmmmxGp$*FN$\"1LLL`v&Q(=Fgt7$$\"1++D\"oK0e*FN$\"
1++DOl5;>Fgt7$$\"1++v=5s#y*FN$\"1++v.Uac>Fgt7$$\"\"\"F5$\"\"#F5-F26&F4
$\"#5F-F5F5-%+AXESLABELSG6$Q\"x6\"%!G-%%VIEWG6$;F5Fg[l%(DEFAULTG7&-F:6
$7jnF=7$F?$\"1+D1s#eS-&FA7$FE$\"1P#fA\\(3x$*FA7$FJ$\"1h)Q*G$\\^U\"FN7$
FP$\"1_g#ov/N\">FN7$FU$\"1e(RttdrR#FN7$FZ$\"1cwr@`PVGFN7$Fin$\"1\"))f<
A9JI$FN7$F^o$\"1KUxl,/wPFN7$Fco$\"1-\">7:#zWUFN7$Fho$\"1W$3^t!4CZFN7$F
]p$\"1bSLWqvV^FN7$Fbp$\"1Y;DSCH8cFN7$Fgp$\"1)G&\\$RK:3'FN7$F\\q$\"1mZ*
Qe$eHlFN7$Faq$\"1MSo$*ejLpFN7$Ffq$\"1t#fI%\\W5uFN7$F[r$\"1Fnj^q76yFN7$
F`r$\"1Be;&e)Ht#)FN7$Fer$\"1R!zr`:(y')FN7$Fjr$\"1LF63kL>\"*FN7$F_s$\"1
x*)QcjiM&*FN7$Fds$\"1h$)[6#HK'**FN7$Fis$\"1zx`AUBN5Fgt7$F^t$\"1-w***\\
&pw5Fgt7$Fct$\"1-$R/\"e;>6Fgt7$Fit$\"1w\")='\\3c:\"Fgt7$F^u$\"1<F-;rP%
>\"Fgt7$Fcu$\"16`[&yPPB\"Fgt7$Fhu$\"18J/42^r7Fgt7$F]v$\"1@:3$>4tI\"Fgt
7$Fbv$\"1GZJ8f6Y8Fgt7$Fgv$\"1(>ABCf+Q\"Fgt7$F\\w$\"1^?&G0J_T\"Fgt7$Faw
$\"1d\"4'=V/Y9Fgt7$Ffw$\"1\"psr>V%y9Fgt7$F[x$\"1(oY'GMa2:Fgt7$F`x$\"1F
r@^@KO:Fgt7$Fex$\"1mZ%pC(ei:Fgt7$Fjx$\"14\\3A/v(e\"Fgt7$F_y$\"1mWb_#z#
4;Fgt7$Fdy$\"14`sMf\"zi\"Fgt7$Fiy$\"1H?ML57U;Fgt7$F^z$\"1c]foiD];Fgt7$
$\"1nmT5ASg!*FN$\"1Jx<1f;_;Fgt7$Fcz$\"15FrA!=:l\"Fgt7$$\"1++voTAq#*FN$
\"1*)>`5FC[;Fgt7$Fhz$\"1K!Qu!)H<k\"Fgt7$$\"1L$eRA5\\Z*FN$\"1qII3d3I;Fg
t7$F][l$\"1gA)4m_;h\"Fgt7$$\"1+++]oi\"o*FN$\"1!y%)HMgVe\"Fgt7$Fb[l$\"1
h'GwK'*3a\"Fgt7$$\"1+D1k2/P)*FN$\"1A(3=W7b]\"Fgt7$$\"1+]P40O\"*)*FN$\"
1,W_'>tOX\"Fgt7$$\"1^7.#Q?&=**FN$\"1&y/LwFjT\"Fgt7$$\"1+voa-oX**FN$\"1
Ag!R\\tPO\"Fgt7$$\"1Cc,\">g#f**FN$\"1*RcGW3pK\"Fgt7$$\"1\\PMF,%G(**FN$
\"1:_:%[?fF\"Fgt7$$\"17y]&4I'z**FN$\"1n@#[c\"eS7Fgt7$$\"1v=nj+U')**FN$
\"1Uvxnp4#>\"Fgt7$$\"1Pf$=.5K***FN$\"1i*p>0AI6\"Fgt7$Fg[lF5F[\\l-F(6%F
*%,beta~is~1.1GF1F_\\lFe\\l7&-F:6$7gnF=7$F?$\"199f^49HdFA7$FE$\"1_hKqk
@n5FN7$FJ$\"1j-mrZL=;FN7$FP$\"1AO)p\"H'y;#FN7$FU$\"1O`&H72%4FFN7$FZ$\"
1'oNi?jl?$FN7$Fin$\"1$fUGY,ir$FN7$F^o$\"1T\"*>wwgPUFN7$Fco$\"1YlsUBV^Z
FN7$Fho$\"14LL@dgt_FN7$F]p$\"1\"Q#4%o>!GdFN7$Fbp$\"1\\le#=)=LiFN7$Fgp$
\"1$\\`(=jPLnFN7$F\\q$\"1BjD$eg%3sFN7$Faq$\"1&R#**4=wLwFN7$Ffq$\"1$H$p
AjgJ\")FN7$F[r$\"1Qz+(H%QY&)FN7$F`r$\"16#zdb)[?!*FN7$Fer$\"1U&\\sL3BV*
FN7$Fjr$\"1&)p5SHFv)*FN7$F_s$\"1!Q\"yZ\\!)G5Fgt7$Fds$\"1Oip#4()32\"Fgt
7$Fis$\"1:$z<S)f36Fgt7$F^t$\"1%R\\\\\"*=#[6Fgt7$Fct$\"1]rSnc9)=\"Fgt7$
Fit$\"1:TVD?#=A\"Fgt7$F^u$\"1')=qZJ*pD\"Fgt7$Fcu$\"1&\\4S-L>H\"Fgt7$Fh
u$\"1tQ:]SkC8Fgt7$F]v$\"1<JMST![N\"Fgt7$Fbv$\"1z4%*GTV'Q\"Fgt7$Fgv$\"1
rlh1E/89Fgt7$F\\w$\"1k%\\*zzPR9Fgt7$Faw$\"1@c%[P47Y\"Fgt7$Ffw$\"1r5_Xd
i#[\"Fgt7$F[x$\"1<>*Q9p,]\"Fgt7$F`x$\"1(G/)*z`a^\"Fgt7$Fex$\"1h$4EJ`p_
\"Fgt7$Fjx$\"1Ks:2JvM:Fgt7$F_y$\"1!=^oj>u`\"Fgt7$Fdy$\"1_V\")Q4>M:Fgt7
$Fiy$\"16Gg?PeB:Fgt7$F^z$\"1+>x`p[0:Fgt7$Fcz$\"1Khi\"Qr8Z\"Fgt7$Fhz$\"
1gPRgaBB9Fgt7$F][l$\"1Hc_*\\A8M\"Fgt7$Fhfl$\"1TU\"eqUFG\"Fgt7$Fb[l$\"1
zvv5-z+7Fgt7$F`gl$\"1[mgwd%*R6Fgt7$Fegl$\"1iG;Wu&p0\"Fgt7$Fjgl$\"1F0`l
-g+5Fgt7$F_hl$\"1J#ovVz=D*FN7$Fdhl$\"1y@cD,^Y()FN7$Fihl$\"1i*[L^Bi2)FN
7$F^il$\"1%yEx(H&)HwFN7$Fcil$\"1IsbfYLSqFN7$Fhil$\"1,-+7X8LhFNF\\jlF[
\\l-F(6%F*%,beta~is~1.2GF1F_\\lFe\\l7&-F:6$7hnF=7$F?$\"1`j\")))>SukFA7
$FE$\"1/g'Qr$o.7FN7$FJ$\"1H=Eq\\<@=FN7$FP$\"1aD&QQPRV#FN7$FU$\"1K]pw,y
MIFN7$FZ$\"1@D*p&*4Oe$FN7$Fin$\"1+x(*emLVTFN7$F^o$\"1J+VVH\"Gr%FN7$Fco
$\"1Dt$[>'pq_FN7$Fho$\"1@\\TO-3MeFN7$F]p$\"1DFydJE@jFN7$Fbp$\"1Z/(=bt#
foFN7$Fgp$\"1!o(eO+-)Q(FN7$F\\q$\"12%G>*)Gj)yFN7$Faq$\"1Ja5LP(*G$)FN7$
Ffq$\"1O3wOhnU))FN7$F[r$\"1)*>Xy'GnE*FN7$F`r$\"12EPJ1oY(*FN7$Fer$\"1ki
b79\"f,\"Fgt7$Fjr$\"1*\\W!fnwf5Fgt7$F_s$\"1:@;$39,5\"Fgt7$Fds$\"1G*G[n
w19\"Fgt7$Fis$\"1F&e&Q<[w6Fgt7$F^t$\"15^LHxZ87Fgt7$Fct$\"1!eMj[H+D\"Fg
t7$Fit$\"1plwby?!G\"Fgt7$F^u$\"1$=E:&3*4J\"Fgt7$Fcu$\"1A#*Q)e-2M\"Fgt7
$Fhu$\"1\"4JB&Hen8Fgt7$F]v$\"1uwl!p$R\"R\"Fgt7$Fbv$\"1Y)eeq8^T\"Fgt7$F
gv$\"1UF*RU)zL9Fgt7$F\\w$\"1v[K>qw]9Fgt7$Faw$\"1(4,GE]KY\"Fgt7$Ffw$\"1
'pZrPWMZ\"Fgt7$F[x$\"13#*R26Sz9Fgt7$F`x$\"1.h-_2U\"[\"Fgt7$Fex$\"1xzXa
%3(y9Fgt7$Fjx$\"1zB3z'y,Z\"Fgt7$F_y$\"16M$RVbbX\"Fgt7$Fdy$\"1,>oZZ&GV
\"Fgt7$Fiy$\"1f3y3g)3S\"Fgt7$F^z$\"18\"GC-i5O\"Fgt7$Fcz$\"1.cAB@3*H\"F
gt7$Fhz$\"1Plwc.sA7Fgt7$F`fl$\"1'fE,i^.<\"Fgt7$F][l$\"1<3k/LH16Fgt7$Fh
fl$\"1)HGTh,#H5Fgt7$Fb[l$\"1tu4e(RLF*FN7$F`gl$\"1d3ca^!Qb)FN7$Fegl$\"1
&*\\&fPSfh(FN7$Fjgl$\"1rAj[tR0qFN7$F_hl$\"1x)*yQu.?iFN7$Fdhl$\"1q!=OyA
Nr&FN7$Fihl$\"1s?6zq.m]FN7$F^il$\"1Pw.aXJ]YFN7$Fcil$\"1s2'[)R]?TFN7$Fh
il$\"1t&3L&[;\\LFNF\\jlF[\\l-F(6%F*%,beta~is~1.3GF1F_\\lFe\\l7&-F(6%F*
%,beta~is~1.4GF1-F:6$7hnF=7$F?$\"1#GvRtl&fsFA7$FE$\"1KU6-q,Z8FN7$FJ$\"
1.2V93YL?FN7$FP$\"1:_TERO6FFN7$FU$\"1[yM8essLFN7$FZ$\"1!3&)4&ywtRFN7$F
in$\"1XQs@0b$e%FN7$F^o$\"1UjaSZW+_FN7$Fco$\"1cw%3ID6!eFN7$Fho$\"1o/!G/
.QS'FN7$F]p$\"1Oh'=Eh:#pFN7$Fbp$\"1&QESq'R*[(FN7$Fgp$\"1AWoM66V!)FN7$F
\\q$\"1:'H#zhng&)FN7$Faq$\"1*pH/\"*\\m,*FN7$Ffq$\"13oF?m&4a*FN7$F[r$\"
1?99ACXp**FN7$F`r$\"1Bw[\")G#\\/\"Fgt7$Fer$\"1N!H\"*phc3\"Fgt7$Fjr$\"1
JsayRUG6Fgt7$F_s$\"1&*=9*\\%>n6Fgt7$Fds$\"1#Q#)zxTb?\"Fgt7$Fis$\"12A'f
\"zyQ7Fgt7$F^t$\"1CG&Q9ZCF\"Fgt7$Fct$\"1wN`UK)[I\"Fgt7$Fit$\"1$pZ$He#4
L\"Fgt7$F^u$\"1F!*Q*=[mN\"Fgt7$Fcu$\"1+rFGgY!Q\"Fgt7$Fhu$\"1uV:()f!4S
\"Fgt7$F]v$\"10U$poIyT\"Fgt7$Fbv$\"1grNDc7L9Fgt7$Fgv$\"15Q]^l^V9Fgt7$F
\\w$\"1bu^:g%3X\"Fgt7$Faw$\"1-Gw!3qQX\"Fgt7$Ffw$\"1/#\\)RN!HX\"Fgt7$F[
x$\"1Nf<[jaZ9Fgt7$F`x$\"1&*e$*><'oV\"Fgt7$Fex$\"1B[ohO#3U\"Fgt7$Fjx$\"
13IWl9M(R\"Fgt7$F_y$\"1<+ZzlIn8Fgt7$Fdy$\"1nPGb)yxK\"Fgt7$Fiy$\"1/o33s
-y7Fgt7$F^z$\"1+ME!z)*3A\"Fgt7$Fcz$\"1q4uC[-Q6Fgt7$Fhz$\"1o0e([lA/\"Fg
t7$F`fl$\"1M(>\"3f2&z*FN7$F][l$\"1e,ailK`!*FN7$Fhfl$\"1m*zB!HO$>)FN7$F
b[l$\"1`x$QL'o0rFN7$F`gl$\"1R<R<MZojFN7$Fegl$\"1n<_Ch!\\W&FN7$Fjgl$\"1
NX>:rPm[FN7$F_hl$\"1$fA8EG\"\\TFN7$Fdhl$\"1k0puD<.PFN7$Fihl$\"1?&4Y:QI
:$FN7$F^il$\"1zUKo,A7GFN7$Fcil$\"1;DAA*4GR#FN7$Fhil$\"1KmN%zVY\"=FNF\\
jlF[\\lF_\\lFe\\l7&-F(6%F*%,beta~is~1.5GF1-F:6$7gnF=7$F?$\"1$oSRwdV3)F
A7$FE$\"1P`?_O7(\\\"FN7$FJ$\"1/4xof)\\D#FN7$FP$\"1)*)=j)\\y**HFN7$FU$
\"1$\\M#pfqAPFN7$FZ$\"1smxF2JwVFN7$Fin$\"1G28ks!f.&FN7$F^o$\"1Rg;s8M*p
&FN7$Fco$\"19SE.3LTjFN7$Fho$\"1[\\t%\\d6)pFN7$F]p$\"10\"o:I3r_(FN7$Fbp
$\"1\\d&*Q)f:7)FN7$Fgp$\"1i-ru%*['p)FN7$F\\q$\"1g8XHLAH#*FN7$Faq$\"1O/
'H;UWp*FN7$Ffq$\"1QZr%\\2C-\"Fgt7$F[r$\"1%p-W%=Al5Fgt7$F`r$\"1Cd>g7f76
Fgt7$Fer$\"1$H6k`xA:\"Fgt7$Fjr$\"1q'zVdBL>\"Fgt7$F_s$\"1[nOT!3*H7Fgt7$
Fds$\"1po*=H%Rl7Fgt7$Fis$\"1VQSBd[&H\"Fgt7$F^t$\"1yec$**p^K\"Fgt7$Fct$
\"1(G\"\\1;%GN\"Fgt7$Fit$\"1%)**f@P?u8Fgt7$F^u$\"1**\\%***zI%R\"Fgt7$F
cu$\"1n\\<z:q69Fgt7$Fhu$\"1pm'fmS_U\"Fgt7$F]v$\"1g_=OK!\\V\"Fgt7$Fbv$
\"1;lt$*\\XT9Fgt7$Fgv$\"1Y4+IbPV9Fgt7$F\\w$\"1m]!=A;5W\"Fgt7$Faw$\"1gD
$Hx%oM9Fgt7$Ffw$\"1[ayt]'GU\"Fgt7$F[x$\"1&3!)Hj/nS\"Fgt7$F`x$\"1)pi?OD
TQ\"Fgt7$Fex$\"1k')*GT\")eN\"Fgt7$Fjx$\"1W<tfF/>8Fgt7$F_y$\"163Diljv7F
gt7$Fdy$\"1!QPsp0?A\"Fgt7$Fiy$\"1mA)3l!)z:\"Fgt7$F^z$\"19e>T/p(3\"Fgt7
$Fcz$\"1\"4$eroE,**FN7$Fhel$\"1TImu^4\"R*FN7$Fhz$\"1aC>\\cvB))FN7$F`fl
$\"1Y)R%R5&=9)FN7$F][l$\"1qcJ8H<etFN7$Fhfl$\"1(z(*4k-\"ykFN7$Fb[l$\"1b
*=#p1a2aFN7$F`gl$\"1d1]#*324ZFN7$Fegl$\"1d$*R*)=<mQFN7$Fjgl$\"1vz$oi'R
dLFN7$F_hl$\"1+f.t$4)[FFN7$Fdhl$\"1J)H)f\"*y$Q#FN7$Fihl$\"1?WW\\'4!\\>
FN7$Fcil$\"1m7KmX.!Q\"FNF\\jlF[\\lF_\\lFe\\l7&-F:6$7enF=7$F?$\"1!Ri%))
[][*)FA7$FE$\"1_dcs<\"Rl\"FN7$FJ$\"1_(*pXoa&[#FN7$FP$\"15Et#e\\))H$FN7
$FU$\"1\\\\#)f`>%3%FN7$FZ$\"17\"Q**\\L0z%FN7$Fin$\"1I))R%p.&*\\&FN7$F^
o$\"1f!)o.\"*Q3iFN7$Fco$\"1MP%>&3***)oFN7$Fho$\"1!=0!*e<Yc(FN7$F]p$\"1
z)=6[8i8)FN7$Fbp$\"1$=u[:6Rv)FN7$Fgp$\"1'40'*)f<Y$*FN7$F\\q$\"12\\[8%4
**))*FN7$Faq$\"1wofic-O5Fgt7$Ffq$\"19F'))y&**)3\"Fgt7$F[r$\"1Mt=()GIJ6
Fgt7$F`r$\"192\"Gr*[x6Fgt7$Fer$\"1q!*Rctf:7Fgt7$Fjr$\"10&z^#pLa7Fgt7$F
_s$\"1)oY='o;)G\"Fgt7$Fds$\"1H\"fgX*>?8Fgt7$Fis$\"1.,Lr#*fY8Fgt7$F^t$
\"1v=#oQX<P\"Fgt7$Fct$\"1h8uY[4%R\"Fgt7$Fit$\"16:T#eA.T\"Fgt7$F^u$\"1R
OX[;OC9Fgt7$Fcu$\"1xt^K\"G\\V\"Fgt7$Fhu$\"1.3pLRCT9Fgt7$F]v$\"13.DfSTV
9Fgt7$Fbv$\"1:Hp\\'z5W\"Fgt7$Fgv$\"1I3:N7_M9Fgt7$F\\w$\"1(o3i27EU\"Fgt
7$Faw$\"1=]5l_?29Fgt7$Ffw$\"1/qJR\\.&Q\"Fgt7$F[x$\"1a)*3=@we8Fgt7$F`x$
\"1_;4M[FD8Fgt7$Fex$\"1'yo%fd4'G\"Fgt7$Fjx$\"1#[5\\<9wB\"Fgt7$F_y$\"1G
&)f&QFH=\"Fgt7$Fdy$\"100Tt'oy6\"Fgt7$Fiy$\"1V$)*GxvG/\"Fgt7$F^z$\"1)R4
Pbd;j*FN7$Fcz$\"1#Gse!f[i&)FN7$Fhel$\"11<o^gd=!)FN7$Fhz$\"1jfprw.DuFN7
$F`fl$\"1*G/'p3!os'FN7$F][l$\"1cbE$o:V%fFN7$Fhfl$\"1\"o@.4054&FN7$Fb[l
$\"1wlzV(z.4%FN7$F`gl$\"1D;t6'G5Y$FN7$Fegl$\"1_z\"QJ8'GFFN7$Fjgl$\"1FY
k23M-BFN7$F_hl$\"1!)HDU&*45=FN7$Fihl$\"1OliM:[(>\"FNF\\jlF[\\l-F(6%F*%
,beta~is~1.6GF1F_\\lFe\\l7&-F:6$7YF=7$F?$\"1v!)3C^t^)*FA7$FE$\"1)['Q`-
H<=FN7$FJ$\"1HhhpD%\\s#FN7$FP$\"1nk^1K@3OFN7$FU$\"1;fjE7ocWFN7$FZ$\"1M
]0c;v:_FN7$Fin$\"1pzL6$oM(fFN7$F^o$\"1&z5>h?ls'FN7$Fco$\"1z<l=\"[eW(FN
7$Fho$\"1*fG>8WF:)FN7$F]p$\"1#*G*3\\&HZ()FN7$Fbp$\"1*)3.Lrt%Q*FN7$Fgp$
\"10%[d+i.***FN7$F\\q$\"1]%zZu(3a5Fgt7$Faq$\"1Y6lfNA,6Fgt7$Ffq$\"1pVZ3
3o`6Fgt7$F[r$\"1!f4Td>]>\"Fgt7$F`r$\"1Y=!Hjp%R7Fgt7$Fer$\"1(p54t(\\v7F
gt7$Fjr$\"1@L[pnP68Fgt7$F_s$\"1*3Pg,F>M\"Fgt7$Fds$\"1SAc0$o*p8Fgt7$Fis
$\"1`))H*H*>#R\"Fgt7$F^t$\"1*p<&=(=BT\"Fgt7$Fct$\"1je_bu()G9Fgt7$Fit$
\"1[u@bTgR9Fgt7$F^u$\"1H%*R'>NsW\"Fgt7$Fcu$\"1?J))[-p]9Fgt7$Fhu$\"1R=:
%G'e\\9Fgt7$F]v$\"1aI'43kTW\"Fgt7$Fbv$\"1#*G(pv`HV\"Fgt7$Fgv$\"1_Nv:70
=9Fgt7$F\\w$\"1>a>8u)oR\"Fgt7$Faw$\"1GA)QmEGP\"Fgt7$Ffw$\"1:&**Rbd4M\"
Fgt7$F[x$\"13#*elGR08Fgt7$F`x$\"1uXm-+5i7Fgt7$Fex$\"1N<m6\"RL@\"Fgt7$F
jx$\"1]u-#Ql\\:\"Fgt7$F_y$\"1M\\w_Y0\"4\"Fgt7$Fdy$\"1ky#Rj/r,\"Fgt7$Fi
y$\"1cr0'R(fT$*FN7$F^z$\"1dm8[%*3$[)FN7$Fcz$\"1hu0-+*[O(FN7$Fhel$\"19h
<&y=)4oFN7$Fhz$\"1._5IxU9iFN7$F`fl$\"1!p*\\ynyFbFN7$F][l$\"1()f;*z$HwZ
FN7$Fhfl$\"1'f&[K-RzRFN7$Fb[l$\"1hK=7dSxIFN7$F`gl$\"1>]q[%p+`#FN7$Fegl
$\"1Hcx7GS:>FN7$F_hl$\"1`;r^Pa&=\"FNF\\jlF[\\l-F(6%F*%,beta~is~1.7GF1F
_\\lFe\\l7&-F:6$7VF=7$F?$\"1F:7rxPz5FN7$FE$\"1j^6l(or)>FN7$FJ$\"1\"\\%
Q`\\(H(HFN7$FP$\"1!f&oJx`FRFN7$FU$\"1D#)33JmR[FN7$FZ$\"1Qu&pz+8l&FN7$F
in$\"1]\"R\"[/'pX'FN7$F^o$\"1V*z!4Nr_sFN7$Fco$\"1?[![U2x+)FN7$Fho$\"1&
4?H3\"=W()FN7$F]p$\"1)o#H`t()e$*FN7$Fbp$\"1:kO@bC,5Fgt7$Fgp$\"1@*oX\"*
RF1\"Fgt7$F\\q$\"18!z&)4Y!=6Fgt7$Faq$\"1$*zk^S([;\"Fgt7$Ffq$\"1_Em#>3j
@\"Fgt7$F[r$\"1qKL#QJiD\"Fgt7$F`r$\"1K-y+RT)H\"Fgt7$Fer$\"1WnT*H*)=L\"
Fgt7$Fjr$\"1Y\\R.BRk8Fgt7$F_s$\"1()p4#p#=\"R\"Fgt7$Fds$\"1.lbB4v99Fgt7
$Fis$\"1K4:#[&RK9Fgt7$F^t$\"1l=^DH2Z9Fgt7$Fct$\"1y5B:$euX\"Fgt7$Fit$\"
1Y@(o8+CY\"Fgt7$F^u$\"14DVzxPj9Fgt7$Fcu$\"1t<\\1eaf9Fgt7$Fhu$\"1Z]ur*Q
4X\"Fgt7$F]v$\"1@+_'fRzV\"Fgt7$Fbv$\"1yALHb*zT\"Fgt7$Fgv$\"1]-#=m.]R\"
Fgt7$F\\w$\"1$4eZz1]O\"Fgt7$Faw$\"12')*3$H#GL\"Fgt7$Ffw$\"1hd78e,#H\"F
gt7$F[x$\"1(el6&f1[7Fgt7$F`x$\"1?QHuY8'>\"Fgt7$Fex$\"1AL`SF<R6Fgt7$Fjx
$\"1c)fP+LE2\"Fgt7$F_y$\"1r%*Qq&f9+\"Fgt7$Fdy$\"1#G[=+i&4#*FN7$Fiy$\"1
xGexmPF$)FN7$F^z$\"1(4%Gg3UNuFN7$Fcz$\"1f68Lq@/jFN7$Fhz$\"1:h$[c$4w^FN
7$F`fl$\"1%42Oii0_%FN7$F][l$\"148=j`D>QFN7$Fhfl$\"1$yuR:![&4$FN7$Fb[l$
\"1v'*p.i6/BFN7$Fegl$\"18S$3cj!Q8FNF\\jlF[\\l-F(6%F*%,beta~is~1.8GF1F_
\\lFe\\l7&-F(6%F*%,beta~is~1.9GF1-F:6$7UF=7$F?$\"1\"4#))4jVx6FN7$FE$\"
1&3%*4vdM;#FN7$FJ$\"1ra3m%[%HKFN7$FP$\"1mX:;8\\cUFN7$FU$\"1)o9&*f_EB&F
N7$FZ$\"15(RT;Ol4'FN7$Fin$\"1V2)pTp\"\\pFN7$F^o$\"14#fg))))fy(FN7$Fco$
\"1f&p3ULWd)FN7$Fho$\"1gy![+_wL*FN7$F]p$\"1$H5!\\9ep**FN7$Fbp$\"1\\BIx
1cj5Fgt7$Fgp$\"1*p)eq*yb7\"Fgt7$F\\q$\"1I)H;9<2=\"Fgt7$Faq$\"18l?%fLoA
\"Fgt7$Ffq$\"1\"y?i)ouw7Fgt7$F[r$\"1cphNN#[J\"Fgt7$F`r$\"1E/%3vLUN\"Fg
t7$Fer$\"1*zUc.8ZQ\"Fgt7$Fjr$\"1d@hAZO89Fgt7$F_s$\"1MN925'fV\"Fgt7$Fds
$\"1y@m9/ja9Fgt7$Fis$\"1^ZZC'HtY\"Fgt7$F^t$\"1<29T3Aw9Fgt7$Fct$\"1tAM=
A8![\"Fgt7$Fit$\"1%>CG/$3z9Fgt7$F^u$\"1jr$Q*=Dt9Fgt7$Fcu$\"1\"Q3I!f0i9
Fgt7$Fhu$\"1;;$*QQ'fW\"Fgt7$F]v$\"1!)3c=C]D9Fgt7$Fbv$\"1,L?R$yqR\"Fgt7
$Fgv$\"1F9S\"4]jO\"Fgt7$F\\w$\"1tRg\\3/G8Fgt7$Faw$\"1&yBmrX$)G\"Fgt7$F
fw$\"1t$)zN_VR7Fgt7$F[x$\"1UN#*pj0)=\"Fgt7$F`x$\"1en_:onG6Fgt7$Fex$\"1
'pmO!)y[1\"Fgt7$Fjx$\"1()ftfVG=**FN7$F_y$\"1/@[E)e@:*FN7$Fdy$\"1g)341F
EI)FN7$Fiy$\"1\"yZ*>(>4R(FN7$F^z$\"1$R*))f&Q()['FN7$Fcz$\"1ml\"e[#ys`F
N7$Fhz$\"1p#=o[gCH%FN7$F][l$\"1(G#R$)>nSIFN7$Fhfl$\"1rFh.BT(R#FN7$Fb[l
$\"1D*)[*[?wr\"FN7$Fegl$\"1X&>f]=nI*FAF\\jlF[\\lF_\\lFe\\l7&-F:6$7SF=7
$F?$\"1uS@%HA$z7FN7$FE$\"1k!G?UogM#FN7$FJ$\"1G%eY?qT\\$FN7$FP$\"1Mba3$
[Zf%FN7$FU$\"1$G-J7t^j&FN7$FZ$\"1Pcp%=K3b'FN7$Fin$\"1!3.Ao8$\\uFN7$F^o
$\"1RZX0*4aK)FN7$Fco$\"1$3X1N[\\9*FN7$Fho$\"1=)oalc>$**FN7$F]p$\"1v()z
vC\"y0\"Fgt7$Fbp$\"1WHJV]GD6Fgt7$Fgp$\"1iC[`xT(=\"Fgt7$F\\q$\"1j*[$)fo
>C\"Fgt7$Faq$\"1]e#)\\u(pG\"Fgt7$Ffq$\"1rQb4s)[L\"Fgt7$F[r$\"1Kg$4m/2P
\"Fgt7$F`r$\"1w'Qt)e'oS\"Fgt7$Fer$\"1P]yLo$RV\"Fgt7$Fjr$\"1f!Q$zJIe9Fg
t7$F_s$\"1`n%zK<jZ\"Fgt7$Fds$\"1%)R))Qvr*[\"Fgt7$Fis$\"1Dhuh'pr\\\"Fgt
7$F^t$\"1Rf@Q&)***\\\"Fgt7$Fct$\"169%>f7s\\\"Fgt7$Fit$\"19h3([Q+\\\"Fg
t7$F^u$\"17J9Y`Kx9Fgt7$Fcu$\"1Vt#fpw(e9Fgt7$Fhu$\"1otzi`IN9Fgt7$F]v$\"
1z\\%R^#e29Fgt7$Fbv$\"1%4GffC5P\"Fgt7$Fgv$\"14pS95*HL\"Fgt7$F\\w$\"1#
\\1eskpG\"Fgt7$Faw$\"1[w*)3jUS7Fgt7$Ffw$\"1&G^B-\"H%=\"Fgt7$F[x$\"1ch&
\\Pek7\"Fgt7$F`x$\"1()*QTF531\"Fgt7$Fex$\"1E))3aN#\\\"**FN7$Fjx$\"1JkY
w:$[8*FN7$F_y$\"1)f(>zl!4L)FN7$Fdy$\"10]1z_RbuFN7$Fiy$\"1**zveF#Q`'FN7
$F^z$\"13V*[2)=ScFN7$Fcz$\"10_R&p^3c%FN7$Fhz$\"14UBZYfXNFN7$F][l$\"15/
g8AB6CFN7$Fb[l$\"1wT3%zZ`F\"FNF\\jlF[\\l-F(6%F*%,beta~is~2.0GF1F_\\lFe
\\l7&-F:6$7SF=7$F?$\"1B!3'4!4]Q\"FN7$FE$\"1Kx>^F\"\\`#FN7$FJ$\"1Aakk)
\\pw$FN7$FP$\"1-coa\"*)>%\\FN7$FU$\"1J%G)*pfn/'FN7$FZ$\"1]BMB?e8qFN7$F
in$\"1<;(40Sm&zFN7$F^o$\"1/JjJ/3q))FN7$Fco$\"1?9)[))H#=(*FN7$Fho$\"1va
<qnf_5Fgt7$F]p$\"1d_<H9L=6Fgt7$Fbp$\"15;SnbH'=\"Fgt7$Fgp$\"1V15PR8[7Fg
t7$F\\q$\"17mMZOo,8Fgt7$Faq$\"1g&QXF)>X8Fgt7$Ffq$\"1r;jd!R1R\"Fgt7$F[r
$\"1Hp&[h/QU\"Fgt7$F`r$\"1!e#3H)piX\"Fgt7$Fer$\"1=)=\")Q_&z9Fgt7$Fjr$
\"1?M:=6C*\\\"Fgt7$F_s$\"1y:.o5L7:Fgt7$Fds$\"1\\QlTf9?:Fgt7$Fis$\"1#y,
ZQ/@_\"Fgt7$F^t$\"1MUB^&f'=:Fgt7$Fct$\"1Uov$GD!4:Fgt7$Fit$\"1Z!Rzpec\\
\"Fgt7$F^u$\"1`owRY1w9Fgt7$Fcu$\"1+t#o*GD]9Fgt7$Fhu$\"1'frxc%e>9Fgt7$F
]v$\"1XyQ+F([Q\"Fgt7$Fbv$\"1wTXl=gS8Fgt7$Fgv$\"13!=i%Rv&H\"Fgt7$F\\w$
\"1!)e3:*eEC\"Fgt7$Faw$\"16%[p%)z**=\"Fgt7$Ffw$\"1lIGhq^F6Fgt7$F[x$\"1
r@C*>+U1\"Fgt7$F`x$\"1<$*fJ!pU$**FN7$Fex$\"1@k6aFK)>*FN7$Fjx$\"18@tdk!
HQ)FN7$F_y$\"1CHO`Y)fb(FN7$Fdy$\"14^X\\=YqmFN7$Fiy$\"1Kas<zFbdFN7$F^z$
\"1p^.wY\"\\)[FN7$Fcz$\"15K;t\"\\w&QFN7$Fhz$\"1[-iL>6=HFN7$F][l$\"1Ros
$H\">0>FN7$Fb[l$\"1'exFG'RN%*FAF\\jlF[\\l-F(6%F*%,beta~is~2.1GF1F_\\lF
e\\l7&-F:6$7SF=7$F?$\"1a#G>')pW\\\"FN7$FE$\"1b`lpM!*HFFN7$FJ$\"1V469(*
fZSFN7$FP$\"1#fR\"4.!zH&FN7$FU$\"1of!*H(epY'FN7$FZ$\"1MA+\\r>%[(FN7$Fi
n$\"1ajn*)GUq%)FN7$F^o$\"10&>jqV\">%*FN7$Fco$\"1<dF.4LH5Fgt7$Fho$\"1,o
IcF'=6\"Fgt7$F]p$\"1#e>AF/%y6Fgt7$Fbp$\"1I`)[nzkC\"Fgt7$Fgp$\"1%)\\Ljw
h28Fgt7$F\\q$\"1tS\"[&)f(f8Fgt7$Faq$\"1Z#eAz/9S\"Fgt7$Ffq$\"1YTw@-$RW
\"Fgt7$F[r$\"1YyFqC2u9Fgt7$F`r$\"1xCdoaU-:Fgt7$Fer$\"1$z&\\XBd@:Fgt7$F
jr$\"1EpfhHBO:Fgt7$F_s$\"15'e5#>5W:Fgt7$Fds$\"1#ez_#z1Y:Fgt7$Fis$\"1w*
4`\")QBa\"Fgt7$F^t$\"1$*pV$))pC`\"Fgt7$Fct$\"1AB-'G.f^\"Fgt7$Fit$\"1L%
QX6Pj\\\"Fgt7$F^u$\"1<sw.'H*p9Fgt7$Fcu$\"16yPvE,P9Fgt7$Fhu$\"1Hi2/XR*R
\"Fgt7$F]v$\"1LMAS]-e8Fgt7$Fbv$\"1J/8\"z?lI\"Fgt7$Fgv$\"1!)H*[D$Rb7Fgt
7$F\\w$\"1S*f%[=\"f>\"Fgt7$Faw$\"1,#\\m76y8\"Fgt7$Ffw$\"1#Q&*>9;*p5Fgt
7$F[x$\"1(R*4w$f?+\"Fgt7$F`x$\"1Sn8tI[s#*FN7$Fex$\"1?^O#>/`])FN7$Fjx$
\"1LpLqUWnwFN7$F_y$\"1(o[h4*[IoFN7$Fdy$\"1:&QSvR%[fFN7$Fiy$\"1@L/.Fu_]
FN7$F^z$\"1R_5\"G$z;UFN7$Fcz$\"1&=4Bk\"3_KFN7$Fhz$\"1(p<%3(QPR#FN7$F][
l$\"1\"Q+I(eP+:FN7$Fb[l$\"1q^.kf]dpFAF\\jlF[\\l-F(6%F*%,beta~is~2.2GF1
F_\\lFe\\l7&-F:6$7UF=7$$\"1LLL3x&)*3\"FA$\"1'3h0(G,b\")FA7$F?$\"1o`6w$
ywg\"FN7$$\"1++D\"y%*z7$FA$\"1lN_q@1yAFN7$FE$\"1dj#)fS&4$HFN7$FJ$\"12$
zJcMfL%FN7$FP$\"1*zM=9u@m&FN7$FU$\"1,$4&pxK&*oFN7$FZ$\"1gej,p5izFN7$Fi
n$\"1_&p&\\L'**)*)FN7$F^o$\"1)*[$30\"yr**FN7$Fco$\"1oQ%4\"o#p3\"Fgt7$F
ho$\"1VB\"f`%*3<\"Fgt7$F]p$\"1WJq<%GzB\"Fgt7$Fbp$\"1hQb'oMdI\"Fgt7$Fgp
$\"1]d!=wqdO\"Fgt7$F\\q$\"1)H^n;3hT\"Fgt7$Faq$\"1/&3$\\0_b9Fgt7$Ffq$\"
1>&=S#[q%\\\"Fgt7$F[r$\"1WoF]YZ@:Fgt7$F`r$\"1&*G`F3LX:Fgt7$Fer$\"1.Z.2
x-g:Fgt7$Fjr$\"19+r86Np:Fgt7$F_s$\"1l.&))[Y<d\"Fgt7$Fds$\"1\"zQqq]wc\"
Fgt7$Fis$\"1W9_k,4e:Fgt7$F^t$\"1\\.*)3PqT:Fgt7$Fct$\"1`;v\"G#==:Fgt7$F
it$\"1;kIARY#\\\"Fgt7$F^u$\"1'[6w3p$f9Fgt7$Fcu$\"1KC$fvj&>9Fgt7$Fhu$\"
1:EiGqHv8Fgt7$F]v$\"1;n4='[wK\"Fgt7$Fbv$\"1.!**>WM%p7Fgt7$Fgv$\"1B8e69
f77Fgt7$F\\w$\"1#HaLxBu9\"Fgt7$Faw$\"1f0Gf9i%3\"Fgt7$Ffw$\"1D6%))zq@,
\"Fgt7$F[x$\"1)exUw!y1%*FN7$F`x$\"1.3<1nYG')FN7$Fex$\"1)f')\\l&eSyFN7$
Fjx$\"1jxp\")3s\"*pFN7$F_y$\"11'p@rxe:'FN7$Fdy$\"12y0d6W)G&FN7$Fiy$\"1
F?u*GwCU%FN7$F^z$\"1*ys^F%)*GOFN7$Fcz$\"1sk(\\#*QKt#FN7$Fhz$\"1.A:nEid
>FN7$F][l$\"1&Gr@%H)z<\"FN7$Fb[l$\"1,a!Hw]Z6&FAF\\jlF[\\l-F(6%F*%,beta
~is~2.3GF1F_\\lFe\\l7&-F:6$7UF=7$Fh[t$\"1o[01A%yv)FA7$F?$\"1NZ%Q>3Ys\"
FN7$F`\\t$\"1CS#H,r8W#FN7$FE$\"1v.mY(yz8$FN7$FJ$\"1bk4J<xJYFN7$FP$\"1*
3\\B%)3X.'FN7$FU$\"1Ny)pIN9L(FN7$FZ$\"1^W0j!enW)FN7$Fin$\"1c%odg)e9&*F
N7$F^o$\"1&QA*f5s_5Fgt7$Fco$\"1c$fj(Q_W6Fgt7$Fho$\"1#)=X'R*fH7Fgt7$F]p
$\"10]B?!4oH\"Fgt7$Fbp$\"19_3js'RO\"Fgt7$Fgp$\"1AK44g]A9Fgt7$F\\q$\"12
H(y&>lq9Fgt7$Faq$\"1B&)eXF[2:Fgt7$Ffq$\"1kURe=#Ha\"Fgt7$F[r$\"1tLW+K*f
c\"Fgt7$F`r$\"1X2!f****\\e\"Fgt7$Fer$\"1(\\/5Yl\\f\"Fgt7$Fjr$\"1=3JcKo
)f\"Fgt7$F_s$\"1A*p*p_R&f\"Fgt7$Fds$\"1TN8=J2&e\"Fgt7$Fis$\"1s=q7Vep:F
gt7$F^t$\"1!*3%HpRma\"Fgt7$Fct$\"1o0h9p>;:Fgt7$Fit$\"1E\"*Q0CU%[\"Fgt7
$F^u$\"1Yf[rv\"[W\"Fgt7$Fcu$\"13Q4A0R)R\"Fgt7$Fhu$\"1(ohhm?yM\"Fgt7$F]
v$\"1/PrS%3VH\"Fgt7$Fbv$\"1#=!H!yQ*H7Fgt7$Fgv$\"19(oUHhz;\"Fgt7$F\\w$
\"1IG*=_6y4\"Fgt7$Faw$\"1\\P`lh,J5Fgt7$Ffw$\"1R1N`Na[&*FN7$F[x$\"1Z?xw
/y0))FN7$F`x$\"1N/OLJk1!)FN7$Fex$\"11.f%RHv?(FN7$Fjx$\"15z!et_wN'FN7$F
_y$\"1t?hk<KKbFN7$Fdy$\"1\"fKPUu%)o%FN7$Fiy$\"1GHE0F'*fQFN7$F^z$\"1eAh
7zM9JFN7$Fcz$\"1USWR`s!H#FN7$Fhz$\"1%*ev6!pkf\"FN7$F][l$\"1wd%H@\"oA#*
FA7$Fb[l$\"1'>sD)4^\\PFAF\\jlF[\\l-F(6%F*%,beta~is~2.4GF1F_\\lFe\\l7&-
F:6$7UF=7$Fh[t$\"1lTZxIy!Q*FA7$F?$\"1mRL\"3L_%=FN7$F`\\t$\"1&f,3O&e4EF
N7$FE$\"1cQQ2D*3N$FN7$FJ$\"1b-$3/J\\$\\FN7$FP$\"1b<#4O3YT'FN7$FU$\"17'
Qfeg[x(FN7$FZ$\"1y]9'[9w$*)FN7$Fin$\"1)*\\1<^O/5Fgt7$F^o$\"1(RBHho%36F
gt7$Fco$\"1\"fkO,S??\"Fgt7$Fho$\"1LEaC2*yG\"Fgt7$F]p$\"1IB\"pfe\\N\"Fg
t7$Fbp$\"1)fZL)G4@9Fgt7$Fgp$\"1NvwMkux9Fgt7$F\\q$\"1:\\oVhKB:Fgt7$Faq$
\"13'Qx9Tsb\"Fgt7$Ffq$\"11V3UQb)e\"Fgt7$F[r$\"1x+c+Ui2;Fgt7$F`r$\"1e*3
7Dh9i\"Fgt7$Fer$\"1>W>RkWE;Fgt7$Fjr$\"1VvmB*HVi\"Fgt7$F_s$\"1SqW')**=:
;Fgt7$Fds$\"1&o;0rA&)f\"Fgt7$Fis$\"1V\"3yw_qd\"Fgt7$F^t$\"1f__qybZ:Fgt
7$Fct$\"1cnT-xF5:Fgt7$Fit$\"1**fR;ges9Fgt7$F^u$\"1UB)yc#pE9Fgt7$Fcu$\"
1bVWw>&RP\"Fgt7$Fhu$\"1g<?n$fuJ\"Fgt7$F]v$\"1$p%pV__e7Fgt7$Fbv$\"1=p$y
*Rd)=\"Fgt7$Fgv$\"1uT$[E\\?7\"Fgt7$F\\w$\"1JU`kQhZ5Fgt7$Faw$\"1_f3cQ7v
(*FN7$Ffw$\"1dR)Q`=W)*)FN7$F[x$\"1oR?3([<A)FN7$F`x$\"1p9\"pq<.T(FN7$Fe
x$\"1.3*=Ui$3mFN7$Fjx$\"1$4a:Pegw&FN7$F_y$\"1(e!e@K+f\\FN7$Fdy$\"1_(ej
Xnd9%FN7$Fiy$\"1HC(4PR-O$FN7$F^z$\"1XSuraulEFN7$Fcz$\"1T*)[!4k[\">FN7$
Fhz$\"1&>9<[e&)H\"FN7$F][l$\"1!QB&=Q'=?(FA7$Fb[l$\"108cm\"Q:u#FAF\\jlF
[\\l-F(6%F*%,beta~is~2.5GF1F_\\lFe\\l7&-F:6$7YF=7$Fh[t$\"1jW\\>nP-5FN7
$F?$\"1F[%G\"p_p>FN7$F`\\t$\"1'\\!z1Nl#y#FN7$FE$\"1C_0P5hpNFN7$$\"1++v
oMrU^FA$\"1ueoOalBWFN7$FJ$\"1!G['[ZBX_FN7$$\"1nmmm6m#G(FA$\"1kR@3H\")R
gFN7$FP$\"1)3lbE#=-oFN7$FU$\"1(fI&GL>D#)FN7$FZ$\"1NlZ8m:M%*FN7$Fin$\"1
!>)44Gld5Fgt7$F^o$\"1S'ozd\\V;\"Fgt7$Fco$\"1+GH#p(Rf7Fgt7$Fho$\"1](pGs
(oX8Fgt7$F]p$\"1$e(yXmH79Fgt7$Fbp$\"1-b?G`.x9Fgt7$Fgp$\"1GS&RkC9`\"Fgt
7$F\\q$\"1K(*\\Bj2u:Fgt7$Faq$\"1%\\e+0dZg\"Fgt7$Ffq$\"1S)f(RbeJ;Fgt7$F
[r$\"1)=%pviPY;Fgt7$F`r$\"1*4<VJbZl\"Fgt7$Fer$\"1_#>#[Laa;Fgt7$Fjr$\"1
t;\"4I-kk\"Fgt7$F_s$\"1%p2o=\"GJ;Fgt7$Fds$\"1M*o0?$>3;Fgt7$Fis$\"1$=G,
-I2e\"Fgt7$F^t$\"1f37))ptW:Fgt7$Fct$\"1$*f0%[[2]\"Fgt7$Fit$\"1Ts;PgJd9
Fgt7$F^u$\"1(4C(oER09Fgt7$Fcu$\"1dU\\(Q!oY8Fgt7$Fhu$\"1P\\`r>n%G\"Fgt7
$F]v$\"1K2X\"*fx?7Fgt7$Fbv$\"1Uq4$[Ee9\"Fgt7$Fgv$\"1w:xi(Q`2\"Fgt7$F\\
w$\"1[xo+=(H(**FN7$Faw$\"1u*44OpaC*FN7$Ffw$\"1qqJkh?L%)FN7$F[x$\"1XY3v
K\"zl(FN7$F`x$\"1[$\\-qU=%oFN7$Fex$\"1lU>!*>PWgFN7$Fjx$\"1T&4$[Q)o@&FN
7$F_y$\"1u^)y3jVV%FN7$Fdy$\"1vw0'\\Fql$FN7$Fiy$\"1Y*))[RZ\"=HFN7$F^z$
\"1gfT<4DwAFN7$Fcz$\"1LZ,M$3of\"FN7$Fhz$\"1Rseq*)o`5FN7$F][l$\"1>H4iQD
5cFA7$Fhfl$\"1!=#e&[))ok$FA7$Fb[l$\"1hE!GZ&p**>FA7$Fegl$\"1mZS56zpm!#=
F\\jlF[\\l-F(6%F*%,beta~is~2.6GF1F_\\lFe\\l7&-F:6$7YF=7$Fh[t$\"1@'=rks
'o5FN7$F?$\"1.3I!pju4#FN7$F`\\t$\"1?5f'4C0'HFN7$FE$\"1J8#)z20%z$FN7$Ff
iu$\"1?u#otRlp%FN7$FJ$\"1P!>3d2Dc&FN7$F^ju$\"1oei6)yxR'FN7$FP$\"1;!Hks
Xp>(FN7$FU$\"1\\cY:O.#o)FN7$FZ$\"1t:Y!=\")e$**FN7$Fin$\"1=A4O?E66Fgt7$
F^o$\"1Y)3@5'H?7Fgt7$Fco$\"1;:&GxBlJ\"Fgt7$Fho$\"1dP*G;:HS\"Fgt7$F]p$
\"1lky1$\\(o9Fgt7$Fbp$\"1_#\\j@E<`\"Fgt7$Fgp$\"1o?I/A[$e\"Fgt7$F\\q$\"
1uc'H+eGi\"Fgt7$Faq$\"1^\">=L-+l\"Fgt7$Ffq$\"1#ej(3G,s;Fgt7$F[r$\"1DR7
`#pAo\"Fgt7$F`r$\"10d6&yL\\o\"Fgt7$Fer$\"1jCx:!R$z;Fgt7$Fjr$\"1H+$3G?]
m\"Fgt7$F_s$\"1H8Q`h#Qk\"Fgt7$Fds$\"1%4])oAG9;Fgt7$Fis$\"1jn+.8&3e\"Fg
t7$F^t$\"1[v;1BXQ:Fgt7$Fct$\"1TGF\"QCz[\"Fgt7$Fit$\"1>Zx'zf*Q9Fgt7$F^u
$\"1<4(f='H\"Q\"Fgt7$Fcu$\"1t_M^0)pJ\"Fgt7$Fhu$\"1N:,%G#))\\7Fgt7$F]v$
\"1hhtc\\\\\"=\"Fgt7$Fbv$\"1e+D&GJ@5\"Fgt7$Fgv$\"1(fyzEa#G5Fgt7$F\\w$
\"1])H-(Ghs%*FN7$Faw$\"15u$yiS[s)FN7$Ffw$\"1D0>xJ+)*yFN7$F[x$\"1?B([$z
p;rFN7$F`x$\"1BWtRgw-jFN7$Fex$\"1dzr2v2;bFN7$Fjx$\"1=pn#G&R4ZFN7$F_y$
\"1%G'eGnIcRFN7$Fdy$\"1IO7kqk=KFN7$Fiy$\"1/Wec\"=&GDFN7$F^z$\"1.X,3IHR
>FN7$Fcz$\"1@5<%Q&eG8FN7$Fhz$\"1'4YkS52`)FA7$F][l$\"1)422)pbgVFA7$Fhfl
$\"1'3Qf1Quv#FA7$Fb[l$\"1%Q4\"*>4`X\"FA7$Fegl$\"1:Ym;D)*GXF\\cvF\\jlF[
\\l-F(6%F*%,beta~is~2.7GF1F_\\lFe\\l7&-F:6$7ZF=7$Fh[t$\"1\"HuRHfp8\"FN
7$F?$\"1\\%=o_<!HAFN7$F`\\t$\"1qBZ/h9VJFN7$FE$\"1s%HY*)GT-%FN7$Ffiu$\"
1x9kk/yv\\FN7$FJ$\"1(QFRhwl)eFN7$F^ju$\"1Yn=%y?Fw'FN7$FP$\"1HIev$>')f(
FN7$$\"1++v=ddC%*FA$\"1;x*Q<i6R)FN7$FU$\"1'4Mph\"*\\9*FN7$FZ$\"1%4B^2I
U/\"Fgt7$Fin$\"183[:_8l6Fgt7$F^o$\"1;T8WNCw7Fgt7$Fco$\"1xM@D$\\LP\"Fgt
7$Fho$\"1lX1AJ]f9Fgt7$F]p$\"1*GF3,\\U_\"Fgt7$Fbp$\"1/=yMX5&e\"Fgt7$Fgp
$\"1+,-P!pQj\"Fgt7$F\\q$\"1I)yH$ejp;Fgt7$Faq$\"1HeFX&eHp\"Fgt7$Ffq$\"1
W/L'\\T)4<Fgt7$F[r$\"1!=%G$*GL:<Fgt7$F`r$\"11jb#od?r\"Fgt7$Fer$\"1$psA
xC4q\"Fgt7$Fjr$\"1!HwWp5.o\"Fgt7$F_s$\"1*)pqBq)Hl\"Fgt7$Fds$\"1W'R)='*
)ph\"Fgt7$Fis$\"1i#z]l]wd\"Fgt7$F^t$\"15')H[P(*G:Fgt7$Fct$\"1,Fz],6s9F
gt7$Fit$\"1rmq6$\\yT\"Fgt7$F^u$\"1_4WQ-wa8Fgt7$Fcu$\"1/so2&H_G\"Fgt7$F
hu$\"1.Vb*ezM@\"Fgt7$F]v$\"1]g&e>v59\"Fgt7$Fbv$\"1K)3A)[(y0\"Fgt7$Fgv$
\"1]LAhVl6)*FN7$F\\w$\"1\"HGeW_%y*)FN7$Faw$\"1m%=]7Hi@)FN7$Ffw$\"1uc_(
4C7Q(FN7$F[x$\"19HLpc$)*f'FN7$F`x$\"1?$=k$R'Rz&FN7$Fex$\"1S#))4/!QB]FN
7$Fjx$\"18>Oj9MUUFN7$F_y$\"1KSO/:PANFN7$Fdy$\"1U@&H[ko#GFN7$Fiy$\"1x0n
G%3j=#FN7$F^z$\"19N+1Su[;FN7$Fcz$\"1X`\\DV4.6FN7$Fhz$\"1WooMs)>*oFA7$F
][l$\"1cV0\"[6@Q$FA7$Fhfl$\"1*e?*3v`!3#FA7$Fb[l$\"1_`Wn#)*o0\"FA7$Fegl
$\"1vjJb#\\)oIF\\cvF\\jlF[\\l-F(6%F*%,beta~is~2.8GF1F_\\lFe\\l7&-F(6%F
*%,beta~is~2.9GF1-F:6$7XF=7$Fh[t$\"1ph6z)Hs?\"FN7$F?$\"1b[W`E;kBFN7$F`
\\t$\"1McgT)o/L$FN7$FE$\"13I7jKwfUFN7$Ffiu$\"1pf')fQDh_FN7$FJ$\"14([vO
rs@'FN7$F^ju$\"1BKb`wTMrFN7$FP$\"1<=n[#Hp+)FN7$Fc_w$\"1wO=hjpJ))FN7$FU
$\"1l'=\\U(o8'*FN7$FZ$\"1H#4vL%H&4\"Fgt7$Fin$\"1IDK?q@>7Fgt7$F^o$\"1[d
Lq.8K8Fgt7$Fco$\"1$o_uY4)H9Fgt7$Fho$\"1o0#ou'Q::Fgt7$F]p$\"1guQgTty:Fg
t7$Fbp$\"1C`)*3i6P;Fgt7$Fgp$\"13vEeGa#o\"Fgt7$F\\q$\"1h&R>\"HQ9<Fgt7$F
aq$\"1CjU\"3;Ot\"Fgt7$Ffq$\"1FGBNk3X<Fgt7$F[r$\"1IZ')RdgX<Fgt7$F`r$\"1
e5tJh>O<Fgt7$Fer$\"1$))\\v+*R><Fgt7$Fjr$\"1RUt]dS#p\"Fgt7$F_s$\"1Q:mb
\"H*e;Fgt7$Fds$\"1r%)=<`^;;Fgt7$Fis$\"1))=u)Hf8d\"Fgt7$F^t$\"1>oK-Wc;:
Fgt7$Fct$\"1aa6?*)f`9Fgt7$Fit$\"1QRUI.I%R\"Fgt7$F^u$\"1<5=a-7E8Fgt7$Fc
u$\"1*z(ylmx^7Fgt7$Fhu$\"1kL2]&>e<\"Fgt7$F]v$\"1.(p4Nq)*4\"Fgt7$Fbv$\"
17\\tu\")R85Fgt7$Fgv$\"1h-!HD8RM*FN7$F\\w$\"1L#\\#e/L$\\)FN7$Faw$\"1.&
\\FgY?s(FN7$Ffw$\"1Xo#>\"))o%)oFN7$F[x$\"1JWq_9Z3hFN7$F`x$\"1#[oMIedJ&
FN7$Fex$\"18^4Z8plXFN7$Fjx$\"1e<@%***39QFN7$F_y$\"1ijz\"3i)HJFN7$Fdy$
\"1&Q^\"zn)yZ#FN7$Fiy$\"1h$)z`Yp')=FN7$F^z$\"1_8vr#o*)R\"FN7$Fcz$\"1ka
X9bsS\"*FA7$Fhz$\"1]'z-a/rb&FA7$F][l$\"14PnaY0=EFA7$Fb[l$\"1A%zZ9z/m(F
\\cvF\\jlF[\\lF_\\lFe\\l7&-F(6%F*%,beta~is~3.0GF1-F:6$7XF=7$Fh[t$\"1'f
Tojx%z7FN7$F?$\"1sk(yTtG]#FN7$F`\\t$\"10#fI&>WANFN7$FE$\"1\\Z*H[s3]%FN
7$Ffiu$\"1i+k\\v$Gb&FN7$FJ$\"1*e+dnBWb'FN7$F^ju$\"1RgG1>l7vFN7$FP$\"19
7u*p1;U)FN7$Fc_w$\"1JASs;?y#*FN7$FU$\"1f#*\\&3v(35Fgt7$FZ$\"15V=@_tY6F
gt7$Fin$\"1Ti:9VXt7Fgt7$F^o$\"1Crb[!)*yQ\"Fgt7$Fco$\"1Xy.0K%e[\"Fgt7$F
ho$\"1$ef\">g]q:Fgt7$F]p$\"1GN$z\")[@j\"Fgt7$Fbp$\"1ewm(o8xo\"Fgt7$Fgp
$\"1fFDW'o%H<Fgt7$F\\q$\"1[l6B,3d<Fgt7$Faq$\"1sbp$Qt>x\"Fgt7$Ffq$\"11j
)e]qxx\"Fgt7$F[r$\"1mD(\\0MJx\"Fgt7$F`r$\"1@@)4;Duv\"Fgt7$Fer$\"1V!\\C
'e'[t\"Fgt7$Fjr$\"1mglS;W,<Fgt7$F_s$\"1u=b(o>=m\"Fgt7$Fds$\"1\"GA6OeIh
\"Fgt7$Fis$\"1J\\euU?i:Fgt7$F^t$\"1(*G_0$z9]\"Fgt7$Fct$\"1p)f7BrEV\"Fg
t7$Fit$\"1BU*))p6'o8Fgt7$F^u$\"18<]'z*o&H\"Fgt7$Fcu$\"1zQ5SU%p@\"Fgt7$
Fhu$\"1oThv`AP6Fgt7$F]v$\"1LGmmm>e5Fgt7$Fbv$\"1LD\"z\"f***o*FN7$Fgv$\"
10I#G-Y?)))FN7$F\\w$\"1Gq;F5f>!)FN7$Faw$\"1DQM3@>WsFN7$Ffw$\"1U[=\\Hq4
kFN7$F[x$\"1=3$[`aKk&FN7$F`x$\"11(p7s>!o[FN7$Fex$\"1e8%*pT/UTFN7$Fjx$
\"1X#3Y.SFU$FN7$F_y$\"1npg)4efx#FN7$Fdy$\"1`#z\"*f\")z;#FN7$Fiy$\"1\\@
q3^8D;FN7$F^z$\"1!QCjCT[=\"FN7$Fcz$\"1t.XJuUgvFA7$Fhz$\"1.O!p$)*\\sWFA
7$F][l$\"1#=XIAmG-#FA7$Fb[l$\"1')3w)QD@a&F\\cvF\\jlF[\\lF_\\lFe\\l7&-F
(6%F*%,beta~is~3.1GF1-F:6$7XF=7$Fh[t$\"1vAM;ep`8FN7$F?$\"1?')R$GC^k#FN
7$F`\\t$\"1%4=^T:!>PFN7$FE$\"1>SyhePZZFN7$Ffiu$\"15KcM0T]eFN7$FJ$\"1!)
*z\"4x'y*oFN7$F^ju$\"11'\\zj4s*yFN7$FP$\"1nN,=$)QU))FN7$Fc_w$\"1LdJ@aO
I(*FN7$FU$\"10ADD@oc5Fgt7$FZ$\"1'40m^3&)>\"Fgt7$Fin$\"1c7g(3'zF8Fgt7$F
^o$\"1:OYX4\\V9Fgt7$Fco$\"1QGcvKRT:Fgt7$Fho$\"1\">7B`0[i\"Fgt7$F]p$\"1
<1&ySUWo\"Fgt7$Fbp$\"1WvnZb&ot\"Fgt7$Fgp$\"1\\eND\"=Yx\"Fgt7$F\\q$\"1(
*y!>^:xz\"Fgt7$Faq$\"1+fd8i.3=Fgt7$Ffq$\"1h*=wwBz!=Fgt7$F[r$\"17B^S3(z
z\"Fgt7$F`r$\"1.a\"ygEex\"Fgt7$Fer$\"1:&H90Muu\"Fgt7$Fjr$\"1V9)*)Hdvq
\"Fgt7$F_s$\"11&G8GE=m\"Fgt7$Fds$\"1]M!fX:og\"Fgt7$Fis$\"1[+94tS]:Fgt7
$F^t$\"1*)3\"[[kR[\"Fgt7$Fct$\"1`3VbVf49Fgt7$Fit$\"1B[1.]1T8Fgt7$F^u$
\"1a`-i1wj7Fgt7$Fcu$\"1hcYOz-\"=\"Fgt7$Fhu$\"1k=j/#*)z4\"Fgt7$F]v$\"1p
T#=:Nj,\"Fgt7$Fbv$\"1h!)pvBQ\\#*FN7$Fgv$\"1/#fIjc$G%)FN7$F\\w$\"1e&)y$
pM\"fvFN7$Faw$\"1d)p'*R9Ty'FN7$Ffw$\"1.F#f0Jr&fFN7$F[x$\"1#Q]Fn?W?&FN7
$F`x$\"1#47<.d-X%FN7$Fex$\"1h!H)=d=^PFN7$Fjx$\"1;UOmY@mIFN7$F_y$\"1T$)
4/&)zdCFN7$Fdy$\"1T@[WRa$*=FN7$Fiy$\"1*HcJC2uR\"FN7$F^z$\"1(yIm<Z<+\"F
N7$Fcz$\"1n>5\"o([UiFA7$Fhz$\"1Q,xhaL$f$FA7$F][l$\"1RuQoaFg:FA7$Fb[l$
\"1z>;U@g-SF\\cvF\\jlF[\\lF_\\lFe\\l7&-F(6%F*%,beta~is~3.2GF1-F:6$7XF=
7$Fh[t$\"1)p$y\"ox)H9FN7$F?$\"1;`mG)*)3z#FN7$F`\\t$\"1k`zL&R,#RFN7$FE$
\"1(o@AT$>**\\FN7$Ffiu$\"1f/twJ&Q:'FN7$FJ$\"1V]PS*RuC(FN7$F^ju$\"1)*)>
j]!)yG)FN7$FP$\"1Q4i[e,p#*FN7$Fc_w$\"1!4^-?)y=5Fgt7$FU$\"1r8cIZ006Fgt7
$FZ$\"1nVG`9d]7Fgt7$Fin$\"1R3'pR$>#Q\"Fgt7$F^o$\"1>zEFi&))\\\"Fgt7$Fco
$\"1Kk=**fS'f\"Fgt7$Fho$\"1\"\\ebFM#y;Fgt7$F]p$\"1I%=<Vpbt\"Fgt7$Fbp$
\"1Cif=h]%y\"Fgt7$Fgp$\"1([o#3$pz\"=Fgt7$F\\q$\"1a=G,PGO=Fgt7$Faq$\"1V
#Hc'p\"=%=Fgt7$Ffq$\"1Km6bEeN=Fgt7$F[r$\"1s%e-%\\<?=Fgt7$F`r$\"1>\"=e7
([\"z\"Fgt7$Fer$\"1yC&e!e@d<Fgt7$Fjr$\"1G)*=4L*3r\"Fgt7$F_s$\"1R5[Jg6f
;Fgt7$Fds$\"1OrI!)*zzf\"Fgt7$Fis$\"1f%4\"*)Q=O:Fgt7$F^t$\"1<6O>iDk9Fgt
7$Fct$\"1'os(R=i%Q\"Fgt7$Fit$\"1lP\"QWC>J\"Fgt7$F^u$\"1A^T+KgI7Fgt7$Fc
u$\"1ss:LyHW6Fgt7$Fhu$\"1iB(Qjt$e5Fgt7$F]v$\"1Yf>d#Q`u*FN7$Fbv$\"19665
-P9))FN7$Fgv$\"1F[oihw%)zFN7$F\\w$\"15iAUwY8rFN7$Faw$\"1s`&3cpGM'FN7$F
fw$\"1`^4!piu_&FN7$F[x$\"1?G?`['=z%FN7$F`x$\"1cht'o%phSFN7$Fex$\"1Wv!4
=c;R$FN7$Fjx$\"1FcencLUFFN7$F_y$\"1w4j)QYD<#FN7$Fdy$\"1Bu6iE9^;FN7$Fiy
$\"1\"eR69E'*>\"FN7$F^z$\"1Nk=**3ib%)FA7$Fcz$\"18S@ed'e9&FA7$Fhz$\"1#p
])Q'pA)GFA7$F][l$\"1Po1nG],7FA7$Fb[l$\"1DmxU0,')GF\\cvF\\jlF[\\lF_\\lF
e\\l7&-F:6$7YF=7$Fh[t$\"1UwF7l,3:FN7$F?$\"1#eqsuW,%HFN7$F`\\t$\"1>e0V
\\wDTFN7$FE$\"1HsAZeCc_FN7$Ffiu$\"1rwR(=ZIY'FN7$FJ$\"1;Dx<\"zHg(FN7$F^
ju$\"1KB]%odWo)FN7$FP$\"1tKp8hB,(*FN7$Fc_w$\"1Inuw_/l5Fgt7$FU$\"1TH/'o
eQ:\"Fgt7$$\"1++v=JN[6FN$\"1<v0pH(3B\"Fgt7$FZ$\"1[=,lE)GI\"Fgt7$Fin$\"
1!4TUI*fO9Fgt7$F^o$\"1\"4EKwVRb\"Fgt7$Fco$\"1u0(R8J3l\"Fgt7$Fho$\"1-i>
FauI<Fgt7$F]p$\"1&=;d>*[&y\"Fgt7$Fbp$\"19&Ga7N1$=Fgt7$Fgp$\"1q41Cg]f=F
gt7$F\\q$\"1Y)=EM&ys=Fgt7$Faq$\"1FHCGSLt=Fgt7$Ffq$\"1A\\8N#*yg=Fgt7$F[
r$\"1_;H;-\")R=Fgt7$F`r$\"1Hn<%G(\\/=Fgt7$Fer$\"1w\")GFfKk<Fgt7$Fjr$\"
1W&H%Q4f6<Fgt7$F_s$\"1pYgAX&Ql\"Fgt7$Fds$\"1Q#y!>6u'e\"Fgt7$Fis$\"1^4#
p^U(>:Fgt7$F^t$\"1,Hh&\\!eU9Fgt7$Fct$\"1Q=-^K*zN\"Fgt7$Fit$\"1U.p/pV\"
G\"Fgt7$F^u$\"1%z.;\"oY'>\"Fgt7$Fcu$\"1#3a*3%**p5\"Fgt7$Fhu$\"1jbuZLh=
5Fgt7$F]v$\"1dh1#)**4I$*FN7$Fbv$\"1O]*R@doQ)FN7$Fgv$\"1)*G&*e3&Gb(FN7$
F\\w$\"1CLEjwu$o'FN7$Faw$\"12^%*oP<@fFN7$Ffw$\"1&p?Jor37&FN7$F[x$\"1Go
lR^?0WFN7$F`x$\"1k%4\"***Q8q$FN7$Fex$\"1dI&e.a=1$FN7$Fjx$\"1(4DfA$))[C
FN7$F_y$\"10,aXwV<>FN7$Fdy$\"1e<Yc3bP9FN7$Fiy$\"1!*HD;*[#G5FN7$F^z$\"1
E<bc-FErFA7$Fcz$\"19A%=JV`B%FA7$Fhz$\"1KYd]dM3BFA7$F][l$\"1()pD.c*zB*F
\\cv7$Fb[l$\"1c*p`')*px?F\\cvF\\jlF[\\l-F(6%F*%,beta~is~3.3GF1F_\\lFe
\\l7&-F:6$7fnF=7$Fh[t$\"15Z&=g0\")e\"FN7$F?$\"1&=@t%Q'G4$FN7$F`\\t$\"1
K#[IgUeL%FN7$FE$\"1*RP\\da%=bFN7$Ffiu$\"1!*fu9c(yx'FN7$FJ$\"1x]rSiKkzF
N7$F^ju$\"1TTf9yt'3*FN7$FP$\"1[3X$4!)Q,\"Fgt7$Fc_w$\"1$e_-fy<6\"Fgt7$F
U$\"1h&oRngI?\"Fgt7$F`cz$\"1cCYi:$>G\"Fgt7$FZ$\"17B!e:-aN\"Fgt7$Fin$\"
1==m=)o4\\\"Fgt7$F^o$\"1l)\\>.1(3;Fgt7$Fco$\"1?h4O<i/<Fgt7$Fho$\"1mM^b
hH#y\"Fgt7$F]p$\"1'zI)\\b;M=Fgt7$Fbp$\"1B+w[t@v=Fgt7$$\"1+++]jB4EFN$\"
1$fSqA$H*)=Fgt7$Fgp$\"1'Q$3,v@**=Fgt7$$\"1+++Dg(=#GFN$\"1$fQBm.]!>Fgt7
$F\\q$\"1VdB+mA2>Fgt7$$\"1L$eky#*4-$FN$\"1KG9>rF1>Fgt7$Faq$\"1'=cw=6E!
>Fgt7$Ffq$\"1?^z>0f$)=Fgt7$F[r$\"1\">4[zWp&=Fgt7$F`r$\"1![-Hv]\\\"=Fgt
7$Fer$\"14o)=%4))o<Fgt7$Fjr$\"1E)o1H\"z4<Fgt7$F_s$\"1JY)4-0ik\"Fgt7$Fd
s$\"1yg;WJGt:Fgt7$Fis$\"1Q8#e7%G,:Fgt7$F^t$\"1AW$)GE:>9Fgt7$Fct$\"1,(H
e3M*H8Fgt7$Fit$\"1\\Xgy@$)\\7Fgt7$F^u$\"1oHF$e!eh6Fgt7$Fcu$\"1'3N$yYNp
5Fgt7$Fhu$\"1(\\\\[1o\"*y*FN7$F]v$\"1XPAYa_>*)FN7$Fbv$\"1[)eMbR%ozFN7$
Fgv$\"1\\8-`\"yQ8(FN7$F\\w$\"1\\7RRn#3F'FN7$Faw$\"1$>3zF^%>bFN7$Ffw$\"
1g[)o\"*ost%FN7$F[x$\"1$*GsL$QQ/%FN7$F`x$\"1V;0LW.oLFN7$Fex$\"1eI'H$)*
3gFFN7$Fjx$\"1[xAqGk$=#FN7$F_y$\"1*R9yO;)*o\"FN7$Fdy$\"1l#*30Pw\\7FN7$
Fiy$\"17..V*)o+))FA7$F^z$\"1<]BAK:(*fFA7$Fcz$\"1,up'QY3[$FA7$Fhz$\"13O
j;j+Y=FA7$F][l$\"1\"o!HIyX#4(F\\cv7$Fb[l$\"1RpF*>)f$\\\"F\\cvF\\jlF[\\
l-F(6%F*%,beta~is~3.4GF1F_\\lFe\\l7&-F:6$7fnF=7$Fh[t$\"1>pVf#Q,n\"FN7$
F?$\"1'y550A!\\KFN7$F`\\t$\"1ugM)zB.b%FN7$FE$\"1_jw$pTdy&FN7$Ffiu$\"1[
[uJGA)4(FN7$FJ$\"1([1W`C8L)FN7$F^ju$\"1/a)='4_%\\*FN7$FP$\"1L\"paqY\"e
5Fgt7$Fc_w$\"1LI(3jf*e6Fgt7$FU$\"1K(GkDGED\"Fgt7$F`cz$\"1U<I&=kKL\"Fgt
7$FZ$\"1Cpbm7439Fgt7$Fin$\"1dbiR)e_a\"Fgt7$F^o$\"1Q1YI!)4j;Fgt7$Fco$\"
1yu![-Mxv\"Fgt7$Fho$\"1+')[Fu%G$=Fgt7$F]p$\"1=DTQmc\")=Fgt7$Fbp$\"1l`i
,BB=>Fgt7$F`_[l$\"1@E=Z?#)H>Fgt7$Fgp$\"1Fd]hz4P>Fgt7$Fh_[l$\"1*4.o?(>S
>Fgt7$F\\q$\"1CC!ym='R>Fgt7$F``[l$\"1@osr,/O>Fgt7$Faq$\"1S#\\F2x'H>Fgt
7$Ffq$\"1Kr$G$y./>Fgt7$F[r$\"1'=vkP];(=Fgt7$F`r$\"1^`=nN%H#=Fgt7$Fer$
\"1I4OZ$)*4x\"Fgt7$Fjr$\"1$H#>nXj0<Fgt7$F_s$\"1<6m'yFjj\"Fgt7$Fds$\"1$
3$4G[yd:Fgt7$Fis$\"1!4\"yM;+\"[\"Fgt7$F^t$\"1*[N!Gq<%R\"Fgt7$Fct$\"1C1
.@el+8Fgt7$Fit$\"1%=ARKBt@\"Fgt7$F^u$\"1ZbdOS:E6Fgt7$Fcu$\"1p=P+McJ5Fg
t7$Fhu$\"1P.+(fzYR*FN7$F]v$\"1xj<T9C:&)FN7$Fbv$\"1MAC&>S/c(FN7$Fgv$\"1
$H[3ZS)GnFN7$F\\w$\"1Rv3A-HveFN7$Faw$\"1\\kMox(y8&FN7$Ffw$\"1/O9?!\\jP
%FN7$F[x$\"18Ong\"))pq$FN7$F`x$\"1+]>I5^gIFN7$Fex$\"1>hMh*HY[#FN7$Fjx$
\"1l')=X;WW>FN7$F_y$\"1alRs%fr[\"FN7$Fdy$\"1r=,il+&3\"FN7$Fiy$\"1:)y\"
>j-AvFA7$F^z$\"1L=uoy'*R]FA7$Fcz$\"1:29Yn!o&GFA7$Fhz$\"1!pMb4IUZ\"FA7$
F][l$\"1R(R#3PqPaF\\cv7$Fb[l$\"1?!4`^@A2\"F\\cvF\\jlF[\\l-F(6%F*%,beta
~is~3.5GF1F_\\lFe\\l7&-F:6$7fnF=7$Fh[t$\"1L.\")3y5a<FN7$F?$\"1?b>%R%f3
MFN7$F`\\t$\"1Jn>O,;pZFN7$FE$\"1;q\\()*H!egFN7$Ffiu$\"1kF6CX(RU(FN7$FJ
$\"1DA;D%>Qq)FN7$F^ju$\"1fHfp0h2**FN7$FP$\"18[W1'**G5\"Fgt7$Fc_w$\"1$f
^$[0c17Fgt7$FU$\"1`Y!y&)HDI\"Fgt7$F`cz$\"1dQ=hh$[Q\"Fgt7$FZ$\"1dTUUE\"
4Y\"Fgt7$Fin$\"1d:6,\"G%*f\"Fgt7$F^o$\"1FB\"f=xqr\"Fgt7$Fco$\"1s=%>DF,
\"=Fgt7$Fho$\"1P![\\#QO#)=Fgt7$F]p$\"1w'Q;mkw#>Fgt7$$\"1LLe9r5$R#FN$\"
1g/@?M3Y>Fgt7$Fbp$\"1\"\\iB#Rmf>Fgt7$F`_[l$\"1v@Hy%Q'o>Fgt7$Fgp$\"1`XN
Si9t>Fgt7$Fh_[l$\"1jwW0GXt>Fgt7$F\\q$\"1K![\\Jx*p>Fgt7$Faq$\"1g'>#QYca
>Fgt7$Ffq$\"1YNTDi=A>Fgt7$F[r$\"1#yyng,S)=Fgt7$F`r$\"1N'[ZYt&G=Fgt7$Fe
r$\"1(3`Z%fzq<Fgt7$Fjr$\"1a8WC%f#*p\"Fgt7$F_s$\"1pah$\\zVi\"Fgt7$Fds$
\"1EtQu*=/a\"Fgt7$Fis$\"1vw\\D'z!f9Fgt7$F^t$\"1U)GO3ZyO\"Fgt7$Fct$\"1C
]R!3c.F\"Fgt7$Fit$\"1UlNCr5%=\"Fgt7$F^u$\"1a9\"G&zP!4\"Fgt7$Fcu$\"1WW_
LL/Q**FN7$Fhu$\"1*e9GezU+*FN7$F]v$\"1NkLsXj=\")FN7$Fbv$\"15pc5f$R;(FN7
$Fgv$\"1cT+Yn[QjFN7$F\\w$\"1.2SVE\\(\\&FN7$Faw$\"1#3)>q#>kx%FN7$Ffw$\"
1>dAB9jPSFN7$F[x$\"1Uu+'oYPR$FN7$F`x$\"1'pgk+Cux#FN7$Fex$\"1RUf1=tLAFN
7$Fjx$\"13?()4`<H<FN7$F_y$\"1prHuE428FN7$Fdy$\"1)4ps7dtS*FA7$Fiy$\"19/
%\\a@2U'FA7$F^z$\"1ND`7\"3+B%FA7$Fcz$\"1@ZfoGdTBFA7$Fhz$\"1#pUjp&yv6FA
7$F][l$\"1Q;)G(GcjTF\\cv7$Fb[l$\"1+n0JD;(o(!#>F\\jlF[\\l-F(6%F*%,beta~
is~3.6GF1F_\\lFe\\l7&-F(6%F*%,beta~is~3.7GF1-F:6$7fnF=7$Fh[t$\"1Sxf)e2
+%=FN7$F?$\"1x4(f-c:d$FN7$F`\\t$\"1X\"zZa.B*\\FN7$FE$\"1QNS?HCNjFN7$Ff
iu$\"1)>v$yw,bxFN7$FJ$\"1#Q.f^e;3*FN7$F^ju$\"1V@TT8eK5Fgt7$FP$\"1>CeKa
6[6Fgt7$Fc_w$\"1\"z@/9aXD\"Fgt7$FU$\"1IOaZZt_8Fgt7$F`cz$\"1.\"QJ'QhO9F
gt7$FZ$\"1Po%3?IQ^\"Fgt7$Fin$\"1RBY<rV`;Fgt7$F^o$\"1Z@\"*pKgq<Fgt7$Fco
$\"1eI!fdj<'=Fgt7$Fho$\"1sB#zO83$>Fgt7$F]p$\"1#)=YZcVs>Fgt7$Fae\\l$\"1
2V$*Q4[))>Fgt7$Fbp$\"15tv#G+&**>Fgt7$F`_[l$\"1pV)*ext0?Fgt7$Fgp$\"1WZ&
fUlt+#Fgt7$Fh_[l$\"1&)oQ-<y/?Fgt7$F\\q$\"1\"oPCYA$)*>Fgt7$Faq$\"1dp*Qo
5t(>Fgt7$Ffq$\"1%[3#QR4Q>Fgt7$F[r$\"1%pb@]vS*=Fgt7$F`r$\"1+!*\\!HR>$=F
gt7$Fer$\"1!RXxC\"Ro<Fgt7$Fjr$\"17r+?C!3p\"Fgt7$F_s$\"1?F!ou70h\"Fgt7$
Fds$\"1spW^?N@:Fgt7$Fis$\"1XVhDTpN9Fgt7$F^t$\"1!Gf&f^MS8Fgt7$Fct$\"1`4
K(*)=#R7Fgt7$Fit$\"1A$G0jk.:\"Fgt7$F^u$\"1Vd*yDDW0\"Fgt7$Fcu$\"1i$4+7l
Bc*FN7$Fhu$\"1'R\"HI%o$>')FN7$F]v$\"1g;(RCs3t(FN7$Fbv$\"1DT&et#yznFN7$
Fgv$\"1<mJ,;NjfFN7$F\\w$\"1wp3d-fP^FN7$Faw$\"14Xl0p'[V%FN7$Ffw$\"1s+QD
i\\?PFN7$F[x$\"1rsQ]'4J5$FN7$F`x$\"1C44%['Q<DFN7$Fex$\"1.#)Q[:n0?FN7$F
jx$\"1O3Q7\"Ge`\"FN7$F_y$\"1CGw,'*RZ6FN7$Fdy$\"1')G1;qLY\")FA7$Fiy$\"1
Yv26D%QZ&FA7$F^z$\"1^UVe*)zXNFA7$Fcz$\"1'oquwvo\">FA7$Fhz$\"1'[%GPA#fO
*F\\cv7$F][l$\"1WFo*G3S=$F\\cv7$Fb[l$\"1m^,EKO/bFg\\]lF\\jlF[\\lF_\\lF
e\\l7&-F(6%F*%,beta~is~3.8GF1-F:6$7fnF=7$Fh[t$\"1r8B_4$y#>FN7$F?$\"1.1
D3A)yt$FN7$F`\\t$\"1[)p9F1(>_FN7$FE$\"1)f/Cj/th'FN7$Ffiu$\"1L(=+dS74)F
N7$FJ$\"1G;*=c\"pk%*FN7$F^ju$\"1uX3cR*[2\"Fgt7$FP$\"1]r*)*GrP>\"Fgt7$F
c_w$\"1MvLTQ\"HI\"Fgt7$FU$\"15KBBI@.9Fgt7$F`cz$\"1l![-pk&)[\"Fgt7$FZ$
\"1J@G+\"4oc\"Fgt7$Fin$\"1_5`I\"[sq\"Fgt7$F^o$\"1\"3q`JQO#=Fgt7$Fco$\"
1'GV*Rzg7>Fgt7$Fho$\"1H*[\\Mn\"y>Fgt7$F]p$\"1OWjL#fe,#Fgt7$Fae\\l$\"1s
xyq))RH?Fgt7$Fbp$\"1J3\"3JLx.#Fgt7$F`_[l$\"18wPR!>6/#Fgt7$Fgp$\"1sNt?D
wR?Fgt7$Fh_[l$\"17/0/!*>M?Fgt7$F\\q$\"1A)zVyxY-#Fgt7$Faq$\"1#Hm!3a&z*>
Fgt7$Ffq$\"1;N&o!>#=&>Fgt7$F[r$\"1kq*y#4&>!>Fgt7$F`r$\"1LB;j/9L=Fgt7$F
er$\"1x.\"G'4!Rw\"Fgt7$Fjr$\"1!)RLQvR!o\"Fgt7$F_s$\"1fFv&ov[f\"Fgt7$Fd
s$\"1,$=v\"Ru+:Fgt7$Fis$\"1z.$R[75T\"Fgt7$F^t$\"1Q3rtE%=J\"Fgt7$Fct$\"
11^^b]T27Fgt7$Fit$\"1E19k<E;6Fgt7$F^u$\"1oh1X>X=5Fgt7$Fcu$\"1St%HG0+>*
FN7$Fhu$\"11zlH>:T#)FN7$F]v$\"1vC/>F#HN(FN7$Fbv$\"1%46/#)R'3kFN7$Fgv$
\"1.-;8Ay.cFN7$F\\w$\"1y&zJWqbz%FN7$Faw$\"1YsTCx'G6%FN7$Ffw$\"12**HI`@
CMFN7$F[x$\"1:<**yj+MGFN7$F`x$\"1e\"ebC'**yAFN7$Fex$\"1!f9wrl()z\"FN7$
Fjx$\"1WSa#['[i8FN7$F_y$\"126)=bDg+\"FN7$Fdy$\"1SDEgx+YqFA7$Fiy$\"1a9l
4A3hYFA7$F^z$\"1[CoReuoHFA7$Fcz$\"1W4'*y4Nn:FA7$Fhz$\"1I9'H8h<X(F\\cv7
$F][l$\"1l`'3$=.KCF\\cv7$Fb[l$\"1Org3irORFg\\]lF\\jlF[\\lF_\\lFe\\l7&-
F(6%F*%,beta~is~3.9GF1-F:6$7gnF=7$Fh[t$\"1wc#zErv,#FN7$F?$\"1)\\X`J[v!
RFN7$F`\\t$\"1kt6\")3K^aFN7$FE$\"1duCM*RT!pFN7$Ffiu$\"1**3u^F`K%)FN7$F
J$\"1SIqY/x_)*FN7$F^ju$\"1Y4/K-o<6Fgt7$FP$\"1#RTpuW)R7Fgt7$Fc_w$\"11/e
5Ph^8Fgt7$FU$\"1,$pRfNRX\"Fgt7$F`cz$\"1()RtWqlS:Fgt7$FZ$\"1=:e4d\")>;F
gt7$Fin$\"1&fe\"e]#3w\"Fgt7$F^o$\"10'4e`Yh(=Fgt7$Fco$\"1z7iazii>Fgt7$F
ho$\"14u2],SC?Fgt7$$\"1++Dc#o%*=#FN$\"1=h(\\n#\\V?Fgt7$F]p$\"1N`Tf%=z0
#Fgt7$Fae\\l$\"1DgE_h#)o?Fgt7$Fbp$\"1Sz[F&eV2#Fgt7$F`_[l$\"1BV^*3&yu?F
gt7$Fgp$\"1C5R@\"[.2#Fgt7$Fh_[l$\"1mmlKLsh?Fgt7$F\\q$\"1>.+O.2\\?Fgt7$
Faq$\"1!3'y#*>a;?Fgt7$Ffq$\"1E6z2LVj>Fgt7$F[r$\"1RI7C\"3x!>Fgt7$F`r$\"
1(ol*)\\wA$=Fgt7$Fer$\"1qw+M0Wd<Fgt7$Fjr$\"1PdQ)yv\"o;Fgt7$F_s$\"18#z`
m6wd\"Fgt7$Fds$\"1n#ociZ(y9Fgt7$Fis$\"1*=$)[K$>&Q\"Fgt7$F^t$\"1PBG_-]#
G\"Fgt7$Fct$\"1Uv-#\\-^<\"Fgt7$Fit$\"1g*G%o*\\>3\"Fgt7$F^u$\"1=uB%>!)f
#)*FN7$Fcu$\"1%*=T/!)>A))FN7$Fhu$\"1H_!=?d1(yFN7$F]v$\"1B:;gTd&)pFN7$F
bv$\"1n/0J;*40'FN7$Fgv$\"1^773H'*f_FN7$F\\w$\"1IYxO\"y7Z%FN7$Faw$\"1K[
g;>&*4QFN7$Ffw$\"1(*=-'Hzz9$FN7$F[x$\"1\")GK#)[K&e#FN7$F`x$\"1)>liJd31
#FN7$Fex$\"1$zY>](Q6;FN7$Fjx$\"1gke$zZt?\"FN7$F_y$\"1$*p^88x5))FA7$Fdy
$\"1PpCenV(3'FA7$Fiy$\"1J@q'4JX'RFA7$F^z$\"1H&HL`/G[#FA7$Fcz$\"1\"=5-
\\:,G\"FA7$Fhz$\"1K6F]&H@#fF\\cv7$F][l$\"1heY`'fb&=F\\cv7$Fb[l$\"1*3SW
JlB\"GFg\\]lF\\jlF[\\lF_\\lFe\\l7&-F:6$7inF=7$$\"1mmmT&)G\\aF\\cv$\"1Z
Pvtx8s5FN7$Fh[t$\"1G,l=>A4@FN7$$\"1++]ilyM;FA$\"1[8u?'G=6$FN7$F?$\"17c
aL)H03%FN7$F`\\t$\"1A\\Ka-5(o&FN7$FE$\"16Ds-Vn&>(FN7$Ffiu$\"1e[zT]yy()
FN7$FJ$\"1hQ%e\"\\dC5Fgt7$F^ju$\"1]Lb?=#4;\"Fgt7$FP$\"1Y(Hw#QJ'G\"Fgt7
$Fc_w$\"1#RT<UG1S\"Fgt7$FU$\"1uN,kT([]\"Fgt7$F`cz$\"1qhZ4.'Gf\"Fgt7$FZ
$\"1\\!=!yv\"Gn\"Fgt7$Fin$\"1!3]RWLT\"=Fgt7$F^o$\"1_Q2ZU4G>Fgt7$Fco$\"
12xI%y$z6?Fgt7$Fho$\"1JJME\"*[p?Fgt7$Faf^l$\"1\\'e!y=Y'3#Fgt7$F]p$\"1#
e!em&*f)4#Fgt7$Fae\\l$\"1Q*pT,bn5#Fgt7$Fbp$\"1nG$ozu$4@Fgt7$F`_[l$\"1
\")3bB?u1@Fgt7$Fgp$\"1m\\[<h8*4#Fgt7$Fh_[l$\"1!*e(3]wt3#Fgt7$F\\q$\"1J
:f0-`r?Fgt7$Faq$\"1#[#H>i6L?Fgt7$Ffq$\"1mY!>9$*H(>Fgt7$F[r$\"1JmLw#G9
\">Fgt7$F`r$\"1N<x(eY%H=Fgt7$Fer$\"1G4qYP7\\<Fgt7$Fjr$\"1eq;m[Ea;Fgt7$
F_s$\"1ewZ0!f)e:Fgt7$Fds$\"1Fos)H4bX\"Fgt7$Fis$\"1Qa%4d'Qe8Fgt7$F^t$\"
13/^XzY_7Fgt7$Fct$\"1\\?1\\nUU6Fgt7$Fit$\"1(*f$4*ocZ5Fgt7$F^u$\"1!Hzj]
%))p%*FN7$Fcu$\"18IGw\"=+Y)FN7$Fhu$\"1QM:8![(3vFN7$F]v$\"1t!\\7f_%HmFN
7$Fbv$\"1+()=:&orq&FN7$Fgv$\"1\"*=lov$>$\\FN7$F\\w$\"1YHLf%RW;%FN7$Faw
$\"1>]w#pcb_$FN7$Ffw$\"12+_G.#4*GFN7$F[x$\"185*=sKfN#FN7$F`x$\"1;#yO5(
fh=FN7$Fex$\"1U(*[n'y>W\"FN7$Fjx$\"1Ixls^so5FN7$F_y$\"1*4&\\q!)=3xFA7$
Fdy$\"1S$HzLFOD&FA7$Fiy$\"1n-+**=XoLFA7$F^z$\"1HT3$[vT2#FA7$Fcz$\"1*))
*3EnRW5FA7$Fhz$\"1.u_MRV,ZF\\cv7$F][l$\"1-XG^/@99F\\cv7$Fb[l$\"12irI*y
p+#Fg\\]lF\\jlF[\\l-F(6%F*%,beta~is~4.0GF1F_\\lFe\\l-%&TITLEG6#QFAlpha
~is~Fixed~at~2~While~Beta~VariesFc\\l" 1 2 0 1 0 2 9 1 4 2 1.000000 
45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }
}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 31 "Sample Probability Calculation
s" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
44 "We can calculate probabilities for the Beta(" }{XPPEDIT 18 0 "alph
a,beta;" "6$%&alphaG%%betaG" }{TEXT -1 141 ") distribution using eithe
r the probability density function (PDF) or the cumulative distributio
n function (CDF).  We will denote the PDF by " }{TEXT 256 1 "f" }
{TEXT -1 16 " and the CDF by " }{TEXT 257 1 "F" }{TEXT -1 128 ".  The \+
graph of the CDF for the Beta(3,4) distribution appears below, but you
 are encouraged to plot it for different values of " }{XPPEDIT 18 0 "a
lpha;" "6#%&alphaG" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "beta;" "6#%%be
taG" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {MPLTEXT 0 21 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "f:=(alpha,beta,x)->GAMMA(alpha+beta
)/(GAMMA(alpha)*GAMMA(beta))*x^(alpha-1)*(1-x)^(beta-1);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"fGR6%%&alphaG%%betaG%\"xG6\"6$%)operatorG%&a
rrowGF**&*(-%&GAMMAG6#,&9$\"\"\"9%F5F5)9&,&F4F5!\"\"F5F5),&F5F5F8F:,&F
6F5F:F5F5\"\"\"*&-F16#F4\"\"\"-F16#F6\"\"\"!\"\"F*F*F*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "F:=(alpha,beta,x)->int(f(alpha,beta
,t),t=0..x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FGR6%%&alphaG%%bet
aG%\"xG6\"6$%)operatorG%&arrowGF*-%$intG6$-%\"fG6%9$9%%\"tG/F6;\"\"!9&
F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "alpha:=3; beta:=4
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&alphaG\"\"$" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%%betaG\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 85 "plot(F(alpha,beta,x),x=0..1, title=\"Cumulative Distribution F
unction for Beta(3,4)\");" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 
{PLOTDATA 2 "6&-%'CURVESG6$7S7$\"\"!F(7$$\"1nmm;arz@!#<$\"1RStI[Tr>!#>
7$$\"1LL$e9ui2%F,$\"1T7J`ERM7!#=7$$\"1nmm\"z_\"4iF,$\"1#R;]y#[^TF57$$
\"1mmmT&phN)F,$\"1X\")Rpgs='*F57$$\"1LLe*=)H\\5!#;$\"1w2T*y^&4=F,7$$\"
1nm\"z/3uC\"FC$\"1lD&z[8u*GF,7$$\"1++DJ$RDX\"FC$\"1A+PHl_\\VF,7$$\"1nm
\"zR'ok;FC$\"1nuV,E[4iF,7$$\"1++D1J:w=FC$\"1n#*pk$RcU)F,7$$\"1LLL3En$4
#FC$\"1;ki\"*oC26FC7$$\"1nm;/RE&G#FC$\"121(RzU(p8FC7$$\"1+++D.&4]#FC$
\"1E90n'Rep\"FC7$$\"1+++vB_<FFC$\"16Ha(GNG0#FC7$$\"1+++v'Hi#HFC$\"1XNh
V0\\@CFC7$$\"1nm\"z*ev:JFC$\"17cz-$[Tx#FC7$$\"1LLL347TLFC$\"1hG$f$4b6K
FC7$$\"1LLLLY.KNFC$\"1XL\"4]@Rf$FC7$$\"1++D\"o7Tv$FC$\"1zkt3$3![SFC7$$
\"1LLL$Q*o]RFC$\"1Hz]b\"eXX%FC7$$\"1++D\"=lj;%FC$\"1l+2hdW,\\FC7$$\"1+
+vV&R<P%FC$\"1rI?lf+C`FC7$$\"1LL$e9Ege%FC$\"1<&4\"Gg#zv&FC7$$\"1LLeR\"
3Gy%FC$\"1>3U:\"\\p9'FC7$$\"1nm;/T1&*\\FC$\"1QWDL1C`lFC7$$\"1mm\"zRQb@
&FC$\"1b&G0kRu&pFC7$$\"1***\\(=>Y2aFC$\"1#=uh$>>#H(FC7$$\"1mm;zXu9cFC$
\"1fn&RE!zLwFC7$$\"1+++]y))GeFC$\"1QI!)z*4J'zFC7$$\"1****\\i_QQgFC$\"1
8!>TbQ1E)FC7$$\"1***\\7y%3TiFC$\"1P%*[*oUV_)FC7$$\"1****\\P![hY'FC$\"1
Ka_Uci)y)FC7$$\"1LLL$Qx$omFC$\"1Bh]()pJ+!*FC7$$\"1+++v.I%)oFC$\"1tf4qg
j*>*FC7$$\"1mm\"zpe*zqFC$\"1kup$>opN*FC7$$\"1+++D\\'QH(FC$\"1'>EQA*f/&
*FC7$$\"1KLe9S8&\\(FC$\"1IN%*f:X@'*FC7$$\"1***\\i?=bq(FC$\"1ko//()GA(*
FC7$$\"1LLL3s?6zFC$\"1Q+]'G\"e,)*FC7$$\"1++DJXaE\")FC$\"1UQMr;Gm)*FC7$
$\"1nmmm*RRL)FC$\"1dopuq48**FC7$$\"1mm;a<.Y&)FC$\"1+#Q*)z8w%**FC7$$\"1
LLe9tOc()FC$\"1t&oF+*)3(**FC7$$\"1+++]Qk\\*)FC$\"1!QazkwY)**FC7$$\"1LL
$3dg6<*FC$\"1)zOCMFQ***FC7$$\"1mmmmxGp$*FC$\"1M%=:ffy***FC7$$\"1++D\"o
K0e*FC$\"169xJic****FC7$$\"1++v=5s#y*FC$\"13lu>x'*****FC7$$\"\"\"F(Fcz
-%'COLOURG6&%$RGBG$\"#5!\"\"F(F(-%&TITLEG6#QOCumulative~Distribution~F
unction~for~Beta(3,4)6\"-%+AXESLABELSG6$Q\"xF`[l%!G-%%VIEWG6$;F(Fcz%(D
EFAULTG" 1 2 0 1 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 }}}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "a:=plot(f(alpha,beta,x),x=0.
.1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "b:=plot(f(alpha,bet
a,x),x=0..0.4,color=yellow,filled=true):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "display([a,b]);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 
300 300 {PLOTDATA 2 "6&-%'CURVESG6$7en7$\"\"!F(7$$\"1mmmT&)G\\a!#=$\"1
\"H\"oDkr_<F,7$$\"1LLL3x&)*3\"!#<$\"1%Rz)*Hbi*oF,7$$\"1++]ilyM;F2$\"1f
s>%o_h_\"F27$$\"1nmm;arz@F2$\"1\"H/f8=$oEF27$$\"1++D\"y%*z7$F2$\"1s@zu
fwO`F27$$\"1LL$e9ui2%F2$\"1AvgOBY*z)F27$$\"1nmm\"z_\"4iF2$\"1k]pfE_3>!
#;7$$\"1mmmT&phN)F2$\"11$R#GpfCKFN7$$\"1LLe*=)H\\5FN$\"1F0b2_=PZFN7$$
\"1nm\"z/3uC\"FN$\"1V&[&G$e+E'FN7$$\"1++DJ$RDX\"FN$\"1B0UQ0I0zFN7$$\"1
nm\"zR'ok;FN$\"1ac,,o,H'*FN7$$\"1++D1J:w=FN$\"1/!ps%*HB8\"!#:7$$\"1LLL
3En$4#FN$\"1)[?\"4)\\)*H\"Fgo7$$\"1nm;/RE&G#FN$\"1C>k^hvQ9Fgo7$$\"1+++
D.&4]#FN$\"1!z0^ZKEe\"Fgo7$$\"1+++vB_<FFN$\"133B5[L6<Fgo7$$\"1+++v'Hi#
HFN$\"1P#y![>`==Fgo7$$\"1nm\"z*ev:JFN$\"1vJUb\"3/!>Fgo7$$\"1LLL347TLFN
$\"1(yC:f-w(>Fgo7$$\"1LLLLY.KNFN$\"1'3Y8Ep`-#Fgo7$$\"1n;HdO2VOFN$\"1u+
rvvjX?Fgo7$$\"1++D\"o7Tv$FN$\"1BqW!f%Qg?Fgo7$$\"1m;HK5S_QFN$\"1s1?X'e)
o?Fgo7$$\"1LLL$Q*o]RFN$\"1t#o[QtI2#Fgo7$$\"1m;H#GF&eSFN$\"1IL8!eiG2#Fg
o7$$\"1++D\"=lj;%FN$\"1(3*oh9on?Fgo7$$\"1++]iB0pUFN$\"1$>G9DG#e?Fgo7$$
\"1++vV&R<P%FN$\"1UK@nwZW?Fgo7$$\"1LL$e9Ege%FN$\"1J%R)46]-?Fgo7$$\"1LL
eR\"3Gy%FN$\"1gbY/22\\>Fgo7$$\"1nm;/T1&*\\FN$\"1C:(GIZo(=Fgo7$$\"1mm\"
zRQb@&FN$\"1o?'H<6vy\"Fgo7$$\"1***\\(=>Y2aFN$\"1@R-@MS*p\"Fgo7$$\"1mm;
zXu9cFN$\"1Ee#4[H^f\"Fgo7$$\"1+++]y))GeFN$\"1cav9\\Pz9Fgo7$$\"1****\\i
_QQgFN$\"1cNF+9Ag8Fgo7$$\"1***\\7y%3TiFN$\"1*)yDq#\\7C\"Fgo7$$\"1****
\\P![hY'FN$\"1w]#[*=526Fgo7$$\"1LLL$Qx$omFN$\"1wIk\"G1k')*FN7$$\"1+++v
.I%)oFN$\"1z^YRcx+')FN7$$\"1mm\"zpe*zqFN$\"10?eJ(Q#)[(FN7$$\"1+++D\\'Q
H(FN$\"1m%[br%zDjFN7$$\"1KLe9S8&\\(FN$\"1mX(RW4uH&FN7$$\"1***\\i?=bq(F
N$\"1F%GD6rLI%FN7$$\"1LLL3s?6zFN$\"1ABb3wLAMFN7$$\"1++DJXaE\")FN$\"1n7
=7G^0EFN7$$\"1nmmm*RRL)FN$\"1q%Q*)H(=F>FN7$$\"1mm;a<.Y&)FN$\"1n]j\")*H
pM\"FN7$$\"1LLe9tOc()FN$\"1IcuK1i[))F27$$\"1+++]Qk\\*)FN$\"1'R,obR*obF
27$$\"1LL$3dg6<*FN$\"1/pQA!*\\tGF27$$\"1mmmmxGp$*FN$\"1unXBEZ@8F27$$\"
1++D\"oK0e*FN$\"1X*3S$omkSF,7$$\"1++v=5s#y*FN$\"1]<\"4\\9,*e!#>7$$\"\"
\"F(F(-%'COLOURG6&%$RGBG$\"#5!\"\"F(F(-%)POLYGONSG6U7&F'F'7$$\"1mmmm;'
)=()F,$\"1.NG_p%GW%F,7$Fj]lF(7&F^^lFi]l7$$\"1LLLe'40j\"F2$\"1,B;tdP=:F
27$Fa^lF(7&Fe^lF`^l7$$\"1nmm;6m$[#F2$\"1#p>aYk@V$F27$Fh^lF(7&F\\_lFg^l
7$$\"1nmm;yYULF2$\"1q&H,x3L0'F27$F__lF(7&Fc_lF^_l7$$\"1LLLeF>(>%F2$\"1
_&>'4R-%H*F27$Ff_lF(7&Fj_lFe_l7$$\"1nmm\">K'*)\\F2$\"1s'=Q$R:\"G\"FN7$
F]`lF(7&Fa`lF\\`l7$$\"1+++Dt:5eF2$\"1I#Q0?TDp\"FN7$Fd`lF(7&Fh`lFc`l7$$
\"1mmm\"fX(emF2$\"1e[*4Z+N;#FN7$F[alF(7&F_alFj`l7$$\"1+++DCh/vF2$\"1:F
2=2/uEFN7$FbalF(7&FfalFaal7$$\"1MLLL/pu$)F2$\"1y`*)eO%pB$FN7$FialF(7&F
]blFhal7$$\"1nmm;c0T\"*F2$\"1!Go))H70w$FN7$F`blF(7&FdblF_bl7$$\"1+++I,
Q+5FN$\"1oas\"QrnP%FN7$FgblF(7&F[clFfbl7$$\"1+++]*3q3\"FN$\"1DET!><)>]
FN7$F^clF(7&FbclF]cl7$$\"1+++q=\\q6FN$\"1LsTV8XecFN7$FeclF(7&FiclFdcl7
$$\"1nm;fBIY7FN$\"1Zi1#4M8D'FN7$F\\dlF(7&F`dlF[dl7$$\"1LLLj$[kL\"FN$\"
1!Gg\\nn&opFN7$FcdlF(7&FgdlFbdl7$$\"1LLL`Q\"GT\"FN$\"161qb7d$e(FN7$Fjd
lF(7&F^elFidl7$$\"1++]s]k,:FN$\"1#>dh>fSI)FN7$FaelF(7&FeelF`el7$$\"1LL
L`dF!e\"FN$\"1R4ZwPcV*)FN7$FhelF(7&F\\flFgel7$$\"1++]sgam;FN$\"1mTG)o%
3W'*FN7$F_flF(7&FcflF^fl7$$\"1++]<ep[<FN$\"1a%>ZLO2.\"Fgo7$FfflF(7&Fjf
lFefl7$$\"1LLLe/TM=FN$\"1yduXkF*4\"Fgo7$F]glF(7&FaglF\\gl7$$\"1LL$eDBJ
\">FN$\"12v$H7%Rh6Fgo7$FdglF(7&FhglFcgl7$$\"1nmmTc-)*>FN$\"1P_/>LGF7Fg
o7$F[hlF(7&F_hlFjgl7$$\"1nm;f`@'3#FN$\"14muG?E%H\"Fgo7$FbhlF(7&FfhlFah
l7$$\"1++]nZ)H;#FN$\"1RY#4yq6N\"Fgo7$FihlF(7&F]ilFhhl7$$\"1nmmJy*eC#FN
$\"1cXZ`g*4T\"Fgo7$F`ilF(7&FdilF_il7$$\"1+++S^bJBFN$\"1#o'3Up$3Z\"Fgo7
$FgilF(7&F[jlFfil7$$\"1+++0TN:CFN$\"1')*[FZ!GF:Fgo7$F^jlF(7&FbjlF]jl7$
$\"1++]7RV'\\#FN$\"1Se'4Ws(z:Fgo7$FejlF(7&FijlFdjl7$$\"1+++:#fke#FN$\"
1PMGI'eaj\"Fgo7$F\\[mF(7&F`[mF[[m7$$\"1LLL`4NnEFN$\"1luo`$RIo\"Fgo7$Fc
[mF(7&Fg[mFb[m7$$\"1+++],s`FFN$\"1`Z`He:J<Fgo7$Fj[mF(7&F^\\mFi[m7$$\"1
mm;zM)>$GFN$\"1jsgN\"pAx\"Fgo7$Fa\\mF(7&Fe\\mF`\\m7$$\"1+++qfa<HFN$\"1
c_Oh0U9=Fgo7$Fh\\mF(7&F\\]mFg\\m7$$\"1LL$eg`!)*HFN$\"103tW3M^=Fgo7$F_]
mF(7&Fc]mF^]m7$$\"1++]#G2A3$FN$\"1)QfCjCq)=Fgo7$Ff]mF(7&Fj]mFe]m7$$\"1
LLL$)G[kJFN$\"1lL_'*=)*=>Fgo7$F]^mF(7&Fa^mF\\^m7$$\"1++]7yh]KFN$\"1YoT
wSG\\>Fgo7$Fd^mF(7&Fh^mFc^m7$$\"1nmm')fdLLFN$\"1yX<E0Qv>Fgo7$F[_mF(7&F
__mFj^m7$$\"1nmm,FT=MFN$\"1$=N#*40*)*>Fgo7$Fb_mF(7&Ff_mFa_m7$$\"1ML$e#
pa-NFN$\"1U+HNs0>?Fgo7$Fi_mF(7&F]`mFh_m7$$\"1+++Sv&)zNFN$\"1\"\\pmfwZ.
#Fgo7$F``mF(7&Fd`mF_`m7$$\"1MLLGUYoOFN$\"1tbU]d\\\\?Fgo7$Fg`mF(7&F[amF
f`m7$$\"1mmm1^rZPFN$\"1M=1NVof?Fgo7$F^amF(7&FbamF]am7$$\"1++]sI@KQFN$
\"1xE$>Anu1#Fgo7$FeamF(7&FiamFdam7$$\"1++]2%)38RFN$\"1ksO%)3'>2#Fgo7$F
\\bmF(7&F`bmF[bm7$$\"1+++++++SFN$\"1+++++gt?Fgo7$FcbmF(7\"-%&STYLEG6#%
,PATCHNOGRIDG-F_]l6&Fa]l$\"*++++\"!\")F_cmF(-%+AXESLABELSG6$Q\"x6\"%!G
-%%VIEWG6$;F(F\\]l%(DEFAULTG" 1 2 0 1 0 2 9 1 4 2 1.000000 45.000000 
45.000000 0 }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 103 "Find the value of the yellow shaded area, the area und
er the Beta(3,4) density curve to the left of 0.4" }}{PARA 0 "" 0 "" 
{MPLTEXT 0 21 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "evalf(
F(alpha,beta,0.4));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+++!ob%!#5" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 74 
"The value of this area can also be found by using the integration com
mand." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 37 "evalf(int(f(alpha,beta,x),x=0..0.4));" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#$\"+++!ob%!#5" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "a:=plot(f(alpha,beta,x),x=0..1):" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 61 "b:=plot(f(alpha,beta,x),x=0.4..0.6,color=yel
low,filled=true):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "displa
y([a,b]);" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 105 "Find the value of the yellow shaded area, the are
a under the Beta(3,4) density curve between 0.4 and 0.6." }}{PARA 13 "
" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURVESG6$7en7$\"\"!F(7$
$\"1mmmT&)G\\a!#=$\"1\"H\"oDkr_<F,7$$\"1LLL3x&)*3\"!#<$\"1%Rz)*Hbi*oF,
7$$\"1++]ilyM;F2$\"1fs>%o_h_\"F27$$\"1nmm;arz@F2$\"1\"H/f8=$oEF27$$\"1
++D\"y%*z7$F2$\"1s@zufwO`F27$$\"1LL$e9ui2%F2$\"1AvgOBY*z)F27$$\"1nmm\"
z_\"4iF2$\"1k]pfE_3>!#;7$$\"1mmmT&phN)F2$\"11$R#GpfCKFN7$$\"1LLe*=)H\\
5FN$\"1F0b2_=PZFN7$$\"1nm\"z/3uC\"FN$\"1V&[&G$e+E'FN7$$\"1++DJ$RDX\"FN
$\"1B0UQ0I0zFN7$$\"1nm\"zR'ok;FN$\"1ac,,o,H'*FN7$$\"1++D1J:w=FN$\"1/!p
s%*HB8\"!#:7$$\"1LLL3En$4#FN$\"1)[?\"4)\\)*H\"Fgo7$$\"1nm;/RE&G#FN$\"1
C>k^hvQ9Fgo7$$\"1+++D.&4]#FN$\"1!z0^ZKEe\"Fgo7$$\"1+++vB_<FFN$\"133B5[
L6<Fgo7$$\"1+++v'Hi#HFN$\"1P#y![>`==Fgo7$$\"1nm\"z*ev:JFN$\"1vJUb\"3/!
>Fgo7$$\"1LLL347TLFN$\"1(yC:f-w(>Fgo7$$\"1LLLLY.KNFN$\"1'3Y8Ep`-#Fgo7$
$\"1n;HdO2VOFN$\"1u+rvvjX?Fgo7$$\"1++D\"o7Tv$FN$\"1BqW!f%Qg?Fgo7$$\"1m
;HK5S_QFN$\"1s1?X'e)o?Fgo7$$\"1LLL$Q*o]RFN$\"1t#o[QtI2#Fgo7$$\"1m;H#GF
&eSFN$\"1IL8!eiG2#Fgo7$$\"1++D\"=lj;%FN$\"1(3*oh9on?Fgo7$$\"1++]iB0pUF
N$\"1$>G9DG#e?Fgo7$$\"1++vV&R<P%FN$\"1UK@nwZW?Fgo7$$\"1LL$e9Ege%FN$\"1
J%R)46]-?Fgo7$$\"1LLeR\"3Gy%FN$\"1gbY/22\\>Fgo7$$\"1nm;/T1&*\\FN$\"1C:
(GIZo(=Fgo7$$\"1mm\"zRQb@&FN$\"1o?'H<6vy\"Fgo7$$\"1***\\(=>Y2aFN$\"1@R
-@MS*p\"Fgo7$$\"1mm;zXu9cFN$\"1Ee#4[H^f\"Fgo7$$\"1+++]y))GeFN$\"1cav9
\\Pz9Fgo7$$\"1****\\i_QQgFN$\"1cNF+9Ag8Fgo7$$\"1***\\7y%3TiFN$\"1*)yDq
#\\7C\"Fgo7$$\"1****\\P![hY'FN$\"1w]#[*=526Fgo7$$\"1LLL$Qx$omFN$\"1wIk
\"G1k')*FN7$$\"1+++v.I%)oFN$\"1z^YRcx+')FN7$$\"1mm\"zpe*zqFN$\"10?eJ(Q
#)[(FN7$$\"1+++D\\'QH(FN$\"1m%[br%zDjFN7$$\"1KLe9S8&\\(FN$\"1mX(RW4uH&
FN7$$\"1***\\i?=bq(FN$\"1F%GD6rLI%FN7$$\"1LLL3s?6zFN$\"1ABb3wLAMFN7$$
\"1++DJXaE\")FN$\"1n7=7G^0EFN7$$\"1nmmm*RRL)FN$\"1q%Q*)H(=F>FN7$$\"1mm
;a<.Y&)FN$\"1n]j\")*HpM\"FN7$$\"1LLe9tOc()FN$\"1IcuK1i[))F27$$\"1+++]Q
k\\*)FN$\"1'R,obR*obF27$$\"1LL$3dg6<*FN$\"1/pQA!*\\tGF27$$\"1mmmmxGp$*
FN$\"1unXBEZ@8F27$$\"1++D\"oK0e*FN$\"1X*3S$omkSF,7$$\"1++v=5s#y*FN$\"1
]<\"4\\9,*e!#>7$$\"\"\"F(F(-%'COLOURG6&%$RGBG$\"#5!\"\"F(F(-%)POLYGONS
G6U7&7$$\"1+++++++SFNF(7$Fj]l$\"1+++++gt?Fgo7$$\"1MLL3VfVSFN$\"1-cg:0>
t?Fgo7$F`^lF(7&Fd^lF_^l7$$\"1nm\"H[D:3%FN$\"1Q/wT6<s?Fgo7$Fg^lF(7&F[_l
Ff^l7$$\"1ML$e0$=CTFN$\"1Og*4O$Hq?Fgo7$F^_lF(7&Fb_lF]_l7$$\"1LL$3RBr;%
FN$\"1/xp'oFw1#Fgo7$Fe_lF(7&Fi_lFd_l7$$\"1nm\"zjf)4UFN$\"1X$o@V4U1#Fgo
7$F\\`lF(7&F``lF[`l7$$\"1LLe4;[\\UFN$\"15x(z#\\Og?Fgo7$Fc`lF(7&Fg`lFb`
l7$$\"1++Dmy]!H%FN$\"1m_a?kqb?Fgo7$Fj`lF(7&F^alFi`l7$$\"1LLezs$HL%FN$
\"1B37G6<]?Fgo7$FaalF(7&FealF`al7$$\"1++D@1BvVFN$\"1d!R**3OR/#Fgo7$Fha
lF(7&F\\blFgal7$$\"1nmm@Xt=WFN$\"19:2WYyO?Fgo7$F_blF(7&FcblF^bl7$$\"1L
L$3y_qX%FN$\"1\\xS\"yt)H?Fgo7$FfblF(7&FjblFebl7$$\"1+++l+>+XFN$\"1/$[U
V<9-#Fgo7$F]clF(7&FaclF\\cl7$$\"1+++vW]VXFN$\"1=CL?f@7?Fgo7$FdclF(7&Fh
clFccl7$$\"1+++NfC&e%FN$\"1hO?!Q&o-?Fgo7$F[dlF(7&F_dlFjcl7$$\"1MLez6:B
YFN$\"1+hurbZ$*>Fgo7$FbdlF(7&FfdlFadl7$$\"1nmm\"=C#oYFN$\"1@%Qe!y%=)>F
go7$FidlF(7&F]elFhdl7$$\"1nmmEpS1ZFN$\"1P$3GEK9(>Fgo7$F`elF(7&FdelF_el
7$$\"1++DOD#3v%FN$\"1Jg%39w'e>Fgo7$FgelF(7&F[flFfel7$$\"1nmmwy8!z%FN$
\"1Uq')f2#o%>Fgo7$F^flF(7&FbflF]fl7$$\"1++DOIFL[FN$\"1f07&G;K$>Fgo7$Fe
flF(7&FiflFdfl7$$\"1++v3zMu[FN$\"1jk3=Dp>>Fgo7$F\\glF(7&F`glF[gl7$$\"1
nm;H_?<\\FN$\"1Aqd4H+0>Fgo7$FcglF(7&FgglFbgl7$$\"1nm\"zihl&\\FN$\"1>Sd
2R+\"*=Fgo7$FjglF(7&F^hlFigl7$$\"1LL$3#G,**\\FN$\"1P-)f/q`(=Fgo7$FahlF
(7&FehlF`hl7$$\"1LLezw5V]FN$\"1qWz#He&e=Fgo7$FhhlF(7&F\\ilFghl7$$\"1++
v$Q#\\\"3&FN$\"1uNqq0YV=Fgo7$F_ilF(7&FcilF^il7$$\"1LL$e\"*[H7&FN$\"1,@
K;JoE=Fgo7$FfilF(7&FjilFeil7$$\"1+++qvxl^FN$\"1Ak^\\*\\)3=Fgo7$F]jlF(7
&FajlF\\jl7$$\"1****\\_qn2_FN$\"1e@;-d#4z\"Fgo7$FdjlF(7&FhjlFcjl7$$\"1
++Dcp@[_FN$\"1%=$>2l9t<Fgo7$F[[mF(7&F_[mFjjl7$$\"1++]2'HKH&FN$\"1IGsB'
=Hv\"Fgo7$Fb[mF(7&Ff[mFa[m7$$\"1mmmwanL`FN$\"11%\\7/?Vt\"Fgo7$Fi[mF(7&
F]\\mFh[m7$$\"1,++v+'oP&FN$\"1jqO&eNSr\"Fgo7$F`\\mF(7&Fd\\mF_\\m7$$\"1
LLeR<*fT&FN$\"1H/S-xG&p\"Fgo7$Fg\\mF(7&F[]mFf\\m7$$\"1+++&)HxeaFN$\"1v
XB5nSu;Fgo7$F^]mF(7&Fb]mF]]m7$$\"1nm\"H!o-*\\&FN$\"1eiG3kSa;Fgo7$Fe]mF
(7&Fi]mFd]m7$$\"1++DTO5TbFN$\"18_/c%\\Jj\"Fgo7$F\\^mF(7&F`^mF[^m7$$\"1
nmmT9C#e&FN$\"1(Q&\\/[.7;Fgo7$Fc^mF(7&Fg^mFb^m7$$\"1***\\i!*3`i&FN$\"1
D;OnQf*e\"Fgo7$Fj^mF(7&F^_mFi^m7$$\"1LLL$*zymcFN$\"1Id&4Drwc\"Fgo7$Fa_
mF(7&Fe_mF`_m7$$\"1LL$3N1#4dFN$\"1/>zJU&\\a\"Fgo7$Fh_mF(7&F\\`mFg_m7$$
\"1mm\"HYt7v&FN$\"1>j&RfV@_\"Fgo7$F_`mF(7&Fc`mF^`m7$$\"1+++q(G**y&FN$
\"1iAL-$\\4]\"Fgo7$Ff`mF(7&Fj`mFe`m7$$\"1mm;9@BMeFN$\"16!*)3S*Rw9Fgo7$
F]amF(7&FaamF\\am7$$\"1LLL`v&Q(eFN$\"1m9QQ?Aa9Fgo7$FdamF(7&FhamFcam7$$
\"1++DOl5;fFN$\"1Md\">bj.V\"Fgo7$F[bmF(7&F_bmFjam7$$\"1++v.UacfFN$\"1%
)\\*4%pL29Fgo7$FbbmF(7&FfbmFabm7$$\"1+++++++gFN$\"1+++++S#Q\"Fgo7$Fibm
F(7\"-%&STYLEG6#%,PATCHNOGRIDG-F_]l6&Fa]l$\"*++++\"!\")FecmF(-%+AXESLA
BELSG6$Q\"x6\"%!G-%%VIEWG6$;F(F\\]l%(DEFAULTG" 1 2 0 1 0 2 9 1 4 2 
1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 138 "Using the CDF, we can easily find th
e shaded area by finding the area to the left of 0.6 and then subtract
ing the area to the left of 0.4." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "area:=evalf(F(alpha,beta,0.6
)-F(alpha,beta,0.4));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%areaG$\"++
+?^O!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 93 "Or, using the integration command, we can simply integrat
e the Beta(3,4) PDF from 0.4 to 0.6." }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "evalf(int(f(alpha,beta,x)
,x=0.4..0.6));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*++7l$!\"*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "a:=plot(f(alpha,beta,x),x=0.
.1,labels=[\" \",\" \"]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
76 "b:=plot(f(alpha,beta,x),x=0.7..1,color=yellow,filled=true,labels=[
\" \",\" \"]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "c:=textpl
ot([0.7,-.04,\"x\"],color=blue):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 43 "d:=textplot([0.75,0.2,\".070\"],color=black):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "display([a,b,c,d]);" }}
{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6(-%'CURVESG6$7en7
$\"\"!F(7$$\"1mmmT&)G\\a!#=$\"1\"H\"oDkr_<F,7$$\"1LLL3x&)*3\"!#<$\"1%R
z)*Hbi*oF,7$$\"1++]ilyM;F2$\"1fs>%o_h_\"F27$$\"1nmm;arz@F2$\"1\"H/f8=$
oEF27$$\"1++D\"y%*z7$F2$\"1s@zufwO`F27$$\"1LL$e9ui2%F2$\"1AvgOBY*z)F27
$$\"1nmm\"z_\"4iF2$\"1k]pfE_3>!#;7$$\"1mmmT&phN)F2$\"11$R#GpfCKFN7$$\"
1LLe*=)H\\5FN$\"1F0b2_=PZFN7$$\"1nm\"z/3uC\"FN$\"1V&[&G$e+E'FN7$$\"1++
DJ$RDX\"FN$\"1B0UQ0I0zFN7$$\"1nm\"zR'ok;FN$\"1ac,,o,H'*FN7$$\"1++D1J:w
=FN$\"1/!ps%*HB8\"!#:7$$\"1LLL3En$4#FN$\"1)[?\"4)\\)*H\"Fgo7$$\"1nm;/R
E&G#FN$\"1C>k^hvQ9Fgo7$$\"1+++D.&4]#FN$\"1!z0^ZKEe\"Fgo7$$\"1+++vB_<FF
N$\"133B5[L6<Fgo7$$\"1+++v'Hi#HFN$\"1P#y![>`==Fgo7$$\"1nm\"z*ev:JFN$\"
1vJUb\"3/!>Fgo7$$\"1LLL347TLFN$\"1(yC:f-w(>Fgo7$$\"1LLLLY.KNFN$\"1'3Y8
Ep`-#Fgo7$$\"1n;HdO2VOFN$\"1u+rvvjX?Fgo7$$\"1++D\"o7Tv$FN$\"1BqW!f%Qg?
Fgo7$$\"1m;HK5S_QFN$\"1s1?X'e)o?Fgo7$$\"1LLL$Q*o]RFN$\"1t#o[QtI2#Fgo7$
$\"1m;H#GF&eSFN$\"1IL8!eiG2#Fgo7$$\"1++D\"=lj;%FN$\"1(3*oh9on?Fgo7$$\"
1++]iB0pUFN$\"1$>G9DG#e?Fgo7$$\"1++vV&R<P%FN$\"1UK@nwZW?Fgo7$$\"1LL$e9
Ege%FN$\"1J%R)46]-?Fgo7$$\"1LLeR\"3Gy%FN$\"1gbY/22\\>Fgo7$$\"1nm;/T1&*
\\FN$\"1C:(GIZo(=Fgo7$$\"1mm\"zRQb@&FN$\"1o?'H<6vy\"Fgo7$$\"1***\\(=>Y
2aFN$\"1@R-@MS*p\"Fgo7$$\"1mm;zXu9cFN$\"1Ee#4[H^f\"Fgo7$$\"1+++]y))GeF
N$\"1cav9\\Pz9Fgo7$$\"1****\\i_QQgFN$\"1cNF+9Ag8Fgo7$$\"1***\\7y%3TiFN
$\"1*)yDq#\\7C\"Fgo7$$\"1****\\P![hY'FN$\"1w]#[*=526Fgo7$$\"1LLL$Qx$om
FN$\"1wIk\"G1k')*FN7$$\"1+++v.I%)oFN$\"1z^YRcx+')FN7$$\"1mm\"zpe*zqFN$
\"10?eJ(Q#)[(FN7$$\"1+++D\\'QH(FN$\"1m%[br%zDjFN7$$\"1KLe9S8&\\(FN$\"1
mX(RW4uH&FN7$$\"1***\\i?=bq(FN$\"1F%GD6rLI%FN7$$\"1LLL3s?6zFN$\"1ABb3w
LAMFN7$$\"1++DJXaE\")FN$\"1n7=7G^0EFN7$$\"1nmmm*RRL)FN$\"1q%Q*)H(=F>FN
7$$\"1mm;a<.Y&)FN$\"1n]j\")*HpM\"FN7$$\"1LLe9tOc()FN$\"1IcuK1i[))F27$$
\"1+++]Qk\\*)FN$\"1'R,obR*obF27$$\"1LL$3dg6<*FN$\"1/pQA!*\\tGF27$$\"1m
mmmxGp$*FN$\"1unXBEZ@8F27$$\"1++D\"oK0e*FN$\"1X*3S$omkSF,7$$\"1++v=5s#
y*FN$\"1]<\"4\\9,*e!#>7$$\"\"\"F(F(-%'COLOURG6&%$RGBG$\"#5!\"\"F(F(-%)
POLYGONSG6U7&7$$\"1+++++++qFNF(7$Fj]l$\"1.+++++QzFN7$$\"1****\\i9RlqFN
$\"1+AN+GipvFN7$F`^lF(7&Fd^lF_^l7$$\"1+]PC#)GArFN$\"1_dW+HC`sFN7$Fg^lF
(7&F[_lFf^l7$$\"1++v$eui=(FN$\"1Qng.<Y-pFN7$F^_lF(7&Fb_lF]_l7$$\"1***
\\i3&o]sFN$\"14$p?^_^b'FN7$Fe_lF(7&Fi_lFd_l7$$\"1**\\(oX*y9tFN$\"1Fj^C
&)p:iFN7$F\\`lF(7&F``lF[`l7$$\"1+]P9CAutFN$\"12_\\E:(o!fFN7$Fc`lF(7&Fg
`lFb`l7$$\"1**\\P*zhdV(FN$\"16T#y7=Mf&FN7$Fj`lF(7&F^alFi`l7$$\"1+]P>fS
*\\(FN$\"1WDS@=Ow_FN7$FaalF(7&FealF`al7$$\"1+](=$f%Gc(FN$\"1#*fZ!evy'
\\FN7$FhalF(7&F\\blFgal7$$\"1++]#y,\"GwFN$\"1ufXP;yeYFN7$F_blF(7&FcblF
^bl7$$\"1++Dr\"zbo(FN$\"10LO60r$R%FN7$FfblF(7&FjblFebl7$$\"1****\\(4&G
]xFN$\"1MuM!>QO5%FN7$F]clF(7&FaclF\\cl7$$\"1****\\7nD:yFN$\"1+:v&3X:#Q
FN7$FdclF(7&FhclFccl7$$\"1++]-*oy(yFN$\"1i#3#H3leNFN7$F[dlF(7&F_dlFjcl
7$$\"1+]PpnsMzFN$\"1:'zZYFxK$FN7$FbdlF(7&FfdlFadl7$$\"1++]siL-!)FN$\"1
d9$\\ENI1$FN7$FidlF(7&F]elFhdl7$$\"1*******Q5'f!)FN$\"17x$p$[QZGFN7$F`
elF(7&FdelF_el7$$\"1**\\P/QBE\")FN$\"1=GR:,h1EFN7$FgelF(7&F[flFfel7$$
\"1+++:o?&=)FN$\"13BG]\"eES#FN7$F^flF(7&FbflF]fl7$$\"1+]Pa&4*\\#)FN$\"
1)eaX8E*)=#FN7$FeflF(7&FiflFdfl7$$\"1+]7j=_6$)FN$\"18*eHCc_*>FN7$F\\gl
F(7&F`glF[gl7$$\"1,+vVy!eP)FN$\"1kv+wI].=FN7$FcglF(7&FgglFbgl7$$\"1+](
=WU[V)FN$\"1Y[AQ)Qnj\"FN7$FjglF(7&F^hlFigl7$$\"1++DJ#>&)\\)FN$\"1M=(>Z
))oY\"FN7$FahlF(7&FehlF`hl7$$\"1+]P>:mk&)FN$\"1[2lU9Z,8FN7$FhhlF(7&F\\
ilFghl7$$\"1+]iv&QAi)FN$\"1+,4Jpdm6FN7$F_ilF(7&FcilF^il7$$\"1++vtLU%o)
FN$\"1-y,PEMI5FN7$FfilF(7&FjilFeil7$$\"1+++bjm[()FN$\"1d6:*ps\")**)F27
$F]jlF(7&FajlF\\jl7$$\"1++vyb^6))FN$\"1q$>6&=Z?yF27$FdjlF(7&FhjlFcjl7$
$\"1+]PMaKs))FN$\"1'R'=TZ%Hx'F27$F[[mF(7&F_[mFjjl7$$\"1++D6W%)R*)FN$\"
1ro!QmLPr&F27$Fb[mF(7&Ff[mFa[m7$$\"1+++:K^+!*FN$\"1u%)*)*fuI&[F27$Fi[m
F(7&F]\\mFh[m7$$\"1++]7,Hl!*FN$\"1/KY))>mESF27$F`\\mF(7&Fd\\mF_\\m7$$
\"1**\\P4w)R7*FN$\"1\"G3wHtxN$F27$Fg\\mF(7&F[]mFf\\m7$$\"1++]x%f\")=*F
N$\"1oq51%>.r#F27$F^]mF(7&Fb]mF]]m7$$\"1+]P/-a[#*FN$\"1%)GDyVyx@F27$Fe
]mF(7&Fi]mFd]m7$$\"1+](=Yb;J*FN$\"1hX,f(onp\"F27$F\\^mF(7&F`^mF[^m7$$
\"1++]i@Ot$*FN$\"17@MY]:(H\"F27$Fc^mF(7&Fg^mFb^m7$$\"1+]PfL'zV*FN$\"1I
A`u1f)[*F,7$Fj^mF(7&F^_mFi^m7$$\"1,++!*>=+&*FN$\"1G^:w1ihnF,7$Fa_mF(7&
Fe_mF`_m7$$\"1++DE&4Qc*FN$\"1J,bR&4Xb%F,7$Fh_mF(7&F\\`mFg_m7$$\"1+]P%>
5pi*FN$\"1yvNVvy()GF,7$F_`mF(7&Fc`mF^`m7$$\"1,++bJ*[o*FN$\"1U!)GUy\"3w
\"F,7$Ff`mF(7&Fj`mFe`m7$$\"1,+Dr\"[8v*FN$\"15!os.I6x)Fj\\l7$F]amF(7&Fa
amF\\am7$$\"1,++Ijy5)*FN$\"1IK#=Ce@\"RFj\\l7$FdamF(7&FhamFcam7$$\"1+]P
/)fT()*FN$\"1m]c)\\hd;\"Fj\\l7$F[bmF(7&F_bmFjam7$$\"1,]i0j\"[$**FN$\"1
\"*)Qo:m,k\"!#?7$FbbmF(7&FgbmFabmF[]lF[]l7\"-%&STYLEG6#%,PATCHNOGRIDG-
F_]l6&Fa]l$\"*++++\"!\")F`cmF(-%%TEXTG6%7$$\"\"(Fd]l$!\"%!\"#%\"xG-F_]
l6&Fa]lF(F(F`cm-Fdcm6%7$$\"#vF[dm$\"\"#Fd]l%%.070G-F_]l6&Fa]lF(F(F(-%+
AXESLABELSG6$Q\"~6\"F\\em-%%VIEWG6$;F(F\\]l%(DEFAULTG" 1 2 0 1 0 2 9 
1 4 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 18 "Find the value of " }{TEXT 267 
3 "x, " }{TEXT -1 137 "which has .070 area to the right of it.  The 3r
d argument of the function call (0..1) tells Maple to look for a solut
ion between 0 and 1." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 35 "fsolve(F(alpha,beta,x)=.93,x,0..1);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+cM$f+(!#5" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 30 "Proper
ties of the Distribution" }}{EXCHG {PARA 257 "" 0 "" {TEXT -1 0 "" }
{TEXT 265 32 "Calculation of Mean and Variance" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 73 "To calculate the mean of \+
the Beta distribution,  we can simply integrate " }{TEXT 266 1 "x" }
{TEXT -1 61 "*(Beta PDF),  per the definition of mathematical expectat
ion." }}{PARA 0 "" 0 "" {MPLTEXT 0 21 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
21 "with(plots, display):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
29 "interface( showassumed = 0 );" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "assume(alpha>0); assume(beta>0);" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 91 "f:=(alpha,beta,x)->GAMMA(alpha+beta)/(GAMMA(
alpha)*GAMMA(beta))*x^(alpha-1)*(1-x)^(beta-1);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"fGR6%%&alphaG%%betaG%\"xG6\"6$%)operatorG%&arrowGF*
*&*(-%&GAMMAG6#,&9$\"\"\"9%F5F5)9&,&F4F5!\"\"F5F5),&F5F5F8F:,&F6F5F:F5
F5\"\"\"*&-F16#F4\"\"\"-F16#F6\"\"\"!\"\"F*F*F*" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 34 "EX:=int(x*f(alpha,beta,x),x=0..1);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#EXG*&%'alpha|irG\"\"\",&F&\"\"\"%&beta|ir
GF)!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Calculating Var(" }
{TEXT 258 1 "X" }{TEXT -1 28 "), the variance of the Beta(" }{XPPEDIT 
18 0 "alpha,beta;" "6$%&alphaG%%betaG" }{TEXT -1 49 ") distribution, w
e will employ the formula:  Var(" }{TEXT 259 1 "X" }{TEXT -1 7 ") = E(
 " }{XPPEDIT 18 0 "X^2;" "6#*$%\"XG\"\"#" }{TEXT -1 5 " ) - " }
{XPPEDIT 18 0 "( E(X) )^2" "6#*$-%\"EG6#%\"XG\"\"#" }}{PARA 0 "" 0 "" 
{MPLTEXT 0 21 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "E_X_SQ
:=int((x^2)*f(alpha,beta,x),x=0..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%'E_X_SQG*&*&%'alpha|irG\"\"\",&F'F(F(F(F(\"\"\"*&,&F'F(%&beta|irGF
(\"\"\",(F'F(F-F(F(F(\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "VarX:=simplify(E_X_SQ-EX^2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%VarXG*&*&%'alpha|irG\"\"\"%&beta|irGF(\"\"\"*&),&F'F
(F)F(\"\"#F*,(F'F(F)F(F(F(\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 10 "Simulation
" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
281 "We will now simulate some data from a Beta distribution in order \+
to compare the sampling distribution to the theoretical distribution. \+
 The next portion of code will simulate a random sample of size 500 fr
om a Beta(3,4) distribution, but you are encouraged to change the valu
es of " }{XPPEDIT 18 0 "alpha" "6#%&alphaG" }{TEXT -1 5 " and " }
{XPPEDIT 18 0 "beta" "6#%%betaG" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "restart: wi
th(plots,display):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "f:=(a
lpha,beta,x)->GAMMA(alpha+beta)/(GAMMA(alpha)*GAMMA(beta))*x^(alpha-1)
*(1-x)^(beta-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6%%&alphaG%
%betaG%\"xG6\"6$%)operatorG%&arrowGF**&*(-%&GAMMAG6#,&9$\"\"\"9%F5F5)9
&,&F4F5!\"\"F5F5),&F5F5F8F:,&F6F5F:F5F5\"\"\"*&-F16#F4\"\"\"-F16#F6\"
\"\"!\"\"F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "alpha:=3
: beta:=4: n:=500:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "sampl
e:=BetaS(alpha-1, beta-1, n):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 121 "Remember that when you plot histogra
ms, the number of bins that you select can make a significant differen
ce in the plot." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 13 "num_bins:=20:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "a:=Histogram(sample,0..1,num_bins):" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 44 "b:=plot(f(alpha,beta,x),x=0..1,color=blac
k):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "display([a,b],title=
\"Simulated vs. Theoretical\");" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 
300 {PLOTDATA 2 "6'-%'CURVESG6%7\\p7$\"\"!F(F'7$$\"1+++++++]!#<F(F)F)7
$F*$\"1+++++++O!#;7$$\"1+++++++5F0F.7$F2F(F47$F2$\"1+++++++kF07$$\"1++
+++++:F0F67$F9F(F;7$F9$\"1++++++?6!#:7$$\"1+++++++?F0F=7$FAF(FC7$FA$\"
1++++++g8F?7$$\"1+++++++DF0FE7$FHF(FJ7$FH$\"1+++++++;F?7$$\"1+++++++IF
0FL7$FOF(FQ7$FO$\"1++++++g:F?7$$\"1+++++++NF0FS7$FVF(FX7$FV$\"1++++++!
G#F?7$$\"1+++++++SF0FZ7$FgnF(Fin7$Fgn$\"1+++++++AF?7$$\"1+++++++XF0F[o
7$F^oF(F`o7$F^o$\"1++++++g>F?7$$F+F0Fbo7$FeoF(Ffo7$FeoFL7$$\"1+++++++b
F0FL7$FioF(F[p7$Fio$\"1++++++S9F?7$$\"1+++++++gF0F]p7$F`pF(Fbp7$F`p$\"
1++++++g<F?7$$\"1+++++++lF0Fdp7$FgpF(Fip7$Fgp$\"1+++++++!)F07$$\"1++++
+++qF0F[q7$F^qF(F`q7$F^qF67$$\"1+++++++vF0F67$FcqF(Feq7$FcqFgn7$F[qFgn
7$F[qF(Fhq7$F[q$\"1+++++++7F07$$\"1+++++++&)F0Fjq7$F]rF(F_rF\\r7$$\"1+
++++++!*F0Fjq7$FarF(Fcr7$Far$FhnF,7$$\"1+++++++&*F0Fer7$FgrF(FirFir7$$
\"\"\"F(F(Fjr-%'COLOURG6&%$RGBG$\"*++++\"!\")F(F(-%*LINESTYLEG6#\"\"$-
F$6$7enF'7$$\"1mmmT&)G\\a!#=$\"1\"H\"oDkr_<F^t7$$\"1LLL3x&)*3\"F,$\"1%
Rz)*Hbi*oF^t7$$\"1++]ilyM;F,$\"1fs>%o_h_\"F,7$$\"1nmm;arz@F,$\"1\"H/f8
=$oEF,7$$\"1++D\"y%*z7$F,$\"1s@zufwO`F,7$$\"1LL$e9ui2%F,$\"1AvgOBY*z)F
,7$$\"1nmm\"z_\"4iF,$\"1k]pfE_3>F07$$\"1mmmT&phN)F,$\"11$R#GpfCKF07$$
\"1LLe*=)H\\5F0$\"1F0b2_=PZF07$$\"1nm\"z/3uC\"F0$\"1V&[&G$e+E'F07$$\"1
++DJ$RDX\"F0$\"1B0UQ0I0zF07$$\"1nm\"zR'ok;F0$\"1ac,,o,H'*F07$$\"1++D1J
:w=F0$\"1/!ps%*HB8\"F?7$$\"1LLL3En$4#F0$\"1)[?\"4)\\)*H\"F?7$$\"1nm;/R
E&G#F0$\"1C>k^hvQ9F?7$$\"1+++D.&4]#F0$\"1!z0^ZKEe\"F?7$$\"1+++vB_<FF0$
\"133B5[L6<F?7$$\"1+++v'Hi#HF0$\"1P#y![>`==F?7$$\"1nm\"z*ev:JF0$\"1vJU
b\"3/!>F?7$$\"1LLL347TLF0$\"1(yC:f-w(>F?7$$\"1LLLLY.KNF0$\"1'3Y8Ep`-#F
?7$$\"1n;HdO2VOF0$\"1u+rvvjX?F?7$$\"1++D\"o7Tv$F0$\"1BqW!f%Qg?F?7$$\"1
m;HK5S_QF0$\"1s1?X'e)o?F?7$$\"1LLL$Q*o]RF0$\"1t#o[QtI2#F?7$$\"1m;H#GF&
eSF0$\"1IL8!eiG2#F?7$$\"1++D\"=lj;%F0$\"1(3*oh9on?F?7$$\"1++]iB0pUF0$
\"1$>G9DG#e?F?7$$\"1++vV&R<P%F0$\"1UK@nwZW?F?7$$\"1LL$e9Ege%F0$\"1J%R)
46]-?F?7$$\"1LLeR\"3Gy%F0$\"1gbY/22\\>F?7$$\"1nm;/T1&*\\F0$\"1C:(GIZo(
=F?7$$\"1mm\"zRQb@&F0$\"1o?'H<6vy\"F?7$$\"1***\\(=>Y2aF0$\"1@R-@MS*p\"
F?7$$\"1mm;zXu9cF0$\"1Ee#4[H^f\"F?7$$\"1+++]y))GeF0$\"1cav9\\Pz9F?7$$
\"1****\\i_QQgF0$\"1cNF+9Ag8F?7$$\"1***\\7y%3TiF0$\"1*)yDq#\\7C\"F?7$$
\"1****\\P![hY'F0$\"1w]#[*=526F?7$$\"1LLL$Qx$omF0$\"1wIk\"G1k')*F07$$
\"1+++v.I%)oF0$\"1z^YRcx+')F07$$\"1mm\"zpe*zqF0$\"10?eJ(Q#)[(F07$$\"1+
++D\\'QH(F0$\"1m%[br%zDjF07$$\"1KLe9S8&\\(F0$\"1mX(RW4uH&F07$$\"1***\\
i?=bq(F0$\"1F%GD6rLI%F07$$\"1LLL3s?6zF0$\"1ABb3wLAMF07$$\"1++DJXaE\")F
0$\"1n7=7G^0EF07$$\"1nmmm*RRL)F0$\"1q%Q*)H(=F>F07$$\"1mm;a<.Y&)F0$\"1n
]j\")*HpM\"F07$$\"1LLe9tOc()F0$\"1IcuK1i[))F,7$$\"1+++]Qk\\*)F0$\"1'R,
obR*obF,7$$\"1LL$3dg6<*F0$\"1/pQA!*\\tGF,7$$\"1mmmmxGp$*F0$\"1unXBEZ@8
F,7$$\"1++D\"oK0e*F0$\"1X*3S$omkSF^t7$$\"1++v=5s#y*F0$\"1]<\"4\\9,*e!#
>Fjr-F^s6&F`sF(F(F(-%&TITLEG6#Q:Simulated~vs.~Theoretical6\"-%+AXESLAB
ELSG6$%!GFjel-%%VIEWG6$;F(F[s%(DEFAULTG" 1 2 0 1 0 2 9 1 4 2 1.000000 
45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 63 "Now let's compare the simulated mean to t
he theoretical mean.  " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "theo_mean:=alpha/(alpha+beta);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*theo_meanG#\"\"$\"\"(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "sim_mean:=Mean(sample);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%)sim_meanG$\"+if*))H%!#5" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 47 "relative_error:=(sim_mean-theo_mean)/theo
_mean;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%/relative_errorG$\"++WsvI!
#7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "3" 0 }
{VIEWOPTS 1 1 0 1 1 1803 }