{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 "" 1 18 0 
0 0 0 0 1 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 "" 0 1 0 0 
0 0 1 0 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 }{CSTYLE "" -1 268 "" 1 18 0 
0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 1 0 0 0 0 0 
0 0 0 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 271 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 272 "" 1 18 0 
0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 0 1 0 0 0 0 1 0 0 0 0 0 
0 0 0 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 275 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 276 "" 0 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 277 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 
0 0 }{CSTYLE "" -1 278 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 279 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 280 "" 0 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 281 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 
0 0 }{CSTYLE "" -1 282 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 283 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 284 "" 0 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 285 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 
0 0 }{CSTYLE "" -1 286 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 287 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 288 "" 0 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 289 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 
0 0 }{CSTYLE "" -1 290 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Nor
mal" -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 Output" 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 }}
{SECT 0 {SECT 1 {PARA 3 "" 0 "" {TEXT -1 34 "Probability Distribution \+
and Shape" }}{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 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 22 "                      " }{TEXT 
256 25 " The Poisson Distribution" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 12 "The Poisson(" }{XPPEDIT 18 0 "lambda" "6#
%'lambdaG" }{TEXT -1 83 ") distribution is a discrete distribution on \+
the non-negative integers \{0,1,2,...\}." }}{PARA 0 "" 0 "" {TEXT -1 
14 "The parameter " }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 
18 " must be positive." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 0 
21 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 3 "If " }{TEXT 257 1 "X" }{TEXT -1 41 " is a random variable \+
having the Poisson(" }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 
49 ") distribution, then the probability distribution" }}{PARA 0 "" 0 
"" {TEXT -1 13 "function for " }{TEXT 259 1 "X" }{TEXT -1 3 " is" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 11 "         \+
  " }{TEXT 260 1 "f" }{TEXT -1 3 " ( " }{TEXT 261 1 "k" }{TEXT -1 8 " \+
) = P( " }{TEXT 262 1 "X" }{TEXT -1 3 " = " }{TEXT 263 1 "k" }{TEXT 
-1 5 " ) = " }{XPPEDIT 18 0 "(exp(-lambda)*lambda^k)/(k!)" "6#*(-%$exp
G6#,$%'lambdaG!\"\"\"\"\")F(%\"kGF*-%*factorialG6#F,F)" }{TEXT -1 5 " \+
 ,  " }{TEXT 264 1 "k" }{TEXT -1 15 " = 0, 1, 2, ..." }}{PARA 0 "" 0 "
" {TEXT 258 3 "   " }}{PARA 0 "" 0 "" {TEXT -1 29 "Recall the conventi
on 0! = 1." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 69 "The following code will draw a probability histogram for the Po
isson(" }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 14 ") distribu
tion" }}{PARA 0 "" 0 "" {TEXT -1 4 "for " }{XPPEDIT 18 0 "lambda" "6#%
'lambdaG" }{TEXT -1 50 "=2, but you are encouraged to try other values
 of " }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 1 "." }}{PARA 0 
"" 0 "" {MPLTEXT 0 21 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
10 "lambda:=2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'lambdaG\"\"#" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "ProbHist(PoissonPDF(lambda,x
),0..20,21);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&
-%'CURVESG6#7`p7$$!1+++++++]!#;\"\"!7$F($\"1+++KGN`8F*7$$\"1+++++++]F*
F-7$F0F+F27$F0$\"1+++kcq1FF*7$$\"1+++++++:!#:F47$F7F+F:F67$$\"1+++++++
DF9F47$F<F+F>7$F<$\"1+++U/Z/=F*7$$\"1+++++++NF9F@7$FCF+FE7$FC$\"1+++9A
NA!*!#<7$$\"1+++++++XF9FG7$FKF+FM7$FK$\"1+++')3%*3OFI7$$\"1+++++++bF9F
O7$FRF+FT7$FR$\"1+++&H!)H?\"FI7$$\"1+++++++lF9FV7$FYF+Fen7$FY$\"1+++el
3PM!#=7$$\"1+++++++vF9Fgn7$F[oF+F]o7$F[o$\"1+++$R;Ff)!#>7$$\"1+++++++&
)F9F_o7$FcoF+Feo7$Fco$\"1+++KD\\4>Fao7$$\"1+++++++&*F9Fgo7$FjoF+F\\p7$
Fjo$\"1+++k])*=Q!#?7$$\"1++++++]5!#9F^p7$FbpF+Fep7$Fbp$\"1+++2#4O%p!#@
7$$\"1++++++]6FdpFgp7$F[qF+F]q7$F[q$\"1+++,#os:\"Fip7$$\"1++++++]7FdpF
_q7$FbqF+Fdq7$Fbq$\"1+++<ET!y\"!#A7$$\"1++++++]8FdpFfq7$FjqF+F\\r7$Fjq
$\"1+++'fYMa#!#B7$$\"1++++++]9FdpF^r7$FbrF+Fdr7$Fbr$\"1+++G@E\"R$!#C7$
$\"1++++++]:FdpFfr7$FjrF+F\\s7$Fjr$\"1+++hw2RU!#D7$$\"1++++++];FdpF^s7
$FbsF+Fds7$Fbs$\"1+++)=]r)\\!#E7$$\"1++++++]<FdpFfs7$FjsF+F\\t7$Fjs$\"
1+++()zFTb!#F7$$\"1++++++]=FdpF^t7$FbtF+Fdt7$Fbt$\"1+++'>CH$e!#G7$$\"1
++++++]>FdpFft7$FjtF+F\\u7$Fjt$\"1*****f>CH$e!#H7$$\"1++++++]?FdpF^u7$
FbuF+-%+AXESLABELSG6$%!GFhu-%'COLOURG6&%$RGBGF+F+$\"*++++\"!\")-%%VIEW
G6$%(DEFAULTGFcv" 1 2 0 1 0 2 6 1 4 2 1.000000 45.000000 45.000000 0 }
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 21 
"To see the effect of " }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT 
-1 29 " on the shape of the Poisson(" }{XPPEDIT 18 0 "lambda" "6#%'lam
bdaG" }{TEXT -1 29 ") distribution, the following" }}{PARA 0 "" 0 "" 
{TEXT -1 58 "animation will draw a series of probability histograms as
 " }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 21 " varies from 1 \+
to 15." }}{PARA 0 "" 0 "" {MPLTEXT 0 21 0 "" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 21 "for n from 1 to 15 do" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "num:=convert(evalf(n), string):" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 59 "tracker[n]:=textplot([18,0.3,`Lambda is `.num],color=
blue):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "H[n]:=ProbHist(PoissonPDF
(n,x),0..25,26):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "P[n]:=display(
\{H[n],tracker[n]\}):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "display([seq(P[n], n=1..15)], inseq
uence=true,title=\"Lambda is Increasing from 1 to 15\");" }}{PARA 13 "
" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6$-%(ANIMATEG617&-%'CURVESG6
$7dq7$$!1+++++++]!#;\"\"!7$F,$\"1+++7WzyOF.7$$\"1+++++++]F.F17$F4F/F6F
37$$\"1+++++++:!#:F17$F8F/F;7$F8$\"1+++1sRR=F.7$$\"1+++++++DF:F=7$F@F/
FB7$F@$\"1+++@SKJh!#<7$$\"1+++++++NF:FD7$FHF/FJ7$FH$\"1+++05$G`\"FF7$$
\"1+++++++XF:FL7$FOF/FQ7$FO$\"1+++5?mlI!#=7$$\"1+++++++bF:FS7$FWF/FY7$
FW$\"1+++%oO%4^!#>7$$\"1+++++++lF:Fen7$FinF/F[o7$Fin$\"1+++h_>*H(!#?7$
$\"1+++++++vF:F]o7$FaoF/Fco7$Fao$\"1,++xS*R7*!#@7$$\"1+++++++&)F:Feo7$
FioF/F[p7$Fio$\"1+++?rx85Fgo7$$\"1+++++++&*F:F]p7$F`pF/Fbp7$F`p$F^p!#A
7$$\"1++++++]5!#9Fdp7$FgpF/Fjp7$Fgp$\"1+++Nc:;#*!#C7$$\"1++++++]6FipF
\\q7$F`qF/Fbq7$F`q$\"1+++'pH,o(!#D7$$\"1++++++]7FipFdq7$FhqF/Fjq7$Fhq$
\"1+++u?z2f!#E7$$\"1++++++]8FipF\\r7$F`rF/Fbr7$F`r$\"1+++\"[^)>U!#F7$$
\"1++++++]9FipFdr7$FhrF/Fjr7$Fhr$\"1+++?VB8G!#G7$$\"1++++++]:FipF\\s7$
F`sF/Fbs7$F`s$\"1+++]9Fe<!#H7$$\"1++++++];FipFds7$FhsF/Fjs7$Fhs$\"1+++
CtFM5!#I7$$\"1++++++]<FipF\\t7$F`tF/Fbt7$F`t$\"1*****>8&)fu&!#K7$$\"1+
+++++]=FipFdt7$FhtF/Fjt7$Fht$\"1+++,F?CI!#L7$$\"1++++++]>FipF\\u7$F`uF
/Fbu7$F`u$\"1+++]857:!#M7$$\"1++++++]?FipFdu7$FhuF/Fju7$Fhu$\"1+++?E[+
s!#O7$$\"1++++++]@FipF\\v7$F`vF/Fbv7$F`v$\"1+++Ym%HF$!#P7$$\"1++++++]A
FipFdv7$FhvF/Fjv7$Fhv$\"1+++\"G?IU\"!#Q7$$\"1++++++]BFipF\\w7$F`wF/Fbw
7$F`w$\"1+++q6DHf!#S7$$\"1++++++]CFipFdw7$FhwF/Fjw7$Fhw$\"1+++o/qrB!#T
7$$\"1++++++]DFipF\\x7$F`xF/-%'COLOURG6&%$RGBGF/F/$\"*++++\"!\")-%%TEX
TG6%7$$\"#=F/$\"\"$!\"\"%-Lambda~is~1.GFcx-%+AXESLABELSG6$%!GFgy-%%VIE
WG6$%(DEFAULTGF[z7&-F[y6%F]y%-Lambda~is~2.GFcx-F(6$7dqF+7$F,$\"1+++KGN
`8F.7$F4FdzF6F67$F4$\"1+++kcq1FF.7$F8FhzF;F;Fjz7$F@FhzFBFB7$F@$\"1+++U
/Z/=F.7$FHF][lFJFJ7$FH$\"1+++9ANA!*FF7$FOFa[lFQFQ7$FO$\"1+++')3%*3OFF7
$FWFe[lFYFY7$FW$\"1+++&H!)H?\"FF7$FinFi[lF[oF[o7$Fin$\"1+++el3PMFU7$Fa
oF]\\lFcoFco7$Fao$\"1+++$R;Ff)Fgn7$FioFa\\lF[pF[p7$Fio$\"1+++KD\\4>Fgn
7$F`pFe\\lFbpFbp7$F`p$\"1+++k])*=QF_o7$FgpFi\\lFjpFjp7$Fgp$\"1+++2#4O%
pFgo7$F`qF]]lFbqFbq7$F`q$\"1+++,#os:\"Fgo7$FhqFa]lFjqFjq7$Fhq$\"1+++<E
T!y\"Fep7$F`rFe]lFbrFbr7$F`r$\"1+++'fYMa#!#B7$FhrFi]lFjrFjr7$Fhr$\"1++
+G@E\"R$F^q7$F`sF^^lFbsFbs7$F`s$\"1+++hw2RUFfq7$FhsFb^lFjsFjs7$Fhs$\"1
+++)=]r)\\F^r7$F`tFf^lFbtFbt7$F`t$\"1+++()zFTbFfr7$FhtFj^lFjtFjt7$Fht$
\"1+++'>CH$eF^s7$F`uF^_lFbuFbu7$F`u$\"1*****f>CH$eFfs7$FhuFb_lFjuFju7$
Fhu$\"1+++-f;bbF^t7$F`vFf_lFbvFbv7$F`v$\"1+++>3:]]!#J7$FhvFj_lFjvFjv7$
Fhv$\"1+++'\\N9R%Fft7$F`wF_`lFbwFbw7$F`w$\"1+++!eH&fOF^u7$FhwFc`lFjwFj
w7$Fhw$\"1+++jOiFHFfu7$F`xFg`lFbxFcxFdyFhy7&-F(6$7dqF+7$F,$\"1+++Poqy
\\FF7$F4F_alF6F67$F4$\"1+++^?h$\\\"F.7$F8FcalF;F;7$F8$\"1+++x!=/C#F.7$
F@FgalFBFBFial7$FHFgalFJFJ7$FH$\"1+++dNJ!o\"F.7$FOF\\blFQFQ7$FO$\"1+++
M\")=35F.7$FWF`blFYFY7$FW$\"1+++s1%4/&FF7$FinFdblF[oF[o7$Fin$\"1+++XJS
g@FF7$FaoFhblFcoFco7$Fao$\"1,++'z6:5)FU7$FioF\\clF[pF[p7$Fio$\"1+++KR]
+FFU7$F`pF`clFbpFbp7$F`p$\"1+++'z6:5)Fgn7$FgpFdclFjpFjp7$Fgp$\"1+++<K]
4AFgn7$F`qFhclFbqFbq7$F`q$\"1+++U!eP_&F_o7$FhqF\\dlFjqFjq7$Fhq$\"1+++%
R8ZF\"F_o7$F`rF`dlFbrFbr7$F`r$\"1+++-(G:t#Fgo7$FhrFddlFjrFjr7$Fhr$\"1+
++/u0jaFep7$F`sFhdlFbsFbs7$F`s$\"1+++kKKC5Fep7$FhsF\\elFjsFjs7$Fhs$\"1
+++)GHw!=F[^l7$F`tF`elFbtFbt7$F`t$\"1+++![:F,$F^q7$FhtFdelFjtFjt7$Fht$
\"1+++z\">pv%Ffq7$F`uFhelFbuFbu7$F`u$\"1+++o(y`8(F^r7$FhuF\\flFjuFju7$
Fhu$\"1+++C)R$>5F^r7$F`vF`flFbvFbv7$F`v$\"1+++^)3+R\"Ffr7$FhvFdflFjvFj
v7$Fhv$\"1+++B]08=F^s7$F`wFhflFbwFbw7$F`w$\"1+++z(=jE#Ffs7$FhwF\\glFjw
Fjw7$Fhw$\"1+++NDe>FF^t7$F`xF`glFbxFcx-F[y6%F]y%-Lambda~is~3.GFcxFdyFh
y7&-F[y6%F]y%-Lambda~is~4.GFcx-F(6$7dqF+7$F,$\"1+++*)QcJ=FF7$F4F^hlF6F
67$F4$\"1+++cbDEtFF7$F8FbhlF;F;7$F8$\"1+++66Dl9F.7$F@FfhlFBFB7$F@$\"1+
++\\\"oO&>F.7$FHFjhlFJFJF\\il7$FOFjhlFQFQ7$FO$\"1+++>X$Hc\"F.7$FWF_ilF
YFY7$FW$\"1+++Yj&>/\"F.7$FinFcilF[oF[o7$Fin$\"1+++ii.afFF7$FaoFgilFcoF
co7$Fao$\"1+++I\"=q(HFF7$FioF[jlF[pF[p7$Fio$\"1+++p\">JK\"FF7$F`pF_jlF
bpFbp7$F`p$\"1+++wmZ#H&FU7$FgpFcjlFjpFjp7$Fgp$\"1+++tp`C>FU7$F`qFgjlFb
qFbq7$F`q$\"1+++XK7:kFgn7$FhqF[[mFjqFjq7$Fhq$\"1+++wS)Q(>Fgn7$F`rF_[mF
brFbr7$F`r$\"1+++'yo'RcF_o7$FhrFc[mFjrFjr7$Fhr$\"1+++w;\"R]\"F_o7$F`sF
g[mFbsFbs7$F`s$\"1+++!>z(fPFgo7$FhsF[\\mFjsFjs7$Fhs$\"1+++u#Rl%))Fep7$
F`tF_\\mFbtFbt7$F`t$\"1+++;w*e'>Fep7$FhtFc\\mFjtFjt7$Fht$\"1+++B=tQTF[
^l7$F`uFg\\mFbuFbu7$F`u$\"1+++[OYx#)F^q7$FhuF[]mFjuFju7$Fhu$\"1+++U(fm
d\"F^q7$F`vF_]mFbvFbv7$F`v$\"1+++xSlmGFfq7$FhvFc]mFjvFjv7$Fhv$\"1+++_`
[&)\\F^r7$F`wFg]mFbwFbw7$F`w$\"1,++_A94$)Ffr7$FhwF[^mFjwFjw7$Fhw$\"1++
+gFYH8Ffr7$F`xF_^mFbxFcxFdyFhy7&-F(6$7dqF+7$F,$\"1+++**p%zt'FU7$F4Fg^m
F6F67$F4$\"1++++N(*oLFF7$F8F[_mF;F;7$F8$\"1+++\\PVA%)FF7$F@F__mFBFB7$F
@$\"1+++e*QPS\"F.7$FHFc_mFJFJ7$FH$\"1+++)ptYv\"F.7$FOFg_mFQFQFi_m7$FWF
g_mFYFY7$FW$\"1+++\"3GAY\"F.7$FinF\\`mF[oF[o7$Fin$\"1+++H'[W/\"F.7$Fao
F``mFcoFco7$Fao$\"1+++NR!y_'FF7$FioFd`mF[pF[p7$Fio$\"1+++UxbEOFF7$F`pF
h`mFbpFbp7$F`p$\"1+++q)yK\"=FF7$FgpF\\amFjpFjp7$Fgp$\"1,++(ow@C)FU7$F`
qF`amFbqFbq7$F`q$\"1+++'GSUV$FU7$FhqFdamFjqFjq7$Fhq$\"1+++\\;'3K\"FU7$
F`rFhamFbrFbr7$F`r$\"1+++IIO<ZFgn7$FhrF\\bmFjrFjr7$Fhr$\"1+++VVXs:Fgn7
$F`sF`bmFbsFbs7$F`s$\"1+++A)>R\"\\F_o7$FhsFdbmFjsFjs7$Fhs$\"1+++O0FX9F
_o7$F`tFhbmFbtFbt7$F`t$\"1+++y.k9SFgo7$FhtF\\cmFjtFjt7$Fht$\"1+++5V[c5
Fgo7$F`uF`cmFbuFbu7$F`u$\"1+++v2@TEFep7$FhuFdcmFjuFju7$Fhu$\"1+++$3(f)
G'F[^l7$F`vFhcmFbvFbv7$F`v$\"1+++5mAH9F[^l7$FhvF\\dmFjvFjv7$Fhv$\"1+++
pV,2JF^q7$F`wF`dmFbwFbw7$F`w$\"1+++.m%HZ'Ffq7$FhwFddmFjwFjw7$Fhw$\"1++
+@$*e%H\"Ffq7$F`xFhdmFbxFcx-F[y6%F]y%-Lambda~is~5.GFcxFdyFhy7&-F(6$7dq
F+7$F,$\"1+++x@vyCFU7$F4FcemF6F67$F4$\"1+++18D([\"FF7$F8FgemF;F;7$F8$
\"1+++>RvhWFF7$F@F[fmFBFB7$F@$\"1+++Py]B*)FF7$FHF_fmFJFJ7$FH$\"1+++wh_
Q8F.7$FOFcfmFQFQ7$FO$\"1+++69B1;F.7$FWFgfmFYFYFifm7$FinFgfmF[oF[o7$Fin
$\"1+++\"ypnP\"F.7$FaoF\\gmFcoFco7$Fao$\"1+++OtdK5F.7$FioF`gmF[pF[p7$F
io$\"1,++.*[Q)oFF7$F`pFdgmFbpFbp7$F`p$\"1+++T$4.8%FF7$FgpFhgmFjpFjp7$F
gp$\"1+++0g*GD#FF7$F`qF\\hmFbqFbq7$F`q$\"1+++-![k7\"FF7$FhqF`hmFjqFjq7
$Fhq$\"1+++z2**)>&FU7$F`rFdhmFbrFbr7$F`r$\"1+++1*Q\"GAFU7$FhrFhhmFjrFj
r7$Fhr$\"1+++Acb7*)Fgn7$F`sF\\imFbsFbs7$F`s$\"1+++d$3AM$Fgn7$FhsF`imFj
sFjs7$Fhs$\"1+++]Hgz6Fgn7$F`tFdimFbtFbt7$F`t$\"1+++M)4?$RF_o7$FhtFhimF
jtFjt7$Fht$\"1+++;toT7F_o7$F`uF\\jmFbuFbu7$F`u$\"1+++[>1DPFgo7$FhuF`jm
FjuFju7$Fhu$\"1+++9MIk5Fgo7$F`vFdjmFbvFbv7$F`v$\"1+++uck-HFep7$FhvFhjm
FjvFjv7$Fhv$\"1+++\\\">@d(F[^l7$F`wF\\[nFbwFbw7$F`w$\"1+++(yHI*=F[^l7$
FhwF`[nFjwFjw7$Fhw$\"1+++*[rKa%F^q7$F`xFd[nFbxFcx-F[y6%F]y%-Lambda~is~
6.GFcxFdyFhy7&-F[y6%F]y%-Lambda~is~7.GFcx-F(6$7dqF+7$F,$\"1+++c'>)=\"*
Fgn7$F4Fb\\nF6F67$F4$\"1+++fP<$Q'FU7$F8Ff\\nF;F;7$F8$\"1+++;36MAFF7$F@
Fj\\nFBFB7$F@$\"1+++P_#H@&FF7$FHF^]nFJFJ7$FH$\"1+++n\">E7*FF7$FOFb]nFQ
FQ7$FO$\"1+++$omrF\"F.7$FWFf]nFYFY7$FW$\"1+++(zF+\\\"F.7$FinFj]nF[oF[o
F\\^n7$FaoFj]nFcoFco7$Fao$\"1+++AVx.8F.7$FioF_^nF[pF[p7$Fio$\"1+++&pYS
,\"F.7$F`pFc^nFbpFbp7$F`p$\"1+++moK)4(FF7$FgpFg^nFjpFjp7$Fgp$\"1+++'4<
r^%FF7$F`qF[_nFbqFbq7$F`q$\"1+++t\\)\\j#FF7$FhqF__nFjqFjq7$Fhq$\"1+++i
!Q)=9FF7$F`rFc_nFbrFbr7$F`r$\"1+++6.>%4(FU7$FhrFg_nFjrFjr7$Fhr$\"1+++X
@i5LFU7$F`sF[`nFbsFbs7$F`s$\"1+++)=(R[9FU7$FhsF_`nFjsFjs7$Fhs$\"1+++B%
))R'fFgn7$F`tFc`nFbtFbt7$F`t$\"1+++K)G$>BFgn7$FhtFg`nFjtFjt7$Fht$\"1++
+%p&*[a)F_o7$F`uF[anFbuFbu7$F`u$\"1+++$\\82*HF_o7$FhuF_anFjuFju7$Fhu$
\"1+++y\\/p**Fgo7$F`vFcanFbvFbv7$F`v$\"1+++c)o><$Fgo7$FhvFganFjvFjv7$F
hv$\"1*****4E=Ql*Fep7$F`wF[bnFbwFbw7$F`w$\"1+++#*pp:GFep7$FhwF_bnFjwFj
w7$Fhw$\"1+++y:&R)yF[^l7$F`xFcbnFbxFcxFdyFhy7&-F[y6%F]y%-Lambda~is~8.G
Fcx-F(6$7dqF+7$F,$\"1+++ziiaLFgn7$F4F^cnF6F67$F4$\"1+++B5q$o#FU7$F8Fbc
nF;F;7$F8$\"1+++4/[t5FF7$F@FfcnFBFB7$F@$\"1+++DWhiGFF7$FHFjcnFJFJ7$FH$
\"1+++^)G_s&FF7$FOF^dnFQFQ7$FO$\"1+++ghOg\"*FF7$FWFbdnFYFY7$FW$\"1+++b
@Q@7F.7$FinFfdnF[oF[o7$Fin$\"1+++>`'eR\"F.7$FaoFjdnFcoFcoF\\en7$FioFjd
nF[pF[p7$Fio$\"1+++t\"p2C\"F.7$F`pF_enFbpFbp7$F`p$\"1+++%Q`h#**FF7$Fgp
FcenFjpFjp7$Fgp$\"1+++T1->sFF7$F`qFgenFbqFbq7$F`q$\"1+++G/o7[FF7$FhqF[
fnFjqFjq7$Fhq$\"1+++%\\\\;'HFF7$F`rF_fnFbrFbr7$F`r$\"1+++S6P#p\"FF7$Fh
rFcfnFjrFjr7$Fhr$\"1+++7%zf-*FU7$F`sFgfnFbsFbs7$F`s$\"1+++1(*)H^%FU7$F
hsF[gnFjsFjs7$Fhs$\"1+++i)fP7#FU7$F`tF_gnFbtFbt7$F`t$\"1+++;F$*Q%*Fgn7
$FhtFcgnFjtFjt7$Fht$\"1+++huGuRFgn7$F`uFggnFbuFbu7$F`u$\"1+++%)\\r*e\"
Fgn7$FhuF[hnFjuFju7$Fhu$\"1+++#3dg0'F_o7$F`vF_hnFbvFbv7$F`v$\"1+++vD?-
AF_o7$FhvFchnFjvFjv7$Fhv$\"1+++V]$)fwFgo7$F`wFghnFbwFbw7$F`w$\"1+++[$y
Kb#Fgo7$FhwF[inFjwFjw7$Fhw$\"1+++82\\q\")Fep7$F`xF_inFbxFcxFdyFhy7&-F[
y6%F]y%-Lambda~is~9.GFcx-F(6$7dqF+7$F,$\"1+++T!)4M7Fgn7$F4FjinF6F67$F4
$\"1+++P#)o56FU7$F8F^jnF;F;7$F8$\"1+++mq4)*\\FU7$F@FbjnFBFB7$F@$\"1+++
?\"H%*\\\"FF7$FHFfjnFJFJ7$FH$\"1+++?brtLFF7$FOFjjnFQFQ7$FO$\"1+++Nzosg
FF7$FWF^[oFYFY7$FW$\"1,++.>.4\"*FF7$FinFb[oF[oF[o7$Fin$\"1+++X7;r6F.7$
FaoFf[oFcoFco7$Fao$\"1++++kb<8F.7$FioFj[oF[pF[pF\\\\o7$F`pFj[oFbpFbp7$
F`p$\"1+++g2!e=\"F.7$FgpF_\\oFjpFjp7$Fgp$\"1,++?i+-(*FF7$F`qFc\\oFbqFb
q7$F`q$\"1+++lY]wsFF7$FhqFg\\oFjqFjq7$Fhq$\"1+++_,eP]FF7$F`rF[]oFbrFbr
7$F`r$\"1+++$QW%QKFF7$FhrF_]oFjrFjr7$Fhr$\"1+++Im1V>FF7$F`sFc]oFbsFbs7
$F`s$\"1+++!)\\(H4\"FF7$FhsFg]oFjsFjs7$Fhs$\"1+++F\"Qjy&FU7$F`tF[^oFbt
Fbt7$F`t$\"1+++k!pJ*GFU7$FhtF_^oFjtFjt7$Fht$\"1+++.&[/P\"FU7$F`uFc^oFb
uFbu7$F`u$\"1+++m#=q;'Fgn7$FhuFg^oFjuFju7$Fhu$\"1+++Gy+VEFgn7$F`vF[_oF
bvFbv7$F`v$\"1+++v/B\"3\"Fgn7$FhvF__oFjvFjv7$Fhv$\"1+++g=!4B%F_o7$F`wF
c_oFbwFbw7$F`w$\"1+++(>)e'e\"F_o7$FhwFg_oFjwFjw7$Fhw$\"1+++6vr6dFgo7$F
`xF[`oFbxFcxFdyFhy7&-F[y6%F]y%.Lambda~is~10.GFcx-F(6$7dqF+7$F,$\"1+++w
H**RXF_o7$F4Ff`oF6F67$F4$Fg`oFgn7$F8Fj`oF;F;7$F8$\"1+++)['**pAFU7$F@F]
aoFBFB7$F@$\"1+++i\\lmvFU7$FHFaaoFJFJ7$FH$\"1+++SPm\"*=FF7$FOFeaoFQFQ7
$FO$\"1+++![FLy$FF7$FWFiaoFYFY7$FW$\"1+++,ea0jFF7$FinF]boF[oF[o7$Fin$
\"1+++rD#z+*FF7$FaoFaboFcoFco7$Fao$\"1+++@.*f7\"F.7$FioFeboF[pF[p7$Fio
$\"1+++d.5^7F.7$F`pFiboFbpFbpF[co7$FgpFiboFjpFjp7$Fgp$\"1+++hROP6F.7$F
`qF^coFbqFbq7$F`q$\"1+++5I.y%*FF7$FhqFbcoFjqFjq7$Fhq$\"1,++BYz!H(FF7$F
`rFfcoFbrFbr7$F`r$\"1+++X/r2_FF7$FhrFjcoFjrFjr7$Fhr$\"1+++jp!=Z$FF7$F`
sF^doFbsFbs7$F`s$\"1+++_$z)p@FF7$FhsFbdoFjsFjs7$Fhs$\"1+++>'*Rw7FF7$F`
tFfdoFbtFbt7$F`t$\"1+++$**364(FU7$FhtFjdoFjtFjt7$Fht$\"1+++GE;KPFU7$F`
uF^eoFbuFbu7$F`u$\"1+++983m=FU7$FhuFbeoFjuFju7$Fhu$\"1+++$\\,h)))Fgn7$
F`vFfeoFbvFbv7$F`v$\"1+++Vq8RSFgn7$FhvFjeoFjvFjv7$Fhv$\"1+++Tl9c<Fgn7$
F`wF^foFbwFbw7$F`w$\"1+++^sF<tF_o7$FhwFbfoFjwFjw7$Fhw$\"1+++,4\"p#HF_o
7$F`xFffoFbxFcxFdyFhy7&-F[y6%F]y%.Lambda~is~11.GFcx-F(6$7dqF+7$F,$\"1+
++z+<q;F_o7$F4FagoF6F67$F4$\"1+++(3(=P=Fgn7$F8FegoF;F;7$F8$\"1+++)*GX5
5FU7$F@FigoFBFB7$F@$\"1+++eR*\\q$FU7$FHF]hoFJFJ7$FH$\"1+++RL()=5FF7$FO
FahoFQFQ7$FO$\"1+++X8_TAFF7$FWFehoFYFY7$FW$\"1+++*zb%4TFF7$FinFihoF[oF
[o7$Fin$\"1+++cirdkFF7$FaoF]ioFcoFco7$Fao$\"1+++_)f$z))FF7$FioFaioF[pF
[p7$Fio$\"1+++$4b_3\"F.7$F`pFeioFbpFbp7$F`p$\"1+++-1y$>\"F.7$FgpFiioFj
pFjpF[jo7$F`qFiioFbqFbq7$F`q$\"1+++&)))H%4\"F.7$FhqF^joFjqFjq7$Fhq$\"1
,++3@Xf#*FF7$F`rFbjoFbrFbr7$F`r$\"1+++*z$GvsFF7$FhrFfjoFjrFjr7$Fhr$\"1
+++>\"3_L&FF7$F`sFjjoFbsFbs7$F`s$\"1+++#ebzm$FF7$FhsF^[pFjsFjs7$Fhs$\"
1+++CIQtBFF7$F`tFb[pFbtFbt7$F`t$\"1+++P2S]9FF7$FhtFf[pFjtFjt7$Fht$\"1+
++'*o0(R)FU7$F`uFj[pFbuFbu7$F`u$\"1+++#H\"Q=YFU7$FhuF^\\pFjuFju7$Fhu$
\"1+++1@:>CFU7$F`vFb\\pFbvFbv7$F`v$\"1+++`gd47FU7$FhvFf\\pFjvFjv7$Fhv$
\"1+++\\*G\\y&Fgn7$F`wFj\\pFbwFbw7$F`w$\"1+++odU^EFgn7$FhwF^]pFjwFjw7$
Fhw$\"1+++Qtim6Fgn7$F`xFb]pFbxFcxFdyFhy7&-F[y6%F]y%.Lambda~is~12.GFcx-
F(6$7dqF+7$F,$\"1+++`B@WhFgo7$F4F]^pF6F67$F4$\"1+++C[0ttF_o7$F8Fa^pF;F
;7$F8$\"1+++%*G$QU%Fgn7$F@Fe^pFBFB7$F@$\"1+++eJ`p<FU7$FHFi^pFJFJ7$FH$
\"1+++t%*f3`FU7$FOF]_pFQFQ7$FO$\"1+++uQ1u7FF7$FWFa_pFYFY7$FW$\"1+++Zx7
[DFF7$FinFe_pF[oF[o7$Fin$\"1+++&**=#oVFF7$FaoFi_pFcoFco7$Fao$\"1*****>
\\GBb'FF7$FioF]`pF[pF[p7$Fio$\"1+++\"*zVO()FF7$F`pFa`pFbpFbp7$F`p$\"1+
++fDP[5F.7$FgpFe`pFjpFjp7$Fgp$\"1+++b\"zO9\"F.7$F`qFi`pFbqFbqF[ap7$Fhq
Fi`pFjqFjq7$Fhq$\"1+++NQqb5F.7$F`rF^apFbrFbr7$F`r$\"1+++@+*)[!*FF7$Fhr
FbapFjrFjr7$Fhr$\"1+++9?6RsFF7$F`sFfapFbsFbs7$F`s$\"1+++6SLHaFF7$FhsFj
apFjsFjs7$Fhs$\"1+++n5ZKQFF7$F`tF^bpFbtFbt7$F`t$\"1+++62)\\b#FF7$FhtFb
bpFjtFjt7$Fht$\"1+++G?n8;FF7$F`uFfbpFbuFbu7$F`u$\"1,++n@.#o*FU7$FhuFjb
pFjuFju7$Fhu$\"1+++5)*eKbFU7$F`vF^cpFbvFbv7$F`v$\"1+++gix<IFU7$FhvFbcp
FjvFjv7$Fhv$\"1+++i>\\u:FU7$F`wFfcpFbwFbw7$F`w$\"1+++3)fC(yFgn7$FhwFjc
pFjwFjw7$Fhw$\"1+++32yyPFgn7$F`xF^dpFbxFcxFdyFhy7&-F[y6%F]y%.Lambda~is
~13.GFcx-F(6$7dqF+7$F,$\"1+++2%H.E#Fgo7$F4FidpF6F67$F4$\"1+++H#G%QHF_o
7$F8F]epF;F;7$F8$\"1+++\\$y*4>Fgn7$F@FaepFBFB7$F@$\"1+++YGdw#)Fgn7$FHF
eepFJFJ7$FH$\"1+++vh))*o#FU7$FOFiepFQFQ7$FO$\"1+++aSq$*pFU7$FWF]fpFYFY
7$FW$\"1+++XDI::FF7$FinFafpF[oF[o7$Fin$\"1+++)HLT\"GFF7$FaoFefpFcoFco7
$Fao$\"1+++4m'Hd%FF7$FioFifpF[pF[p7$Fio$\"1+++8iR0mFF7$F`pF]gpFbpFbp7$
F`p$\"1+++y],(e)FF7$FgpFagpFjpFjp7$Fgp$\"1+++b!H[,\"F.7$F`qFegpFbqFbq7
$F`q$\"1+++V\")R*4\"F.7$FhqFigpFjqFjqF[hp7$F`rFigpFbrFbr7$F`r$\"1+++/(
p3-\"F.7$FhrF^hpFjrFjr7$Fhr$\"1*****>VPv%))FF7$F`sFbhpFbsFbs7$F`s$\"1+
++jTi)=(FF7$FhsFfhpFjsFjs7$Fhs$\"1+++%=$=(\\&FF7$F`tFjhpFbtFbt7$F`t$\"
1+++by=qRFF7$FhtF^ipFjtFjt7$Fht$\"1+++BVW;FFF7$F`uFbipFbuFbu7$F`u$\"1+
++4))ol<FF7$FhuFfipFjuFju7$Fhu$\"1+++`a/$4\"FF7$F`vFjipFbvFbv7$F`v$\"1
+++^\\!*ekFU7$FhvF^jpFjvFjv7$Fhv$\"1+++2ao]OFU7$F`wFbjpFbwFbw7$F`w$\"1
+++'fau(>FU7$FhwFfjpFjwFjw7$Fhw$\"1+++!Rw#G5FU7$F`xFjjpFbxFcxFdyFhy7&-
F(6$7dqF+7$F,$\"1+++\">(G:$)Fep7$F4Fb[qF6F67$F4$\"1+++2-9k6F_o7$F8Ff[q
F;F;7$F8$\"1*****pW\")*[\")F_o7$F@Fj[qFBFB7$F@$\"1+++3!eG!QFgn7$FHF^\\
qFJFJ7$FH$\"1+++..+J8FU7$FOFb\\qFQFQ7$FO$\"1+++\\3!os$FU7$FWFf\\qFYFY7
$FW$\"1*****pkoep)FU7$FinFj\\qF[oF[o7$Fin$\"1+++HP<R<FF7$FaoF^]qFcoFco
7$Fao$\"1+++ESbVIFF7$FioFb]qF[pF[p7$Fio$\"1+++utTMZFF7$F`pFf]qFbpFbp7$
F`p$\"1+++CV=GmFF7$FgpFj]qFjpFjp7$Fgp$\"1*****R&4(eV)FF7$F`qF^^qFbqFbq
7$F`q$\"1*****zW\\=%)*FF7$FhqFb^qFjqFjq7$Fhq$\"1+++z9*)f5F.7$F`rFf^qFb
rFbrFh^q7$FhrFf^qFjrFjr7$Fhr$\"1+++s/K#*)*FF7$F`sF[_qFbsFbs7$F`s$\"1++
+:/yb')FF7$FhsF__qFjsFjs7$Fhs$\"1+++`(*GGrFF7$F`tFc_qFbtFbt7$F`t$\"1++
+j`AWbFF7$FhtFg_qFjtFjt7$Fht$\"1+++*o=_3%FF7$F`uF[`qFbuFbu7$F`u$\"1+++
#3`'fGFF7$FhuF_`qFjuFju7$Fhu$\"1+++)QNk!>FF7$F`vFc`qFbvFbv7$F`v$\"1+++
ch=87FF7$FhvFg`qFjvFjv7$Fhv$\"1+++&Q6YQ(FU7$F`wF[aqFbwFbw7$F`w$\"1+++u
**o2VFU7$FhwF_aqFjwFjw7$Fhw$\"1+++'Q1BT#FU7$F`xFcaqFbxFcx-F[y6%F]y%.La
mbda~is~14.GFcxFdyFhy7&-F(6$7dqF+7$F,$\"1+++0K-fIFep7$F4F^bqF6F67$F4$
\"1+++3[`)e%Fgo7$F8FbbqF;F;7$F8$\"1+++16STMF_o7$F@FfbqFBFB7$F@$\"1+++`
0q?<Fgn7$FHFjbqFJFJ7$FH$\"1+++tqi_kFgn7$FOF^cqFQFQ7$FO$\"1+++A\")yN>FU
7$FWFbcqFYFY7$FW$\"1+++0.ZR[FU7$FinFfcqF[oF[o7$Fin$\"1+++^$Hq.\"FF7$Fa
oFjcqFcoFco7$Fao$\"1+++L+VW>FF7$FioF^dqF[pF[p7$Fio$\"1+++@nrSKFF7$F`pF
bdqFbpFbp7$F`p$\"1+++%3v5'[FF7$FgpFfdqFjpFjp7$Fgp$\"1+++](Q(GmFF7$F`qF
jdqFbqFbq7$F`q$\"1,++OM#fG)FF7$FhqF^eqFjqFjq7$Fhq$\"1,++*)3og&*FF7$F`r
FbeqFbrFbr7$F`r$\"1+++n'eV-\"F.7$FhrFfeqFjrFjrFheq7$F`sFfeqFbsFbs7$F`s
$\"1+++,DO.'*FF7$FhsF[fqFjsFjs7$Fhs$\"1+++Y^bt%)FF7$F`tF_fqFbtFbt7$F`t
$\"1,++bfHhqFF7$FhtFcfqFjtFjt7$Fht$\"1+++MtqubFF7$F`uFgfqFbuFbu7$F`u$
\"1++++0.\"=%FF7$FhuF[gqFjuFju7$Fhu$\"1+++d.X')HFF7$F`vF_gqFbvFbv7$F`v
$\"1+++`h@O?FF7$FhvFcgqFjvFjv7$Fhv$\"1+++cq'zK\"FF7$F`wFggqFbwFbw7$F`w
$\"1,+++Tz*H)FU7$FhwF[hqFjwFjw7$Fhw$\"1+++gk()z\\FU7$F`xF_hqFbxFcx-F[y
6%F]y%.Lambda~is~15.GFcxFdyFhy-%&TITLEG6#QBLambda~is~Increasing~from~1
~to~156\"" 1 2 0 1 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 }}}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "
" {TEXT -1 31 "Sample Probability Calculations" }}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 0 "" }{TEXT 265 0 "" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 47 "We can calculate probabilities for the Poisson(" }
{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 43 ") distribution usin
g either the probability" }}{PARA 0 "" 0 "" {TEXT -1 90 "distribution \+
function (PDF) or the cumulative distribution function (CDF).  We will
 denote" }}{PARA 0 "" 0 "" {TEXT -1 11 "the PDF by " }{TEXT 266 1 "f" 
}{TEXT -1 16 " and the CDF by " }{TEXT 267 1 "F" }{TEXT -1 59 ".  We w
ill consider these functions for a variable X having" }}{PARA 0 "" 0 "
" {TEXT -1 28 "the Poisson(2) distribution." }}{PARA 0 "" 0 "" 
{MPLTEXT 0 21 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "lambda
:=2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'lambdaG\"\"#" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "f:=x->PoissonPDF(lambda,x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"xG6\"6$%)operatorG%&arrowG
F(-%+PoissonPDFG6$%'lambdaG9$F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "F:=x->PoissonCDF(lambda,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"FGR6#%\"xG6\"6$%)operatorG%&arrowGF(-%+PoissonCDFG6
$%'lambdaG9$F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 57 "Below you will find three different ways to calcu
late P( " }{XPPEDIT 18 0 "X <=3" "6#1%\"XG\"\"$" }{TEXT -1 6 " ) .  " 
}}{PARA 0 "" 0 "" {MPLTEXT 0 21 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "evalf(f(0)+f(1)+f(2)+f(3));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"+-YBr&)!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 24 "evalf(sum(f(x),x=0..3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+
-YBr&)!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf(F(3));" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+-YBr&)!#5" }}}}{SECT 1 {PARA 3 "
" 0 "" {TEXT -1 30 "Properties of the Distribution" }}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 268 61 "Calculation of Me
an, Variance, and Moment Generating Function" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }{MPLTEXT 0 21 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 14 "Calculating E(" }{TEXT 269 1 "X" }{TEXT 
-1 42 "), the expectation or mean of the Poisson(" }{XPPEDIT 18 0 "lam
bda" "6#%'lambdaG" }{TEXT -1 15 ") distribution." }}{PARA 0 "" 0 "" 
{MPLTEXT 0 21 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 27 "f:=x->PoissonPDF(lambda,x);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"xG6\"6$%)operatorG%&ar
rowGF(-%+PoissonPDFG6$%'lambdaG9$F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 40 "EX:=simplify(sum(x*f(x),x=0..infinity));" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%#EXG%'lambdaG" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 "Calculating Var(" }{TEXT 
270 1 "X" }{TEXT -1 31 "), the variance of the Poisson(" }{XPPEDIT 18 
0 "lambda" "6#%'lambdaG" }{TEXT -1 15 ") distribution." }}{PARA 0 "" 
0 "" {TEXT -1 33 "We will employ the formula:  Var(" }{TEXT 271 1 "X" 
}{TEXT -1 7 ") = E( " }{XPPEDIT 18 0 "X^2;" "6#*$%\"XG\"\"#" }{TEXT 
-1 5 " ) - " }{XPPEDIT 18 0 "( E(X) )^2" "6#*$-%\"EG6#%\"XG\"\"#" }}
{PARA 0 "" 0 "" {MPLTEXT 0 21 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 46 "E_X_SQ:=simplify(sum(x^2*f(x),x=0..infinity));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'E_X_SQG*&%'lambdaG\"\"\",&F&F'F'F'F
'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "VarX:=simplify(E_X_SQ-
EX^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%VarXG%'lambdaG" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 72 "Th
e Moment Generating Function (MGF) can be easily calculated via Maple.
" }}{PARA 0 "" 0 "" {TEXT -1 71 "Recall the moment generating function
 of a random variable X is defined" }}{PARA 0 "" 0 "" {TEXT -1 3 "as \+
" }{TEXT 273 1 "M" }{TEXT -1 1 "(" }{TEXT 274 3 " t " }{TEXT -1 6 ") =
 E(" }{XPPEDIT 18 0 "exp(tX)" "6#-%$expG6#%#tXG" }{TEXT -1 36 "), prov
ided this expectation exists." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
{MPLTEXT 0 21 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "simpli
fy(sum(exp(t*x)*f(x),x=0..infinity));" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#-%$expG6#*&%'lambdaG\"\"\",&!\"\"F(-F$6#%\"tGF(F(" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 48 "So the moment g
enerating function for a Poisson(" }{XPPEDIT 18 0 "lambda" "6#%'lambda
G" }{TEXT -1 18 ") random variable " }}{PARA 0 "" 0 "" {TEXT -1 11 "is
 given by" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
4 "    " }{TEXT 275 1 "M" }{TEXT -1 2 "( " }{TEXT 276 1 "t" }{TEXT -1 
5 " ) = " }{XPPEDIT 18 0 "exp(lambda*(exp(t) -1))" "6#-%$expG6#*&%'lam
bdaG\"\"\",&-F$6#%\"tGF(\"\"\"!\"\"F(" }{TEXT -1 1 " " }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 15 "We will define " }
{TEXT 277 1 "M" }{TEXT -1 2 "( " }{TEXT 278 1 "t" }{TEXT -1 20 " ) as \+
a function of " }{TEXT 279 1 "t" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }{MPLTEXT 0 21 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 29 "M:=t->exp(lambda*(exp(t)-1));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"MGR6#%\"tG6\"6$%)operatorG%&arrowGF(-%$expG6#*&%'la
mbdaG\"\"\",&-F-6#9$F1!\"\"F1F1F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 76 "The moment generating fun
ction provides us alternative ways to calculate the" }}{PARA 0 "" 0 "
" {TEXT -1 40 "mean and variance by way of the formula." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "    " }{XPPEDIT 18 0 
"M^r;" "6#)%\"MG%\"rG" }{TEXT -1 9 " (0) = E(" }{XPPEDIT 18 0 "X^r" "6
#)%\"XG%\"rG" }{TEXT -1 10 ") , where " }{XPPEDIT 18 0 "M^r" "6#)%\"MG
%\"rG" }{TEXT -1 1 "(" }{TEXT 280 1 "t" }{TEXT -1 14 ") denotes the " 
}{TEXT 281 1 "r" }{TEXT -1 18 " th derivative of " }{TEXT 282 1 "M" }
{TEXT -1 1 "(" }{TEXT 283 1 "t" }{TEXT -1 18 ") with respect to " }
{TEXT 284 1 "t" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 30 "This formula holds as long as " }{TEXT 
285 1 "M" }{TEXT -1 1 "(" }{TEXT 286 1 "t" }{TEXT -1 45 ") exists in a
n open interval containing zero." }}{PARA 0 "" 0 "" {TEXT -1 79 "See, \+
for example, Mathematical Statistics and Data Analysis by John A. Rice
 for" }}{PARA 0 "" 0 "" {TEXT -1 39 "more on the moment generating fun
ction." }}{PARA 0 "" 0 "" {MPLTEXT 0 21 0 "" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 18 "M_p:=diff(M(t),t);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%$M_pG*(-%$expG6#%\"tG\"\"\"%'lambdaG\"\"\"-F'6#*&F+F*,&!\"\"F*
F&F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "simplify(M_p);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%'lambdaG\"\"\"-%$expG6#,(%\"tG
\"\"\"F$!\"\"*&-F'6#F*F+F$F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "simplify(subs(t=0,M_p));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%'lambdaG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 17 "And therefore if " }{TEXT 287 1 "X" }
{TEXT -1 14 " is a Poisson(" }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }
{TEXT -1 19 ") variable, then E(" }{TEXT 288 1 "X" }{TEXT -1 4 ") = " 
}{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 20 " , which agrees wi
th" }}{PARA 0 "" 0 "" {TEXT -1 57 "what we found earlier.  Now turning
 to the second moment." }}{PARA 0 "" 0 "" {MPLTEXT 0 21 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "M_pp:=diff(M_p,t);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%%M_ppG,&*(-%$expG6#%\"tG\"\"\"%'lambdaG\"
\"\"-F(6#*&F,F+,&!\"\"F+F'F+F+F+F+*()F'\"\"#F-)F,F5F-F.F-F+" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "simplify(subs(t=0,M_pp));" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%'lambdaG\"\"#\"\"\"\"\"\"F&F)" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 12 
"Therefore E(" }{XPPEDIT 18 0 "X^2" "6#*$%\"XG\"\"#" }{TEXT -1 4 ") = \+
" }{XPPEDIT 18 0 "lambda^2+lambda" "6#,&*$%'lambdaG\"\"#\"\"\"F%F'" }
{TEXT -1 45 " , which again is in agreement with the value" }}{PARA 0 
"" 0 "" {TEXT -1 64 "calculated previously. The variance is now quickl
y calculated as" }}{PARA 0 "" 0 "" {TEXT -1 4 "Var(" }{TEXT 289 1 "X" 
}{TEXT -1 7 ") = E( " }{XPPEDIT 18 0 "X^2;" "6#*$%\"XG\"\"#" }{TEXT 
-1 5 " ) - " }{XPPEDIT 18 0 "( E(X) )^2" "6#*$-%\"EG6#%\"XG\"\"#" }}
{PARA 0 "" 0 "" {TEXT -1 14 "            = " }{XPPEDIT 18 0 "lambda^2+
lambda-lambda^2" "6#,(*$%'lambdaG\"\"#\"\"\"F%F'*$F%\"\"#!\"\"" }}
{PARA 0 "" 0 "" {TEXT -1 14 "            = " }{XPPEDIT 18 0 "lambda" "
6#%'lambdaG" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 0 21 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 272 18 "S
pecial Properties" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 55 "You proba
bly noticed in the previous animation that as " }{XPPEDIT 18 0 "lambda
" "6#%'lambdaG" }{TEXT -1 56 " grew larger, the probability histogram \+
for the Poisson(" }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 110 
") distribution seemed to become increasingly more bell-shaped (i.e., \+
normal). Look again at the animation for " }{XPPEDIT 18 0 "lambda" "6#
%'lambdaG" }{TEXT -1 53 " varying from 1 to 15 with an overlayed norma
l curve." }}{PARA 0 "" 0 "" {MPLTEXT 0 21 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 21 "for n from 1 to 15 do" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "num:=convert(evalf(n), string):" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 59 "tracker[n]:=textplot([18,0.3,`Lambda is `.num],color=
blue):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "H[n]:=ProbHist(PoissonPDF
(n,x),0..25,26):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "N[n]:=plot(Norm
alPDF(n,n,x),x = 0..25):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "P[n]:=d
isplay(\{H[n],N[n],tracker[n]\}):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 
"od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 120 "display([seq(P[n], n=1..15
)], insequence=true,title=\"Normal Approx. to the Poisson. Lambda is i
ncreasing from 1 to 15\");" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 
{PLOTDATA 2 "6$-%(ANIMATEG617'-%%TEXTG6%7$$\"#=\"\"!$\"\"$!\"\"%-Lambd
a~is~1.G-%'COLOURG6&%$RGBGF-F-$\"*++++\"!\")-%'CURVESG6$7`o7$F-$\"1M9>
Xsq>C!#;7$$\"1nmTN@Ki8F@$\"1(o\")odYsu#F@7$$\"1LL$3FWYs#F@$\"1e&Gc3o<1
$F@7$$\"1++D1k'p3%F@$\"1`.W6Cb\\LF@7$$\"1nmmT&)G\\aF@$\"1mwsra+(f$F@7$
$\"1+]7`p)*>yF@$\"1n@MUCu&*QF@7$$\"1L$ek`o!>5!#:$\"1^#eZd(p))RF@7$$\"1
<H#=XtB:\"Fgn$\"1L!Qa.yL%RF@7$$\"1+v=n$ycG\"Fgn$\"1G_%4!p!*HQF@7$$\"1$
3_DG$)*=9Fgn$\"1gc6?\\=aOF@7$$\"1nm\"z>)G_:Fgn$\"1LXT>j6DMF@7$$\"1n;zW
nZ'o\"Fgn$\"1z;g%G]>:$F@7$$\"1nmm\"Hl1#=Fgn$\"1q3`$R3)[GF@7$$\"1n;aQQ&
[&>Fgn$\"1b!Qvqs)GDF@7$$\"1nmT&QU!*3#Fgn$\"1[ZULo![?#F@7$$\"1%3_v:$fAA
Fgn$\"107E<#Q%*)=F@7$$\"1+voHR9cBFgn$\"1F!pmeb0f\"F@7$$\"1<H#=q%p*[#Fg
n$\"1y<%eT#G:8F@7$$\"1L$eRZXKi#Fgn$\"1xFw))GUo5F@7$$\"1+](oz#)3(GFgn$
\"1;0s[c(=$p!#<7$$\"1n;z>,_=JFgn$\"1kc!\\!e&)HUF[s7$$\"1L$eRAM\\P$Fgn$
\"1f=(pYhvP#F[s7$$\"1+]7G$[8j$Fgn$\"1\"*4?1YO^7F[s7$$\"1n;zW-%Rw$Fgn$
\"1IrbR=q]()!#=7$$\"1L$e9;Kl*QFgn$\"1QX^78m7gF`t7$$\"1+]7yS7HSFgn$\"1H
$eo-S$fSF`t7$$\"1n;z%*frhTFgn$\"1;9Q?,$Gp#F`t7$$\"1L$3-Q\\gU%Fgn$\"1^U
N%*[RF6F`t7$$\"1+]ilFQ!p%Fgn$\"1)3w@Xt9S%!#>7$$\"1ML$3_\"=M_Fgn$\"1^p,
\")*fI5&!#?7$$\"1omTg(fJr&Fgn$\"1'=qw3ks)f!#@7$$\"1,+]7eP_iFgn$\"1S'fI
\"[GxS!#A7$$\"1++]Pf!Qz'Fgn$\"18$*4r!3'\\?!#B7$$\"1,+](=ubJ(Fgn$\"1V?'
4t^Iq)!#D7$$\"1n;zW(*Q*y(Fgn$\"1o!)*3$oR-R!#E7$$\"1NL$3F-GN)Fgn$\"1.!)
3$)\\<js!#G7$$\"1LLL$e'3I))Fgn$\"1ico&y2*Q>!#H7$$\"1,]7.<G&Q*Fgn$\"1bG
T1L.^@!#J7$$\"1MLLeMsw)*Fgn$\"1j)o8*y0%4$!#L7$$\"1+DJ&H\"fT5!#9$\"1%[!
\\a-NKA!#N7$$\"1+v$f)[$H4\"Fjy$\"1U`b$fOdb\"!#P7$$\"1M$ek`1l9\"Fjy$\"1
,Xfk#H))f'!#S7$$\"1Le*[.-d>\"Fjy$\"1VxH.YQ'R$!#U7$$\"1n;/Egw[7Fjy$\"1)
G)p'3/h!))!#X7$$\"1n\"z%*f%)QI\"Fjy$\"1!Rb#>6lX8!#Z7$$\"1+voza'=N\"Fjy
$\"1Z)R!H4)zr$!#]7$$\"1n;zWho.9Fjy$\"1H0sIY9]\\!#`7$$\"1++]i>Ad9Fjy$\"
1l7>t\"RF*R!#c7$$\"1+]i:jf4:Fjy$\"1%>K(oXG[G!#f7$$\"1+DJ&>r-c\"Fjy$\"1
!H5:IM(z>!#i7$$\"1+]P4q`;;Fjy$\"1vgrZj<mX!#m7$$\"1LL$eM%4n;Fjy$\"1'4ts
`#G!)=!#p7$$\"1++v$4v5s\"Fjy$\"17x15K[WM!#t7$$\"1n\"zWn*)*p<Fjy$\"1H#=
J'H=+6!#w7$$\"1++DJiYB=Fjy$\"1yJb>\")\\h7!#!)7$$\"1Lek.Nyt=Fjy$\"1$>zS
V_T!>!#%)7$$\"1+Dc^&zj#>Fjy$\"1Lla9e0s9!#))7$$\"1LL3-=!y(>Fjy$\"1Lr:oQ
(e2\"!##*7$$\"1+D\"G8O;.#Fjy$\"1%)o)[q6\"*y$!#(*7$$\"1nmm\"*\\[$3#Fjy$
\"1\\\")R\")*Q5[\"!$,\"7$$\"1n;aQz]O@Fjy$\"1KvC&4LO[$!$1\"7$$\"1MekG=4
*=#Fjy$\"1rIU'pM,y'!$6\"7$$\"1++]i4TPAFjy$\"1T!))e]3D\\#!$:\"7$$\"1L$3
F9!z#H#Fjy$\"1(\\1^X5ma\"!$?\"7$$\"1nmmT>KUBFjy$\"164zz_)[i#!$D\"7$$\"
1+DJqJ8&R#Fjy$\"1`BO\"=;Ik\"!$I\"7$$\"1+voa-oXCFjy$\"1GESbZwB8!$N\"7$$
\"#DF-$\"1cWzTWrUL!$T\"-F36&F5$\"#5F0F-F--F:6$7dq7$$!1+++++++]F@F-7$F^
el$\"1+++7WzyOF@7$$\"1+++++++]F@Fael7$FdelF-FfelFcel7$$\"1+++++++:FgnF
ael7$FhelF-Fjel7$Fhel$\"1+++1sRR=F@7$$\"1+++++++DFgnF\\fl7$F_flF-Fafl7
$F_fl$\"1+++@SKJhF[s7$$\"1+++++++NFgnFcfl7$FfflF-Fhfl7$Fffl$\"1+++05$G
`\"F[s7$$\"1+++++++XFgnFjfl7$F]glF-F_gl7$F]gl$\"1+++5?mlIF`t7$$\"1++++
+++bFgnFagl7$FdglF-Ffgl7$Fdgl$\"1+++%oO%4^Fju7$$\"1+++++++lFgnFhgl7$F[
hlF-F]hl7$F[hl$\"1+++h_>*H(F`v7$$\"1+++++++vFgnF_hl7$FbhlF-Fdhl7$Fbhl$
\"1,++xS*R7*Ffv7$$\"1+++++++&)FgnFfhl7$FihlF-F[il7$Fihl$\"1+++?rx85Ffv
7$$\"1+++++++&*FgnF]il7$F`ilF-Fbil7$F`il$F^ilF\\w7$$\"1++++++]5FjyFdil
7$FfilF-Fhil7$Ffil$\"1+++Nc:;#*!#C7$$\"1++++++]6FjyFjil7$F^jlF-F`jl7$F
^jl$\"1+++'pH,o(Fhw7$$\"1++++++]7FjyFbjl7$FejlF-Fgjl7$Fejl$\"1+++u?z2f
F^x7$$\"1++++++]8FjyFijl7$F\\[mF-F^[m7$F\\[m$\"1+++\"[^)>U!#F7$$\"1+++
+++]9FjyF`[m7$Fd[mF-Ff[m7$Fd[m$\"1+++?VB8GFdx7$$\"1++++++]:FjyFh[m7$F[
\\mF-F]\\m7$F[\\m$\"1+++]9Fe<Fjx7$$\"1++++++];FjyF_\\m7$Fb\\mF-Fd\\m7$
Fb\\m$\"1+++CtFM5!#I7$$\"1++++++]<FjyFf\\m7$Fj\\mF-F\\]m7$Fj\\m$\"1***
**>8&)fu&!#K7$$\"1++++++]=FjyF^]m7$Fb]mF-Fd]m7$Fb]m$\"1+++,F?CIFfy7$$
\"1++++++]>FjyFf]m7$Fi]mF-F[^m7$Fi]m$\"1+++]857:!#M7$$\"1++++++]?FjyF]
^m7$Fa^mF-Fc^m7$Fa^m$\"1+++?E[+s!#O7$$\"1++++++]@FjyFe^m7$Fi^mF-F[_m7$
Fi^m$\"1+++Ym%HF$Fcz7$$\"1++++++]AFjyF]_m7$F`_mF-Fb_m7$F`_m$\"1+++\"G?
IU\"!#Q7$$\"1++++++]BFjyFd_m7$Fh_mF-Fj_m7$Fh_m$\"1+++q6DHfFiz7$$\"1+++
+++]CFjyF\\`m7$F_`mF-Fa`m7$F_`m$\"1+++o/qrB!#T7$$\"1++++++]DFjyFc`m7$F
g`mF-F2-%+AXESLABELSG6$Q\"x6\"%!G-%%VIEWG6$;F-Fadl%(DEFAULTG7'-F:6$7fo
7$F-$\"1([^Nuox.\"F@7$FB$\"1!z.Q(Rs$=\"F@7$FG$\"1^&H]RNxL\"F@7$FL$\"1X
mD$)4#y\\\"F@7$FQ$\"1^iBeLdh;F@7$$\"1LeRZxjMmF@$\"14Y?[Q([!=F@7$FV$\"1
T#4)H\"3o%>F@7$$\"1nT&)ehL0!*F@$\"1/\"RPO._3#F@7$Fen$\"1I)=$z8!y@#F@7$
F`o$\"1UpAIL5$[#F@7$Fjo$\"1PU%3epIo#F@7$F_p$\"1fn5'>qCv#F@7$Fdp$\"1a*p
>xd$)z#F@7$$\"1nT5l&fx)=Fgn$\"1t%y\"yt27GF@7$Fip$\"1VP(o)3^>GF@7$$\"1n
\"z>6[>-#Fgn$\"1>_q6#31#GF@7$F^q$\"1ln_^>O:GF@7$Fhq$\"1Aygx+!Ht#F@7$Fb
r$\"1(ecK()*))fDF@7$Fgr$\"1d%e*f/sLBF@7$F]s$\"1#oeon)Gj?F@7$$\"1+](=<F
nC$Fgn$\"1uH'G4_E\">F@7$Fbs$\"1#*Q$zM,&e<F@7$$\"1n;/w79.NFgn$\"1W,`z8a
.;F@7$Fgs$\"1XE,y$o-X\"F@7$F\\t$\"1g*e^7&*eH\"F@7$Fbt$\"13tT1*>y9\"F@7
$Fgt$\"1WE2Xow25F@7$F\\u$\"1v\"3Ow*eq()F[s7$Fau$\"1g6qbo\"oZ'F[s7$Ffu$
\"1.ZG^Fs=YF[s7$$\"1n\"HK9#Gi\\Fgn$\"1**[%*p`?XJF[s7$F\\v$\"1&HDeFhS1#
F[s7$$\"1+]iS1ntaFgn$\"1ZV&Qz\\8Q\"F[s7$Fbv$\"1Ac%*pK=$)*)F`t7$$\"1M$e
kynF)fFgn$\"1i(*HqB_Z`F`t7$Fhv$\"1qfq-TmpIF`t7$$\"1,++v34BlFgn$\"1v'H.
k`\\p\"F`t7$F^w$\"192u;d;A!*Fju7$Fdw$\"1pug*=-LT#Fju7$Fjw$\"1Z&f@7OjZ'
F`v7$F`x$\"1]\")o*RO5<\"F`v7$Ffx$\"1kR7'Q&**GCFfv7$F\\y$\"1^CxGx*pP$F
\\w7$Fby$\"1$))*>NKHy^Fbw7$Fhy$\"1Ona_2`fdF\\jl7$F_z$\"1^#*G8QM:iFhw7$
Fez$\"1J2H%4q7H&F^x7$F[[l$\"1=+034pa[Fb[m7$Fa[l$\"1/BGxr3BKFdx7$Fg[l$
\"1J!Hx1?(f;Fjx7$F]\\l$\"1jtD6%[*36Fh\\m7$Fc\\l$\"1]T-d*oJC&F`]m7$Fi\\
l$\"1c)y/PIh%>Ffy7$F_]l$\"1Uz^?k%Rv'F]z7$Fe]l$\"10a)>ezSH#Fg^m7$F[^l$
\"1Uo.%G\\fh%Ff_m7$Fa^l$\"1l+O\"3\"417!#R7$Fg^l$\"1Yc:H)*>Q@Fe`m7$F]_l
$\"1PF!=wu,)[!#V7$Fc_l$\"1Bz67ghFoFe[l7$Fi_l$\"1Y'=lq&zy5!#Y7$F_`l$\"1
YjqRr%QB\"!#[7$Fe`l$\"1`wNfk3k8Fa\\l7$F[al$\"1pVy!3q&f5!#_7$Faal$\"1o!
o)pw%[e)!#b7$Fgal$\"1S\"fQ#[aFa!#d7$F]bl$\"1;4vzz^9JFc]l7$Fcbl$\"1h%yF
\\QWS#!#h7$Fibl$\"1\\tK'4Q-!z!#k7$F_cl$\"1C;lcrGpTF_^l7$Fecl$\"1M_CW7L
e8!#o7$F[dl$\"1HllW'GU'\\!#r7$Fadl$\"1N/A3E-N5F[_lFfdl-F:6$7dqF]el7$F^
el$\"1+++KGN`8F@7$FdelFjanFfelFfel7$Fdel$\"1+++kcq1FF@7$FhelF^bnFjelFj
elF`bn7$F_flF^bnFaflFafl7$F_fl$\"1+++U/Z/=F@7$FfflFcbnFhflFhfl7$Fffl$
\"1+++9ANA!*F[s7$F]glFgbnF_glF_gl7$F]gl$\"1+++')3%*3OF[s7$FdglF[cnFfgl
Ffgl7$Fdgl$\"1+++&H!)H?\"F[s7$F[hlF_cnF]hlF]hl7$F[hl$\"1+++el3PMF`t7$F
bhlFccnFdhlFdhl7$Fbhl$\"1+++$R;Ff)Fju7$FihlFgcnF[ilF[il7$Fihl$\"1+++KD
\\4>Fju7$F`ilF[dnFbilFbil7$F`il$\"1+++k])*=QF`v7$FfilF_dnFhilFhil7$Ffi
l$\"1+++2#4O%pFfv7$F^jlFcdnF`jlF`jl7$F^jl$\"1+++,#os:\"Ffv7$FejlFgdnFg
jlFgjl7$Fejl$\"1+++<ET!y\"F\\w7$F\\[mF[enF^[mF^[m7$F\\[m$\"1+++'fYMa#F
bw7$Fd[mF_enFf[mFf[m7$Fd[m$\"1+++G@E\"R$F\\jl7$F[\\mFcenF]\\mF]\\m7$F[
\\m$\"1+++hw2RUFhw7$Fb\\mFgenFd\\mFd\\m7$Fb\\m$\"1+++)=]r)\\F^x7$Fj\\m
F[fnF\\]mF\\]m7$Fj\\m$\"1+++()zFTbFb[m7$Fb]mF_fnFd]mFd]m7$Fb]m$\"1+++'
>CH$eFdx7$Fi]mFcfnF[^mF[^m7$Fi]m$\"1*****f>CH$eFjx7$Fa^mFgfnFc^mFc^m7$
Fa^m$\"1+++-f;bbFh\\m7$Fi^mF[gnF[_mF[_m7$Fi^m$\"1+++>3:]]F`y7$F`_mF_gn
Fb_mFb_m7$F`_m$\"1+++'\\N9R%F`]m7$Fh_mFcgnFj_mFj_m7$Fh_m$\"1+++!eH&fOF
fy7$F_`mFggnFa`mFa`m7$F_`m$\"1+++jOiFHF_^m7$Fg`mF[hnFi`mF2-F(6%F*%-Lam
bda~is~2.GF2Fj`mF`am7'-F(6%F*%-Lambda~is~3.GF2-F:6$7dqF]el7$F^el$\"1++
+Poqy\\F[s7$FdelFihnFfelFfel7$Fdel$\"1+++^?h$\\\"F@7$FhelF]inFjelFjel7
$Fhel$\"1+++x!=/C#F@7$F_flFainFaflFaflFcin7$FfflFainFhflFhfl7$Fffl$\"1
+++dNJ!o\"F@7$F]glFfinF_glF_gl7$F]gl$\"1+++M\")=35F@7$FdglFjinFfglFfgl
7$Fdgl$\"1+++s1%4/&F[s7$F[hlF^jnF]hlF]hl7$F[hl$\"1+++XJSg@F[s7$FbhlFbj
nFdhlFdhl7$Fbhl$\"1,++'z6:5)F`t7$FihlFfjnF[ilF[il7$Fihl$\"1+++KR]+FF`t
7$F`ilFjjnFbilFbil7$F`il$\"1+++'z6:5)Fju7$FfilF^[oFhilFhil7$Ffil$\"1++
+<K]4AFju7$F^jlFb[oF`jlF`jl7$F^jl$\"1+++U!eP_&F`v7$FejlFf[oFgjlFgjl7$F
ejl$\"1+++%R8ZF\"F`v7$F\\[mFj[oF^[mF^[m7$F\\[m$\"1+++-(G:t#Ffv7$Fd[mF^
\\oFf[mFf[m7$Fd[m$\"1+++/u0jaF\\w7$F[\\mFb\\oF]\\mF]\\m7$F[\\m$\"1+++k
KKC5F\\w7$Fb\\mFf\\oFd\\mFd\\m7$Fb\\m$\"1+++)GHw!=Fbw7$Fj\\mFj\\oF\\]m
F\\]m7$Fj\\m$\"1+++![:F,$F\\jl7$Fb]mF^]oFd]mFd]m7$Fb]m$\"1+++z\">pv%Fh
w7$Fi]mFb]oF[^mF[^m7$Fi]m$\"1+++o(y`8(F^x7$Fa^mFf]oFc^mFc^m7$Fa^m$\"1+
++C)R$>5F^x7$Fi^mFj]oF[_mF[_m7$Fi^m$\"1+++^)3+R\"Fb[m7$F`_mF^^oFb_mFb_
m7$F`_m$\"1+++B]08=Fdx7$Fh_mFb^oFj_mFj_m7$Fh_m$\"1+++z(=jE#Fjx7$F_`mFf
^oFa`mFa`m7$F_`m$\"1+++NDe>FFh\\m7$Fg`mFj^oFi`mF2-F:6$7`o7$F-$\"15BzEV
MR^F[s7$FG$\"1[$Q%o4)fm'F[s7$FQ$\"1+#o^mvZV)F[s7$FV$\"14%yiBBX,\"F@7$F
en$\"1')yoErg(>\"F@7$F`o$\"1Me)G$zJ69F@7$Fjo$\"1SuC[=AC;F@7$Fdp$\"1:+C
#QWn#=F@7$F^q$\"1akf9-y0?F@7$Fhq$\"1!Gp=xG&\\@F@7$Fbr$\"1#Rar-W%\\AF@7
$$\"1mmTNT1ZFFgn$\"1yX5I`')yAF@7$Fgr$\"1x![DT.pH#F@7$$\"1mTgF@zKHFgn$
\"1WgoC5c,BF@7$$\"1LLLe9q%*HFgn$\"1&>6Db$G.BF@7$$\"1+D1*y5m0$Fgn$\"15s
:*Rk?I#F@7$F]s$\"1?x-M#3zH#F@7$Fbs$\"1Rlerq&*\\AF@7$Fgs$\"1#>\\<^]_:#F
@7$Fbt$\"1G*\\je:X,#F@7$F\\u$\"1()[M'QX$R=F@7$Fau$\"1ICt(eh6k\"F@7$Ffu
$\"1iDzh-iI9F@7$Fchm$\"1*)pfpdP77F@7$F\\v$\"1CQP$[:C+\"F@7$F[im$\"1A\"
fK*G)oI)F[s7$Fbv$\"1A*Q?yXMv'F[s7$Fcim$\"11!)4,`TG_F[s7$Fhv$\"1')e/pK'
3&RF[s7$F[jm$\"1i6/bcA5HF[s7$F^w$\"1^X`xL&>4#F[s7$Fdw$\"1!4%y\\CWL5F[s
7$$\"1Me9m>[_vFgn$\"1%=f2iR9G(F`t7$Fjw$\"1Ds>EbFN]F`t7$$\"1-D\"y+'4r!)
Fgn$\"1xsyu<HpJF`t7$F`x$\"1m*eb-KF%>F`t7$Ffx$\"1%e$p4bP\")zFju7$F\\y$
\"1s1B\")yUxDFju7$Fby$\"1qv(yo!H)p)F`v7$Fhy$\"1v*)>Zc\"yS#F`v7$F_z$\"1
eQ@ydVwkFfv7$Fez$\"1&G@!R\"p$)\\\"Ffv7$F[[l$\"1yf9`V=\"f$F\\w7$Fa[l$\"
15*)*=d@u-(Fbw7$Fg[l$\"1>=zFF')o6Fbw7$F]\\l$\"15JmhLVeAF\\jl7$Fc\\l$\"
1E[.[Ry4NFhw7$Fi\\l$\"1Kx1xkQoYF^x7$F_]l$\"1#Q@Cr$R9fFb[m7$Fe]l$\"1yt1
5\\jWtFdx7$F[^l$\"1rsy]/GalFjx7$Fa^l$\"1v)4#\\HiIoFh\\m7$Fg^l$\"1'**3I
@%pfbF`y7$F]_l$\"1(o#3_rml_F`]m7$Fc_l$\"1C#**o`4Rl$Ffy7$Fi_l$\"1zwQ5@!
4s#F_^m7$F_`l$\"17w\"y)H*ek\"F]z7$Fe`l$\"1m4]BaM&p*Fcz7$F[al$\"1F=Hvu5
]XFf_m7$Faal$\"1ikD?X!==#F[^n7$Fgal$\"1A4h=X,-*)Fe`m7$F]bl$\"1slHLn#**
R$F_[l7$Fcbl$\"1h0P8J:g:Fb^n7$Fibl$\"1S^%*>^>ZTFe[l7$F_cl$\"1mtbV!pF[
\"Fi^n7$Fecl$\"1j&[JCpe)QF]_n7$F[dl$\"1:B>LA<\"4\"!#\\7$Fadl$\"1;DlU$G
V8#!#^Ffdl-F[am6$F_amF_amF`am7'-F:6$7`o7$F-$\"1.%fcK[&*p#F[s7$FG$\"1b8
-qOH7NF[s7$FQ$\"1A=x.:q&[%F[s7$FV$\"1&*ztfQ_maF[s7$Fen$\"1W>A,3')olF[s
7$F`o$\"1/-@\\T\"=%zF[s7$Fjo$\"1<MAT+hK%*F[s7$Fdp$\"1`l$=9`;5\"F@7$F^q
$\"15q'[x\"oj7F@7$Fhq$\"1'389tFHU\"F@7$Fbr$\"1q8JEv\"Rd\"F@7$Fgr$\"1h!
*z%oj3q\"F@7$F]s$\"1G%GY]%35=F@7$Fbs$\"1I(pj]L'**=F@7$Fgs$\"1cHAP96h>F
@7$F\\t$\"1_D'fYl3)>F@7$Fbt$\"1!)p/mQ/#*>F@7$$\"1n;z>\"GG'RFgn$\"1\")y
-3pO%*>F@7$Fgt$\"1([o4#**\\%*>F@7$$\"1M$ek.?a4%Fgn$\"144lmCW#*>F@7$F\\
u$\"1#y#G@8?))>F@7$Fau$\"1Rhs#[h*\\>F@7$Ffu$\"1#\\CHMS$z=F@7$Fchm$\"1F
d2,\")ow<F@7$F\\v$\"1JYh(H%))[;F@7$F[im$\"1FbL[a\\?:F@7$Fbv$\"11.,.D9#
Q\"F@7$Fcim$\"1Ao2#fx-A\"F@7$Fhv$\"1vf/uw'z0\"F@7$F[jm$\"1m\\$45.5+*F[
s7$F^w$\"1^l^Ru')=vF[s7$$\"1,+]i+paqFgn$\"1x$=gb0L@'F[s7$Fdw$\"1biId[
\"y/&F[s7$Fieo$\"1$z\"yxr#)=TF[s7$Fjw$\"1e*fm&3)RJ$F[s7$F`x$\"1HqC)\\H
x'=F[s7$Ffx$\"1'**pf*))*)z5F[s7$F\\y$\"1t!\\)>$*)[J&F`t7$Fby$\"1%H5:4a
4m#F`t7$Fhy$\"1@MUB,/i6F`t7$F_z$\"1o*4W/$fM\\Fju7$Fez$\"1hd]3n.#)=Fju7
$F[[l$\"1t!oi&4Z!H(F`v7$Fa[l$\"1=s\"RZw#\\CF`v7$Fg[l$\"1:[Dg\"G;K(Ffv7
$F]\\l$\"1Sl@)ekcS#Ffv7$Fc\\l$\"1ree7)H!ynF\\w7$Fi\\l$\"1*Q]dU[mq\"F\\
w7$F_]l$\"18&ehF168%Fbw7$Fe]l$\"1!oK#p$R\"4)*F\\jl7$F[^l$\"1#4o(fKZV=F
\\jl7$Fa^l$\"1!>%R'*y*o$QFhw7$Fg^l$\"1RY:Y=j\"p'F^x7$F]_l$\"1].&ycZ5H
\"F^x7$Fc_l$\"1x)*>u%z^*>Fb[m7$Fi_l$\"1C;[6/PDKFdx7$F_`l$\"18^B$>`p[%F
jx7$Fe`l$\"1n)e;3R55'Fh\\m7$F[al$\"1X3Ht3(z.(F`y7$Faal$\"1dZ-%**)))4#)
F`]m7$Fgal$\"1On;zxi4&)Ffy7$F]bl$\"1Np'eVBZQ)F_^m7$Fcbl$\"1AjlWKX!Q*F]
z7$Fibl$\"10`2)*3P#4(Fg^m7$F_cl$\"1wVE$zJ-g'Fcz7$Fecl$\"1M+4/Mz0\\Ff_m
7$F[dl$\"17=_*o4&=QF[^n7$Fadl$\"10/E&z(o(G#FizFfdl-F(6%F*%-Lambda~is~4
.GF2-F:6$7dqF]el7$F^el$\"1+++*)QcJ=F[s7$FdelFijpFfelFfel7$Fdel$\"1+++c
bDEtF[s7$FhelF][qFjelFjel7$Fhel$\"1+++66Dl9F@7$F_flFa[qFaflFafl7$F_fl$
\"1+++\\\"oO&>F@7$FfflFe[qFhflFhflFg[q7$F]glFe[qF_glF_gl7$F]gl$\"1+++>
X$Hc\"F@7$FdglFj[qFfglFfgl7$Fdgl$\"1+++Yj&>/\"F@7$F[hlF^\\qF]hlF]hl7$F
[hl$\"1+++ii.afF[s7$FbhlFb\\qFdhlFdhl7$Fbhl$\"1+++I\"=q(HF[s7$FihlFf\\
qF[ilF[il7$Fihl$\"1+++p\">JK\"F[s7$F`ilFj\\qFbilFbil7$F`il$\"1+++wmZ#H
&F`t7$FfilF^]qFhilFhil7$Ffil$\"1+++tp`C>F`t7$F^jlFb]qF`jlF`jl7$F^jl$\"
1+++XK7:kFju7$FejlFf]qFgjlFgjl7$Fejl$\"1+++wS)Q(>Fju7$F\\[mFj]qF^[mF^[
m7$F\\[m$\"1+++'yo'RcF`v7$Fd[mF^^qFf[mFf[m7$Fd[m$\"1+++w;\"R]\"F`v7$F[
\\mFb^qF]\\mF]\\m7$F[\\m$\"1+++!>z(fPFfv7$Fb\\mFf^qFd\\mFd\\m7$Fb\\m$
\"1+++u#Rl%))F\\w7$Fj\\mFj^qF\\]mF\\]m7$Fj\\m$\"1+++;w*e'>F\\w7$Fb]mF^
_qFd]mFd]m7$Fb]m$\"1+++B=tQTFbw7$Fi]mFb_qF[^mF[^m7$Fi]m$\"1+++[OYx#)F
\\jl7$Fa^mFf_qFc^mFc^m7$Fa^m$\"1+++U(fmd\"F\\jl7$Fi^mFj_qF[_mF[_m7$Fi^
m$\"1+++xSlmGFhw7$F`_mF^`qFb_mFb_m7$F`_m$\"1+++_`[&)\\F^x7$Fh_mFb`qFj_
mFj_m7$Fh_m$\"1,++_A94$)Fb[m7$F_`mFf`qFa`mFa`m7$F_`m$\"1+++gFYH8Fb[m7$
Fg`mFj`qFi`mF2Fj`mF`am7'-F(6%F*%-Lambda~is~5.GF2-F:6$7co7$F-$\"1\\E>c#
)\\k9F[s7$FQ$\"13O9WXh^CF[s7$FV$\"1k))32=E6IF[s7$Fen$\"1Y\")*R#>KdOF[s
7$F`o$\"1I-PHi=!\\%F[s7$Fjo$\"1^]=-&**[V&F[s7$Fdp$\"1/Cz#Q7G\\'F[s7$F^
q$\"1aetMVrXwF[s7$Fhq$\"1b\\hLXeo))F[s7$Fbr$\"1(*z$zHIT,\"F@7$Fgr$\"1T
-/jR%Q8\"F@7$F]s$\"1`Y!eCOAD\"F@7$Fbs$\"1*H$o\">X+P\"F@7$Fgs$\"1=z[3gN
z9F@7$Fbt$\"11n^)3(ez:F@7$F\\u$\"1`%ea(Q0j;F@7$Fau$\"1y2#*=\"4js\"F@7$
Ffu$\"1jq[8F5n<F@7$$\"1Ug-5wNeZFgn$\"1QB$\\yOPx\"F@7$$\"1$3FWXKj#[Fgn$
\"1dr-I7vy<F@7$$\"1D\"G))H2V*[Fgn$\"1'QML>K@y\"F@7$Fchm$\"1f$e\"=.(Qy
\"F@7$$\"14-j()pDI]Fgn$\"1#y)o*ygRy\"F@7$$\"1^7.K=B)4&Fgn$\"11KAdLS#y
\"F@7$$\"1#HKkn1i;&Fgn$\"1GXKNB?z<F@7$F\\v$\"1Ig!RemVx\"F@7$F[im$\"1X?
zK0aW<F@7$Fbv$\"1[,1.Il&p\"F@7$Fcim$\"1^1&G\\n)>;F@7$Fhv$\"1*o.oBN^_\"
F@7$F[jm$\"1Q(3NxTZT\"F@7$F^w$\"1Fo!=zVKH\"F@7$Fbcp$\"1\\2T]gqp6F@7$Fd
w$\"1B$*3%plO/\"F@7$Fieo$\"1$**QPYJ)*H*F[s7$Fjw$\"1?\"[A)fL%>)F[s7$Faf
o$\"1\"\\#37fFZpF[s7$F`x$\"1$>/%*=asz&F[s7$$\"1NL3FWW\"f)Fgn$\"1)GWLQA
>\"\\F[s7$Ffx$\"1teP'ogY6%F[s7$F\\y$\"1cv2yNj2EF[s7$Fby$\"1l/PK17a;F[s
7$Fhy$\"1\\QFM-:'\\*F`t7$F_z$\"1QF\">0pNI&F`t7$Fez$\"1n#*GFMCIFF`t7$F[
[l$\"1-5iTzp59F`t7$Fa[l$\"1L8GsmmalFju7$Fg[l$\"1)oK=^j`y#Fju7$F]\\l$\"
1&yCE6=&e7Fju7$Fc\\l$\"1tFZ:];n]F`v7$Fi\\l$\"1&eZh\"\\5r=F`v7$F_]l$\"1
%\\`?0^#zmFfv7$Fe]l$\"1LLHIy))RBFfv7$F[^l$\"1e]]'R$)\\(oF\\w7$Fa^l$\"1
`2fB]+n@F\\w7$Fg^l$\"1'*4(o\"R>qfFbw7$F]_l$\"1<MI$*zBl<Fbw7$Fc_l$\"1!*
)e%)4j/T%F\\jl7$Fi_l$\"1jE+xn=N6F\\jl7$F_`l$\"1WLp'\\]Gg#Fhw7$Fe`l$\"1
g+^$>Hi%eF^x7$F[al$\"1f'R8+Lo:\"F^x7$Faal$\"1xCZuoZ+BFb[m7$Fgal$\"1kpe
,%y=<%Fdx7$F]bl$\"1B@j&[_)esFjx7$Fcbl$\"18flY()>'Q\"Fjx7$Fibl$\"1bk#Q+
sB'>Fh\\m7$F_cl$\"1m;ix&R?C$F`y7$Fecl$\"11u,8l6/XF`]m7$F[dl$\"1mMjDRTj
kFfy7$Fadl$\"1sf#3G\"fzvF_^mFfdl-F:6$7dqF]el7$F^el$\"1+++**p%zt'F`t7$F
delF[`rFfelFfel7$Fdel$\"1++++N(*oLF[s7$FhelF_`rFjelFjel7$Fhel$\"1+++\\
PVA%)F[s7$F_flFc`rFaflFafl7$F_fl$\"1+++e*QPS\"F@7$FfflFg`rFhflFhfl7$Ff
fl$\"1+++)ptYv\"F@7$F]glF[arF_glF_glF]ar7$FdglF[arFfglFfgl7$Fdgl$\"1++
+\"3GAY\"F@7$F[hlF`arF]hlF]hl7$F[hl$\"1+++H'[W/\"F@7$FbhlFdarFdhlFdhl7
$Fbhl$\"1+++NR!y_'F[s7$FihlFharF[ilF[il7$Fihl$\"1+++UxbEOF[s7$F`ilF\\b
rFbilFbil7$F`il$\"1+++q)yK\"=F[s7$FfilF`brFhilFhil7$Ffil$\"1,++(ow@C)F
`t7$F^jlFdbrF`jlF`jl7$F^jl$\"1+++'GSUV$F`t7$FejlFhbrFgjlFgjl7$Fejl$\"1
+++\\;'3K\"F`t7$F\\[mF\\crF^[mF^[m7$F\\[m$\"1+++IIO<ZFju7$Fd[mF`crFf[m
Ff[m7$Fd[m$\"1+++VVXs:Fju7$F[\\mFdcrF]\\mF]\\m7$F[\\m$\"1+++A)>R\"\\F`
v7$Fb\\mFhcrFd\\mFd\\m7$Fb\\m$\"1+++O0FX9F`v7$Fj\\mF\\drF\\]mF\\]m7$Fj
\\m$\"1+++y.k9SFfv7$Fb]mF`drFd]mFd]m7$Fb]m$\"1+++5V[c5Ffv7$Fi]mFddrF[^
mF[^m7$Fi]m$\"1+++v2@TEF\\w7$Fa^mFhdrFc^mFc^m7$Fa^m$\"1+++$3(f)G'Fbw7$
Fi^mF\\erF[_mF[_m7$Fi^m$\"1+++5mAH9Fbw7$F`_mF`erFb_mFb_m7$F`_m$\"1+++p
V,2JF\\jl7$Fh_mFderFj_mFj_m7$Fh_m$\"1+++.m%HZ'Fhw7$F_`mFherFa`mFa`m7$F
_`m$\"1+++@$*e%H\"Fhw7$Fg`mF\\frFi`mF2Fj`mF`am7'-F:6$7dqF]el7$F^el$\"1
+++x@vyCF`t7$FdelFdfrFfelFfel7$Fdel$\"1+++18D([\"F[s7$FhelFhfrFjelFjel
7$Fhel$\"1+++>RvhWF[s7$F_flF\\grFaflFafl7$F_fl$\"1+++Py]B*)F[s7$FfflF`
grFhflFhfl7$Fffl$\"1+++wh_Q8F@7$F]glFdgrF_glF_gl7$F]gl$\"1+++69B1;F@7$
FdglFhgrFfglFfglFjgr7$F[hlFhgrF]hlF]hl7$F[hl$\"1+++\"ypnP\"F@7$FbhlF]h
rFdhlFdhl7$Fbhl$\"1+++OtdK5F@7$FihlFahrF[ilF[il7$Fihl$\"1,++.*[Q)oF[s7
$F`ilFehrFbilFbil7$F`il$\"1+++T$4.8%F[s7$FfilFihrFhilFhil7$Ffil$\"1+++
0g*GD#F[s7$F^jlF]irF`jlF`jl7$F^jl$\"1+++-![k7\"F[s7$FejlFairFgjlFgjl7$
Fejl$\"1+++z2**)>&F`t7$F\\[mFeirF^[mF^[m7$F\\[m$\"1+++1*Q\"GAF`t7$Fd[m
FiirFf[mFf[m7$Fd[m$\"1+++Acb7*)Fju7$F[\\mF]jrF]\\mF]\\m7$F[\\m$\"1+++d
$3AM$Fju7$Fb\\mFajrFd\\mFd\\m7$Fb\\m$\"1+++]Hgz6Fju7$Fj\\mFejrF\\]mF\\
]m7$Fj\\m$\"1+++M)4?$RF`v7$Fb]mFijrFd]mFd]m7$Fb]m$\"1+++;toT7F`v7$Fi]m
F][sF[^mF[^m7$Fi]m$\"1+++[>1DPFfv7$Fa^mFa[sFc^mFc^m7$Fa^m$\"1+++9MIk5F
fv7$Fi^mFe[sF[_mF[_m7$Fi^m$\"1+++uck-HF\\w7$F`_mFi[sFb_mFb_m7$F`_m$\"1
+++\\\">@d(Fbw7$Fh_mF]\\sFj_mFj_m7$Fh_m$\"1+++(yHI*=Fbw7$F_`mFa\\sFa`m
Fa`m7$F_`m$\"1+++*[rKa%F\\jl7$Fg`mFe\\sFi`mF2-F:6$7do7$F-$\"1S-%\\b&p3
\")F`t7$FQ$\"1hbqZ\\:k8F[s7$Fen$\"1t6H#*eNg?F[s7$Fjo$\"1!RI9jFD8$F[s7$
Fdp$\"1&)\\eox;*z$F[s7$F^q$\"1R$fVW&p_XF[s7$Fhq$\"1FS,wRS'Q&F[s7$Fbr$
\"1G_TkvX(H'F[s7$Fgr$\"1?ef;hK-sF[s7$F]s$\"1Fb.y>X`\")F[s7$Fbs$\"1Ct]w
C`r\"*F[s7$Fgs$\"1O#)Qf,V?5F@7$Fbt$\"1d&G1eGk7\"F@7$F\\u$\"1pO:(=\\*G7
F@7$Fau$\"1qQ1i?)[K\"F@7$Ffu$\"1wCl8pw69F@7$Fchm$\"1')*4^l')))[\"F@7$F
\\v$\"1@WN^.*4b\"F@7$F[im$\"1(fClQ2:f\"F@7$Fbv$\"1(=ukJYvh\"F@7$$\"1%3
Fpwh0y&Fgn$\"1k:J]E:A;F@7$$\"1,vVtP'z%eFgn$\"1p*p?#3aD;F@7$$\"1<z%*zdO
:fFgn$\"1;z6`JqF;F@7$Fcim$\"1$ykttM'G;F@7$$\"1^(oHzp,0'Fgn$\"1G%3)fMLG
;F@7$$\"1n\"z%*zrv6'Fgn$\"1'3OX++oi\"F@7$$\"1%e*)f!Q(\\='Fgn$\"1$=O@&y
.C;F@7$Fhv$\"1uZ`mK0?;F@7$F[jm$\"18oi#=e>f\"F@7$F^w$\"1Z0G#))e`a\"F@7$
Fbcp$\"1x$[,'p[%[\"F@7$Fdw$\"1%)zfF$G*49F@7$Fieo$\"1g$*flLJK8F@7$Fjw$
\"11)>BC\\sC\"F@7$Fafo$\"1c'='yb=R6F@7$F`x$\"1A*HGY8o-\"F@7$Fciq$\"1X3
-jMc1$*F[s7$Ffx$\"1(3?Vzb`N)F[s7$$\"1o\"HK9%o2\"*Fgn$\"1RiK&z/IG(F[s7$
F\\y$\"1P8?)HqsE'F[s7$$\"1n\"H2e-5j*Fgn$\"1SAl\"GS&GaF[s7$Fby$\"1?@T3
\\(\\l%F[s7$$\"1<Hd?=j95Fjy$\"1m+E5(*>()QF[s7$Fhy$\"150>ZX(p?$F[s7$F_z
$\"1DJ8lI-]@F[s7$Fez$\"1h[i2W!=N\"F[s7$F[[l$\"1]WWl$*\\j%)F`t7$Fa[l$\"
1NnK#oJ:)[F`t7$Fg[l$\"1#fYaYxDi#F`t7$F]\\l$\"1X()Q\\KMl9F`t7$Fc\\l$\"1
C3l_S>&[(Fju7$Fi\\l$\"1Z575!yxc$Fju7$F_]l$\"1wbc3s0];Fju7$Fe]l$\"1h8=C
\")[\"\\(F`v7$F[^l$\"17%\\4<.]'HF`v7$Fa^l$\"18n$y)3ZK7F`v7$Fg^l$\"1fi_
Kmj0YFfv7$F]_l$\"1\")y*o*375=Ffv7$Fc_l$\"1usa!\\A*HiF\\w7$Fi_l$\"1g[\"
)[bO'=#F\\w7$F_`l$\"1D))zfJ%[*pFbw7$Fe`l$\"1u6Y@iV&>#Fbw7$F[al$\"1<*33
K\\^A'F\\jl7$Faal$\"1Wrt:yem<F\\jl7$Fgal$\"1maj2Yn^YFhw7$F]bl$\"1tR-hW
X#=\"Fhw7$Fcbl$\"1z2V6??DKF^x7$Fibl$\"1#y5nGLf$pFb[m7$F_cl$\"1OOvMn/!o
\"Fb[m7$Fecl$\"1nDBh'f;a$Fdx7$F[dl$\"11+->dOTwFjx7$Fadl$\"1*Rg0<'>-9Fj
xFfdl-F(6%F*%-Lambda~is~6.GF2Fj\\pF`am7'-F(6%F*%-Lambda~is~7.GF2-F:6$7
dqF]el7$F^el$\"1+++c'>)=\"*Fju7$FdelF`\\tFfelFfel7$Fdel$\"1+++fP<$Q'F`
t7$FhelFd\\tFjelFjel7$Fhel$\"1+++;36MAF[s7$F_flFh\\tFaflFafl7$F_fl$\"1
+++P_#H@&F[s7$FfflF\\]tFhflFhfl7$Fffl$\"1+++n\">E7*F[s7$F]glF`]tF_glF_
gl7$F]gl$\"1+++$omrF\"F@7$FdglFd]tFfglFfgl7$Fdgl$\"1+++(zF+\\\"F@7$F[h
lFh]tF]hlF]hlFj]t7$FbhlFh]tFdhlFdhl7$Fbhl$\"1+++AVx.8F@7$FihlF]^tF[ilF
[il7$Fihl$\"1+++&pYS,\"F@7$F`ilFa^tFbilFbil7$F`il$\"1+++moK)4(F[s7$Ffi
lFe^tFhilFhil7$Ffil$\"1+++'4<r^%F[s7$F^jlFi^tF`jlF`jl7$F^jl$\"1+++t\\)
\\j#F[s7$FejlF]_tFgjlFgjl7$Fejl$\"1+++i!Q)=9F[s7$F\\[mFa_tF^[mF^[m7$F
\\[m$\"1+++6.>%4(F`t7$Fd[mFe_tFf[mFf[m7$Fd[m$\"1+++X@i5LF`t7$F[\\mFi_t
F]\\mF]\\m7$F[\\m$\"1+++)=(R[9F`t7$Fb\\mF]`tFd\\mFd\\m7$Fb\\m$\"1+++B%
))R'fFju7$Fj\\mFa`tF\\]mF\\]m7$Fj\\m$\"1+++K)G$>BFju7$Fb]mFe`tFd]mFd]m
7$Fb]m$\"1+++%p&*[a)F`v7$Fi]mFi`tF[^mF[^m7$Fi]m$\"1+++$\\82*HF`v7$Fa^m
F]atFc^mFc^m7$Fa^m$\"1+++y\\/p**Ffv7$Fi^mFaatF[_mF[_m7$Fi^m$\"1+++c)o>
<$Ffv7$F`_mFeatFb_mFb_m7$F`_m$\"1*****4E=Ql*F\\w7$Fh_mFiatFj_mFj_m7$Fh
_m$\"1+++#*pp:GF\\w7$F_`mF]btFa`mFa`m7$F_`m$\"1+++y:&R)yFbw7$Fg`mFabtF
i`mF2-F:6$7bo7$F-$\"1s,k@HM`XF`t7$FQ$\"1BE<m(zto(F`t7$Fen$\"1&oaP?h8<
\"F[s7$Fjo$\"1q)[i)RA5=F[s7$F^q$\"1C*4xUVGp#F[s7$Fbr$\"1ukO3p:QQF[s7$F
gr$\"12D![)>LhWF[s7$F]s$\"1'>//Nc/9&F[s7$Fbs$\"1&z!3iu2)*eF[s7$Fgs$\"1
uCV*H%4/nF[s7$Fbt$\"1!)z'HWq%yvF[s7$F\\u$\"1Rf,UPD\"[)F[s7$Fau$\"1z=Y>
ww$R*F[s7$Ffu$\"1w])3E7,.\"F@7$Fchm$\"1X3FVJ'37\"F@7$F\\v$\"1'e1[4'z17
F@7$F[im$\"1%H7]+4nF\"F@7$Fbv$\"1!=1\\`]'R8F@7$Fhv$\"18f)GaX)[9F@7$F[j
m$\"10q*[[hN[\"F@7$F^w$\"1tB1zyG.:F@7$$\"1++vop-foFgn$\"1?/Bc6s0:F@7$$
\"1++++![U#pFgn$\"1.Fyn@C2:F@7$$\"1,+DJ!p%*)pFgn$\"1z7BV\"[y]\"F@7$Fbc
p$\"1dhGyz`2:F@7$$\"1,+v$46*>rFgn$\"1'f3#QAJ1:F@7$$\"1,++D@8&=(Fgn$\"1
7X4cJ</:F@7$$\"1,+DcJN]sFgn$\"1,`4EY7,:F@7$Fdw$\"1s[g\">sr\\\"F@7$Fieo
$\"1%\\i#=1Mv9F@7$Fjw$\"1m4mat@U9F@7$F`x$\"1%QHFl#4B8F@7$Fciq$\"1%Q&=H
!H$e7F@7$Ffx$\"18-,'oQq=\"F@7$Fjds$\"1z4(G2\")y4\"F@7$F\\y$\"1FczWHI/5
F@7$Fbes$\"1F'G$3bh'>*F[s7$Fby$\"1IQO&R3#\\$)F[s7$Fjes$\"1n5%G$)z[V(F[
s7$Fhy$\"1$yAn%HH_lF[s7$$\"1+]i!4js1\"Fjy$\"1wV:#eQOv&F[s7$F_z$\"18,J%
z()\\+&F[s7$$\"1<z>62s>6Fjy$\"1:7,hnF%G%F[s7$Fez$\"1Q2Az(\\*HOF[s7$F[[
l$\"1dm+<u\"og#F[s7$Fa[l$\"1QJ=a0ha<F[s7$Fg[l$\"1QY/1@a96F[s7$F]\\l$\"
1]n=Qc]ZsF`t7$Fc\\l$\"1C(4;+I\")Q%F`t7$Fi\\l$\"1%)=Cbt#*4DF`t7$F_]l$\"
1)Gu9>(o'R\"F`t7$Fe]l$\"16<=/GHJwFju7$F[^l$\"1'pczMTlt$Fju7$Fa^l$\"1(>
\"4H5d#*=Fju7$Fg^l$\"1r'pINmFz)F`v7$F]_l$\"1S%3d%\\yMUF`v7$Fc_l$\"1S];
KI9K=F`v7$Fi_l$\"1f$o*R^&Q-)Ffv7$F_`l$\"1n@m\\&*ocKFfv7$Fe`l$\"1%paZ*
\\7)H\"Ffv7$F[al$\"1uE<7+GfZF\\w7$Faal$\"1AHj+V;T<F\\w7$Fgal$\"1a_<zJ6
%)fFbw7$F]bl$\"18!f1NCU*>Fbw7$Fcbl$\"1R:L04j;qF\\jl7$Fibl$\"1j.ai3;M?F
\\jl7$F_cl$\"1')Rk)e=fZ'Fhw7$Fecl$\"1)o6R^A)Q=Fhw7$F[dl$\"1;e&*4h**3`F
^x7$Fadl$\"1>Fht;OT8F^xFfdlFj\\pF`am7'-F:6$7_o7$F-$\"12:EpJP$e#F`t7$FQ
$\"1#[?$e92tVF`t7$Fen$\"1D!>j29xq'F`t7$Fjo$\"10`WL'z$\\5F[s7$F^q$\"1f'
z$f5^)e\"F[s7$Fbr$\"1c$G(=wf:BF[s7$F]s$\"1L<th%R5=$F[s7$Fgs$\"1dL$z#*y
)yUF[s7$Fbt$\"1%*eU)GMR#\\F[s7$F\\u$\"1\"z'*3CWmh&F[s7$Fau$\"1,zDcIK[j
F[s7$Ffu$\"1i,\"*>5#H6(F[s7$Fchm$\"1V:*o=iI#zF[s7$F\\v$\"1o7p^THW()F[s
7$F[im$\"1B'zk/J^Y*F[s7$Fbv$\"1nE$)z*>s,\"F@7$Fcim$\"1**y`+et$4\"F@7$F
hv$\"1s\"=`Iq`;\"F@7$F[jm$\"1n*)>&4<2B\"F@7$F^w$\"1@!>B\"f(yG\"F@7$Fdw
$\"12dEsvxp8F@7$Fieo$\"1\"H^f0HHR\"F@7$Fjw$\"1&3&pF\"plS\"F@7$$\"1woa5
j\")fyFgn$\"1U/maEu39F@7$$\"1&3-j(GCIzFgn$\"1\\mte]/59F@7$$\"1%Hd?Wp1+
)Fgn$\"1iEO>RZ59F@7$Fafo$\"1n/;R%G+T\"F@7$$\"1=HKR\"\\>@)Fgn$\"1E0Y#R>
lS\"F@7$F`x$\"1ghMrRa*R\"F@7$Fciq$\"1!Qu'[:(*z8F@7$Ffx$\"1A%4f$4-^8F@7
$F\\y$\"1?.;Yf0^7F@7$Fbes$\"1`h.h`U%>\"F@7$Fby$\"1;,m]RyJ6F@7$Fjes$\"1
$z0&Gjgd5F@7$Fhy$\"1TraCA_$z*F[s7$F\\[u$\"1)[$QR1qD!*F[s7$F_z$\"1#R@e0
M)\\#)F[s7$Fd[u$\"1SP\\%)>jXuF[s7$Fez$\"1-)\\$**p#)fmF[s7$$\"1$3xcG/6<
\"Fjy$\"17<`#>wT'fF[s7$F[[l$\"1sUG$yX4I&F[s7$Fa[l$\"1\">L@2(41SF[s7$Fg
[l$\"1yfX)zD`)GF[s7$F]\\l$\"1n7nkYJ-@F[s7$Fc\\l$\"1$))>>FpfW\"F[s7$Fi
\\l$\"1p\\D`fn#[*F`t7$F_]l$\"1pKfe!y?1'F`t7$Fe]l$\"17)GY8td!QF`t7$F[^l
$\"1%f5$Hg(e=#F`t7$Fa^l$\"1&)4T(\\ZSG\"F`t7$Fg^l$\"1jb_E8%Q-(Fju7$F]_l
$\"1d)G68-+%RFju7$Fc_l$\"1q2cPwmB?Fju7$Fi_l$\"1pZ:SoSY5Fju7$F_`l$\"1LZ
J`f)o2&F`v7$Fe`l$\"1MDbP%[4U#F`v7$F[al$\"1IBX_]Bw5F`v7$Faal$\"1\"RAs=c
Ow%Ffv7$Fgal$\"1:d()=*R#**>Ffv7$F]bl$\"1%y.*=ryi\")F\\w7$Fcbl$\"1Sb,&[
*RwMF\\w7$Fibl$\"1eD$R%G'3E\"F\\w7$F_cl$\"1ZH\\PgHF\\Fbw7$Fecl$\"1D?63
+H\\<Fbw7$F[dl$\"1Q_,SUq$G'F\\jl7$Fadl$\"1F%Q\\@**z,#F\\jlFfdl-F(6%F*%
-Lambda~is~8.GF2-F:6$7dqF]el7$F^el$\"1+++ziiaLFju7$FdelFg^vFfelFfel7$F
del$\"1+++B5q$o#F`t7$FhelF[_vFjelFjel7$Fhel$\"1+++4/[t5F[s7$F_flF__vFa
flFafl7$F_fl$\"1+++DWhiGF[s7$FfflFc_vFhflFhfl7$Fffl$\"1+++^)G_s&F[s7$F
]glFg_vF_glF_gl7$F]gl$\"1+++ghOg\"*F[s7$FdglF[`vFfglFfgl7$Fdgl$\"1+++b
@Q@7F@7$F[hlF_`vF]hlF]hl7$F[hl$\"1+++>`'eR\"F@7$FbhlFc`vFdhlFdhlFe`v7$
FihlFc`vF[ilF[il7$Fihl$\"1+++t\"p2C\"F@7$F`ilFh`vFbilFbil7$F`il$\"1+++
%Q`h#**F[s7$FfilF\\avFhilFhil7$Ffil$\"1+++T1->sF[s7$F^jlF`avF`jlF`jl7$
F^jl$\"1+++G/o7[F[s7$FejlFdavFgjlFgjl7$Fejl$\"1+++%\\\\;'HF[s7$F\\[mFh
avF^[mF^[m7$F\\[m$\"1+++S6P#p\"F[s7$Fd[mF\\bvFf[mFf[m7$Fd[m$\"1+++7%zf
-*F`t7$F[\\mF`bvF]\\mF]\\m7$F[\\m$\"1+++1(*)H^%F`t7$Fb\\mFdbvFd\\mFd\\
m7$Fb\\m$\"1+++i)fP7#F`t7$Fj\\mFhbvF\\]mF\\]m7$Fj\\m$\"1+++;F$*Q%*Fju7
$Fb]mF\\cvFd]mFd]m7$Fb]m$\"1+++huGuRFju7$Fi]mF`cvF[^mF[^m7$Fi]m$\"1+++
%)\\r*e\"Fju7$Fa^mFdcvFc^mFc^m7$Fa^m$\"1+++#3dg0'F`v7$Fi^mFhcvF[_mF[_m
7$Fi^m$\"1+++vD?-AF`v7$F`_mF\\dvFb_mFb_m7$F`_m$\"1+++V]$)fwFfv7$Fh_mF`
dvFj_mFj_m7$Fh_m$\"1+++[$yKb#Ffv7$F_`mFddvFa`mFa`m7$F_`m$\"1+++82\\q\"
)F\\w7$Fg`mFhdvFi`mF2Fj`mF`am7'-F(6%F*%-Lambda~is~9.GF2-F:6$7dqF]el7$F
^el$\"1+++T!)4M7Fju7$FdelFcevFfelFfel7$Fdel$\"1+++P#)o56F`t7$FhelFgevF
jelFjel7$Fhel$\"1+++mq4)*\\F`t7$F_flF[fvFaflFafl7$F_fl$\"1+++?\"H%*\\
\"F[s7$FfflF_fvFhflFhfl7$Fffl$\"1+++?brtLF[s7$F]glFcfvF_glF_gl7$F]gl$
\"1+++NzosgF[s7$FdglFgfvFfglFfgl7$Fdgl$\"1,++.>.4\"*F[s7$F[hlF[gvF]hlF
]hl7$F[hl$\"1+++X7;r6F@7$FbhlF_gvFdhlFdhl7$Fbhl$\"1++++kb<8F@7$FihlFcg
vF[ilF[ilFegv7$F`ilFcgvFbilFbil7$F`il$\"1+++g2!e=\"F@7$FfilFhgvFhilFhi
l7$Ffil$\"1,++?i+-(*F[s7$F^jlF\\hvF`jlF`jl7$F^jl$\"1+++lY]wsF[s7$FejlF
`hvFgjlFgjl7$Fejl$\"1+++_,eP]F[s7$F\\[mFdhvF^[mF^[m7$F\\[m$\"1+++$QW%Q
KF[s7$Fd[mFhhvFf[mFf[m7$Fd[m$\"1+++Im1V>F[s7$F[\\mF\\ivF]\\mF]\\m7$F[
\\m$\"1+++!)\\(H4\"F[s7$Fb\\mF`ivFd\\mFd\\m7$Fb\\m$\"1+++F\"Qjy&F`t7$F
j\\mFdivF\\]mF\\]m7$Fj\\m$\"1+++k!pJ*GF`t7$Fb]mFhivFd]mFd]m7$Fb]m$\"1+
++.&[/P\"F`t7$Fi]mF\\jvF[^mF[^m7$Fi]m$\"1+++m#=q;'Fju7$Fa^mF`jvFc^mFc^
m7$Fa^m$\"1+++Gy+VEFju7$Fi^mFdjvF[_mF[_m7$Fi^m$\"1+++v/B\"3\"Fju7$F`_m
FhjvFb_mFb_m7$F`_m$\"1+++g=!4B%F`v7$Fh_mF\\[wFj_mFj_m7$Fh_m$\"1+++(>)e
'e\"F`v7$F_`mF`[wFa`mFa`m7$F_`m$\"1+++6vr6dFfv7$Fg`mFd[wFi`mF2-F:6$7ao
7$F-$\"1O$zR!GGx9F`t7$FQ$\"1H<NG1(e]#F`t7$Fen$\"1e=`G$>N'QF`t7$Fjo$\"1
N-`Hy0-hF`t7$F^q$\"1r*z+5#Hj$*F`t7$Fbr$\"1xE5)*>(*)Q\"F[s7$F]s$\"1r16(
o[h%>F[s7$Fgs$\"1Jx:)4$\\\"o#F[s7$F\\u$\"17mHl%QBi$F[s7$Fau$\"1y%oTus#
fTF[s7$Ffu$\"1N5tzB')QZF[s7$Fchm$\"1&[=*Hapv`F[s7$F\\v$\"1.SZ:DA[gF[s7
$F[im$\"1'f*>S6WkmF[s7$Fbv$\"1/-AzLz'H(F[s7$Fcim$\"1Kt$RUh$>!)F[s7$Fhv
$\"1.U/xmeU()F[s7$F[jm$\"1L')H'3]sX*F[s7$F^w$\"1J&zinOZ,\"F@7$Fbcp$\"1
WE/lxmx5F@7$Fdw$\"1H'[?Eze8\"F@7$Fjw$\"1HwRbS#eA\"F@7$Fafo$\"1)pQnkkvE
\"F@7$F`x$\"1k_())))>#*H\"F@7$Fciq$\"16qhDI`<8F@7$Ffx$\"1ZYC0knF8F@7$$
\"1$H2L(f[**))Fgn$\"17Q<991H8F@7$$\"1^7Gj`))o*)Fgn$\"1mFD!3O(H8F@7$$\"
13_D`ZGQ!*Fgn$\"1u!>3K*pH8F@7$Fjds$\"1S9([>^*G8F@7$$\"1%3xJ#H[Y#*Fgn$
\"1Ndt$yE`K\"F@7$F\\y$\"1R4')pg))=8F@7$Fbes$\"1\"y/x*[r+8F@7$Fby$\"1\\
3ESp@u7F@7$Fhy$\"1vCv;ik*=\"F@7$F\\[u$\"1$y,]q!QQ6F@7$F_z$\"1$fzQuw83
\"F@7$Fd[u$\"14XOP+(p,\"F@7$Fez$\"1`y+'y_!)[*F[s7$F^iu$\"1g9QXO6S))F[s
7$F[[l$\"1DX-4kB\"=)F[s7$$\"1](o/.MAA\"Fjy$\"1j#*f.\"))*ouF[s7$Fa[l$\"
1k6(Rc@cw'F[s7$$\"1</w7`Kw7Fjy$\"1#*y$>)fragF[s7$Fg[l$\"1Ufpx\\(HP&F[s
7$$\"1LLeR](yK\"Fjy$\"11?\"yjq\"4[F[s7$F]\\l$\"1<#Ra(*)3xUF[s7$Fc\\l$
\"1bmj`\\W[KF[s7$Fi\\l$\"1\">ngG2%pBF[s7$F_]l$\"1y&Rzb/to\"F[s7$Fe]l$
\"15'zXfO,=\"F[s7$F[^l$\"16;?.*GSn(F`t7$Fa^l$\"1#=dN<%ze]F`t7$Fg^l$\"1
%GM4<h>9$F`t7$F]_l$\"1&*QSHbP%)>F`t7$Fc_l$\"1I@IXDsk6F`t7$Fi_l$\"1o\\F
H7;`oFju7$F_`l$\"13#Q&)pV+#QFju7$Fe`l$\"1/0*p/OT4#Fju7$F[al$\"1FWG*z$
\\\"3\"Fju7$Faal$\"1G&eP#>X^bF`v7$Fgal$\"1Z&)Rw*Q:s#F`v7$F]bl$\"1_NWv/
L,8F`v7$Fcbl$\"1+)3Y5;'HkFfv7$Fibl$\"1D&\\l+!zvFFfv7$F_cl$\"1cSNz%RAF
\"Ffv7$Fecl$\"1G&)***zbPP&F\\w7$F[dl$\"1L9ApY&yG#F\\w7$Fadl$\"1XI2&pRV
&))FbwFfdlFj\\pF`am7'-F:6$7^o7$F-$\"1V._-mO+&)Fju7$FQ$\"1I95ACFW9F`t7$
Fen$\"1TdrrL&fB#F`t7$Fjo$\"17v&3Ow%eNF`t7$F^q$\"1'o[ro5*>bF`t7$Fbr$\"1
bf$=N!o.$)F`t7$F]s$\"1zfsJ;*>=\"F[s7$Fgs$\"1e4$*4YAg;F[s7$F\\u$\"18Wda
`$[H#F[s7$Ffu$\"1vYoFhD\"3$F[s7$F\\v$\"1fuU_HJ_SF[s7$Fbv$\"1dz:-qOL]F[
s7$Fcim$\"1>T9!\\g&HcF[s7$Fhv$\"1?;,51x]iF[s7$F[jm$\"1Cf4Xi\"H*oF[s7$F
^w$\"1TvQO\"Gba(F[s7$Fbcp$\"1nx)[>Zf<)F[s7$Fdw$\"1!euWfY*)z)F[s7$Fieo$
\"1rqoxdU]$*F[s7$Fjw$\"1B@0Fn&3))*F[s7$F`x$\"1nXBY*>:5\"F@7$Ffx$\"1%fm
A0>\"y6F@7$Fjds$\"1L.'))=GB@\"F@7$F\\y$\"1i#*=$3azB\"F@7$$\"1&3F>9U\"3
&*Fgn$\"1;0k<!)RY7F@7$Fbes$\"18ZUWn+`7F@7$$\"1]7`>I'Qv*Fgn$\"1,nlV0vd7
F@7$Fby$\"1\\qK<!31E\"F@7$$\"1$H#=X@7W**Fgn$\"1I*zZKp8E\"F@7$$\"1DJ?$3
_6+\"Fjy$\"1]/o))ybh7F@7$$\"1@!))=&>*y+\"Fjy$\"1G57_M<h7F@7$Fjes$\"1'[
Z)Ql@g7F@7$$\"13F%zb6\"G5Fjy$\"1Db]r7fc7F@7$Fhy$\"1+CP+=q]7F@7$F\\[u$
\"1ooanzML7F@7$F_z$\"1?<)4zX#37F@7$Fez$\"1+\"y'fg=L6F@7$F[[l$\"1ycbOPq
T5F@7$F^dw$\"1y(HS\\+_&)*F[s7$Fa[l$\"1O(>Jzi#e#*F[s7$Ffdw$\"1t$HdgN?h)
F[s7$Fg[l$\"1pUAQ:I]zF[s7$F^ew$\"1[3!o[#3qtF[s7$F]\\l$\"1c7FH!**Hz'F[s
7$Fc\\l$\"11YzZaB&e&F[s7$Fi\\l$\"1*=u#>OnNWF[s7$F_]l$\"1!)3l4*HNW$F[s7
$Fe]l$\"1yQZ;/*ei#F[s7$F[^l$\"15Ho%Q&z&)=F[s7$Fa^l$\"1!*[`d2Cj8F[s7$Fg
^l$\"1.\"H$)3![s$*F`t7$F]_l$\"1tm7UaY3lF`t7$Fc_l$\"1hLUG(=0D%F`t7$Fi_l
$\"1Yt_(*\\HtFF`t7$F_`l$\"1C`(yw>us\"F`t7$Fe`l$\"1'R%ev1qe5F`t7$F[al$
\"14())p&)4T;'Fju7$Faal$\"1\"o\"o\\^JiNFju7$Fgal$\"1!4T6D[v(>Fju7$F]bl
$\"1dX!He]H2\"Fju7$Fcbl$\"1/\"yW]2,(fF`v7$Fibl$\"1\">1J_#)G'HF`v7$F_cl
$\"1u>PY(HFa\"F`v7$Fecl$\"1HO<&*>'z[(Ffv7$F[dl$\"1.G(Gbt@l$Ffv7$Fadl$
\"1F(Gnyc4k\"FfvFfdl-F(6%F*%.Lambda~is~10.GF2-F:6$7dqF]el7$F^el$\"1+++
wH**RXF`v7$FdelFdgxFfelFfel7$Fdel$FegxFju7$FhelFhgxFjelFjel7$Fhel$\"1+
++)['**pAF`t7$F_flF[hxFaflFafl7$F_fl$\"1+++i\\lmvF`t7$FfflF_hxFhflFhfl
7$Fffl$\"1+++SPm\"*=F[s7$F]glFchxF_glF_gl7$F]gl$\"1+++![FLy$F[s7$FdglF
ghxFfglFfgl7$Fdgl$\"1+++,ea0jF[s7$F[hlF[ixF]hlF]hl7$F[hl$\"1+++rD#z+*F
[s7$FbhlF_ixFdhlFdhl7$Fbhl$\"1+++@.*f7\"F@7$FihlFcixF[ilF[il7$Fihl$\"1
+++d.5^7F@7$F`ilFgixFbilFbilFiix7$FfilFgixFhilFhil7$Ffil$\"1+++hROP6F@
7$F^jlF\\jxF`jlF`jl7$F^jl$\"1+++5I.y%*F[s7$FejlF`jxFgjlFgjl7$Fejl$\"1,
++BYz!H(F[s7$F\\[mFdjxF^[mF^[m7$F\\[m$\"1+++X/r2_F[s7$Fd[mFhjxFf[mFf[m
7$Fd[m$\"1+++jp!=Z$F[s7$F[\\mF\\[yF]\\mF]\\m7$F[\\m$\"1+++_$z)p@F[s7$F
b\\mF`[yFd\\mFd\\m7$Fb\\m$\"1+++>'*Rw7F[s7$Fj\\mFd[yF\\]mF\\]m7$Fj\\m$
\"1+++$**364(F`t7$Fb]mFh[yFd]mFd]m7$Fb]m$\"1+++GE;KPF`t7$Fi]mF\\\\yF[^
mF[^m7$Fi]m$\"1+++983m=F`t7$Fa^mF`\\yFc^mFc^m7$Fa^m$\"1+++$\\,h)))Fju7
$Fi^mFd\\yF[_mF[_m7$Fi^m$\"1+++Vq8RSFju7$F`_mFh\\yFb_mFb_m7$F`_m$\"1++
+Tl9c<Fju7$Fh_mF\\]yFj_mFj_m7$Fh_m$\"1+++^sF<tF`v7$F_`mF`]yFa`mFa`m7$F
_`m$\"1+++,4\"p#HF`v7$Fg`mFd]yFi`mF2Fj`mF`am7'-F(6%F*%.Lambda~is~11.GF
2-F:6$7dqF]el7$F^el$\"1+++z+<q;F`v7$FdelF_^yFfelFfel7$Fdel$\"1+++(3(=P
=Fju7$FhelFc^yFjelFjel7$Fhel$\"1+++)*GX55F`t7$F_flFg^yFaflFafl7$F_fl$
\"1+++eR*\\q$F`t7$FfflF[_yFhflFhfl7$Fffl$\"1+++RL()=5F[s7$F]glF__yF_gl
F_gl7$F]gl$\"1+++X8_TAF[s7$FdglFc_yFfglFfgl7$Fdgl$\"1+++*zb%4TF[s7$F[h
lFg_yF]hlF]hl7$F[hl$\"1+++cirdkF[s7$FbhlF[`yFdhlFdhl7$Fbhl$\"1+++_)f$z
))F[s7$FihlF_`yF[ilF[il7$Fihl$\"1+++$4b_3\"F@7$F`ilFc`yFbilFbil7$F`il$
\"1+++-1y$>\"F@7$FfilFg`yFhilFhilFi`y7$F^jlFg`yF`jlF`jl7$F^jl$\"1+++&)
))H%4\"F@7$FejlF\\ayFgjlFgjl7$Fejl$\"1,++3@Xf#*F[s7$F\\[mF`ayF^[mF^[m7
$F\\[m$\"1+++*z$GvsF[s7$Fd[mFdayFf[mFf[m7$Fd[m$\"1+++>\"3_L&F[s7$F[\\m
FhayF]\\mF]\\m7$F[\\m$\"1+++#ebzm$F[s7$Fb\\mF\\byFd\\mFd\\m7$Fb\\m$\"1
+++CIQtBF[s7$Fj\\mF`byF\\]mF\\]m7$Fj\\m$\"1+++P2S]9F[s7$Fb]mFdbyFd]mFd
]m7$Fb]m$\"1+++'*o0(R)F`t7$Fi]mFhbyF[^mF[^m7$Fi]m$\"1+++#H\"Q=YF`t7$Fa
^mF\\cyFc^mFc^m7$Fa^m$\"1+++1@:>CF`t7$Fi^mF`cyF[_mF[_m7$Fi^m$\"1+++`gd
47F`t7$F`_mFdcyFb_mFb_m7$F`_m$\"1+++\\*G\\y&Fju7$Fh_mFhcyFj_mFj_m7$Fh_
m$\"1+++odU^EFju7$F_`mF\\dyFa`mFa`m7$F_`m$\"1+++Qtim6Fju7$Fg`mF`dyFi`m
F2-F:6$7[o7$F-$\"1<id+&)z:\\Fju7$FQ$\"1!GE6jqNO)Fju7$Fen$\"18#*H0(z\"*
H\"F`t7$Fjo$\"1Bu<_aa!3#F`t7$F^q$\"1@&=+6VhD$F`t7$Fbr$\"1rCil?ja\\F`t7
$F]s$\"1ONywAXWrF`t7$Fgs$\"1]n(HaB%>5F[s7$F\\u$\"1r45^^\"eV\"F[s7$Ffu$
\"1^&Q#>`Ip>F[s7$F\\v$\"1*[NpE_Ul#F[s7$Fbv$\"1j+=W7OwLF[s7$Fhv$\"1K-z*
\\!y<VF[s7$F^w$\"1/=$y25AQ&F[s7$Fdw$\"1+,ITj%)*['F[s7$Fieo$\"1d_XH&4z+
(F[s7$Fjw$\"1w*))ec:)GvF[s7$Fafo$\"1?\")*z.%eW\")F[s7$F`x$\"1mQ3@)ztu)
F[s7$Fciq$\"1a7JB&)\\S#*F[s7$Ffx$\"1`?rr*35r*F[s7$F\\y$\"1Fw#p#RUo5F@7
$Fby$\"1W-Jp1\"e8\"F@7$Fjes$\"1#RJ\\7jO;\"F@7$Fhy$\"1ah1BsM%=\"F@7$$\"
1](oH>FW0\"Fjy$\"1$z^2Ea:>\"F@7$F\\[u$\"1M#yR!4,(>\"F@7$$\"1]7G))*)4!3
\"Fjy$\"1*)4ilFp+7F@7$F_z$\"1+YV[Le-7F@7$$\"13xc)zFj5\"Fjy$\"19s:Gtj-7
F@7$Fd[u$\"1#\\D]vJ2?\"F@7$$\"1D\"GQi8J8\"Fjy$\"1habQf(o>\"F@7$Fez$\"1
sw'eo)3\">\"F@7$F^iu$\"1D&4%3'Gb<\"F@7$F[[l$\"1YCgdy!Q:\"F@7$Fa[l$\"1f
@B,)Rx3\"F@7$Fg[l$\"1V1*oj#ed**F[s7$F]\\l$\"1axHy+V:!*F[s7$$\"1$eRA\"e
xx8Fjy$\"1UY7U_Cq%)F[s7$Fc\\l$\"1(z')***zg4zF[s7$$\"1Lek`SXI9Fjy$\"1:t
auQFAtF[s7$Fi\\l$\"1\\?v!)=aMnF[s7$$\"1+D1R\"4M[\"Fjy$\"1ED#f&yCmhF[s7
$F_]l$\"1O88S2#3h&F[s7$Fe]l$\"1bNjKB2#f%F[s7$F[^l$\"19ES\\]%pd$F[s7$Fa
^l$\"1BT,C[W)y#F[s7$Fg^l$\"1Xy>>fG$3#F[s7$F]_l$\"1*)[U/gWj:F[s7$Fc_l$
\"1IzgQdC96F[s7$Fi_l$\"13C7kn^6zF`t7$F_`l$\"1k;-y8d'R&F`t7$Fe`l$\"1gTi
o@ZBOF`t7$F[al$\"1TC52x=FBF`t7$Faal$\"1VX6a&z=[\"F`t7$Fgal$\"1vK>$fpq5
*Fju7$F]bl$\"1su<6qRzaFju7$Fcbl$\"1J_'\\qS,O$Fju7$Fibl$\"109!*))R-p=Fj
u7$F_cl$\"1B#*H.%>-3\"Fju7$Fecl$\"17PYlibueF`v7$F[dl$\"1r(44&)HB?$F`v7
$Fadl$\"1!p$y%3;di\"F`vFfdlFj\\pF`am7'-F:6$7en7$F-$\"1]&en\"zkaGFju7$F
Q$\"1)=@'oeEi[Fju7$Fen$\"1m6@&G)=uvFju7$Fjo$\"1;@)[@p#>7F`t7$F^q$\"1:R
>G%)QA>F`t7$Fbr$\"1Ad'\\)==`HF`t7$F]s$\"1_tkE6`/VF`t7$Fgs$\"1TyNd$)3Bi
F`t7$F\\u$\"1`%>I>iK!*)F`t7$Ffu$\"1a#)*>`uHC\"F[s7$F\\v$\"1<&\\r#f*)4<
F[s7$Fbv$\"1w5[k*=(=AF[s7$Fhv$\"1(3d-Yav!HF[s7$F^w$\"1=+!eZ8Es$F[s7$Fd
w$\"1pBN#>Wch%F[s7$Fjw$\"1x!QM-;<]&F[s7$F`x$\"1xR:5JB;mF[s7$Ffx$\"1^1m
:h%od(F[s7$F\\y$\"10\\NiIsh')F[s7$Fby$\"14(z[w(=W&*F[s7$Fhy$\"1$p,)yrJ
P5F@7$F_z$\"1'**=G$[$z4\"F@7$Fd[u$\"1,x@-L8@6F@7$Fez$\"1+)*)RY(*z8\"F@
7$$\"13x16a!)e6Fjy$\"15i64G`V6F@7$F^iu$\"137wMvkZ6F@7$$\"1ekGgJS$=\"Fj
y$\"1z:nVhK]6F@7$F[[l$\"1fNXF&e::\"F@7$$\"1#H#oK!o*37Fjy$\"1)po[Ih7:\"
F@7$F^dw$\"1Er&HWx#\\6F@7$$\"13_DG+]N7Fjy$\"1K=wdchX6F@7$Fa[l$\"12[(3,
#HS6F@7$Ffdw$\"1H^[6'HS7\"F@7$Fg[l$\"1*zjLW355\"F@7$F]\\l$\"1,OY4#Hh/
\"F@7$Fc\\l$\"1a\">@LF#)o*F[s7$Fi\\l$\"1psGTnkT()F[s7$F_]l$\"1>#Gf/_Xs
(F[s7$Fe]l$\"1S$>;vVdq'F[s7$F[^l$\"1*yNgxq#*e&F[s7$Fa^l$\"1XfgUc'*RYF[
s7$Fg^l$\"1y9@KzD:PF[s7$F]_l$\"1WV'>@/X(HF[s7$Fc_l$\"1=g(QB[*zAF[s7$Fi
_l$\"1kY837.P<F[s7$F_`l$\"1))f2R[/y7F[s7$Fe`l$\"1X_?1*G$f#*F`t7$F[al$
\"1*)y2SnZ`kF`t7$Faal$\"1h0\"*p$y_X%F`t7$Fgal$\"1:BdS)H-)HF`t7$F]bl$\"
1z\"f3WPW&>F`t7$Fcbl$\"1?,g$zl'*H\"F`t7$Fibl$\"1n5Z)Hq)\\zFju7$F_cl$\"
1'z/uAj@,&Fju7$Fecl$\"1Z$>gG>n*HFju7$F[dl$\"1;Ge\"\\8Az\"Fju7$Fadl$\"1
d7LC%3t+\"FjuFfdl-F:6$7dqF]el7$F^el$\"1+++`B@WhFfv7$FdelF\\][lFfelFfel
7$Fdel$\"1+++C[0ttF`v7$FhelF`][lFjelFjel7$Fhel$\"1+++%*G$QU%Fju7$F_flF
d][lFaflFafl7$F_fl$\"1+++eJ`p<F`t7$FfflFh][lFhflFhfl7$Fffl$\"1+++t%*f3
`F`t7$F]glF\\^[lF_glF_gl7$F]gl$\"1+++uQ1u7F[s7$FdglF`^[lFfglFfgl7$Fdgl
$\"1+++Zx7[DF[s7$F[hlFd^[lF]hlF]hl7$F[hl$\"1+++&**=#oVF[s7$FbhlFh^[lFd
hlFdhl7$Fbhl$\"1*****>\\GBb'F[s7$FihlF\\_[lF[ilF[il7$Fihl$\"1+++\"*zVO
()F[s7$F`ilF`_[lFbilFbil7$F`il$\"1+++fDP[5F@7$FfilFd_[lFhilFhil7$Ffil$
\"1+++b\"zO9\"F@7$F^jlFh_[lF`jlF`jlFj_[l7$FejlFh_[lFgjlFgjl7$Fejl$\"1+
++NQqb5F@7$F\\[mF]`[lF^[mF^[m7$F\\[m$\"1+++@+*)[!*F[s7$Fd[mFa`[lFf[mFf
[m7$Fd[m$\"1+++9?6RsF[s7$F[\\mFe`[lF]\\mF]\\m7$F[\\m$\"1+++6SLHaF[s7$F
b\\mFi`[lFd\\mFd\\m7$Fb\\m$\"1+++n5ZKQF[s7$Fj\\mF]a[lF\\]mF\\]m7$Fj\\m
$\"1+++62)\\b#F[s7$Fb]mFaa[lFd]mFd]m7$Fb]m$\"1+++G?n8;F[s7$Fi]mFea[lF[
^mF[^m7$Fi]m$\"1,++n@.#o*F`t7$Fa^mFia[lFc^mFc^m7$Fa^m$\"1+++5)*eKbF`t7
$Fi^mF]b[lF[_mF[_m7$Fi^m$\"1+++gix<IF`t7$F`_mFab[lFb_mFb_m7$F`_m$\"1++
+i>\\u:F`t7$Fh_mFeb[lFj_mFj_m7$Fh_m$\"1+++3)fC(yFju7$F_`mFib[lFa`mFa`m
7$F_`m$\"1+++32yyPFju7$Fg`mF]c[lFi`mF2-F(6%F*%.Lambda~is~12.GF2Fj`mF`a
m7'-F:6$7dqF]el7$F^el$\"1+++2%H.E#Ffv7$FdelFhc[lFfelFfel7$Fdel$\"1+++H
#G%QHF`v7$FhelF\\d[lFjelFjel7$Fhel$\"1+++\\$y*4>Fju7$F_flF`d[lFaflFafl
7$F_fl$\"1+++YGdw#)Fju7$FfflFdd[lFhflFhfl7$Fffl$\"1+++vh))*o#F`t7$F]gl
Fhd[lF_glF_gl7$F]gl$\"1+++aSq$*pF`t7$FdglF\\e[lFfglFfgl7$Fdgl$\"1+++XD
I::F[s7$F[hlF`e[lF]hlF]hl7$F[hl$\"1+++)HLT\"GF[s7$FbhlFde[lFdhlFdhl7$F
bhl$\"1+++4m'Hd%F[s7$FihlFhe[lF[ilF[il7$Fihl$\"1+++8iR0mF[s7$F`ilF\\f[
lFbilFbil7$F`il$\"1+++y],(e)F[s7$FfilF`f[lFhilFhil7$Ffil$\"1+++b!H[,\"
F@7$F^jlFdf[lF`jlF`jl7$F^jl$\"1+++V\")R*4\"F@7$FejlFhf[lFgjlFgjlFjf[l7
$F\\[mFhf[lF^[mF^[m7$F\\[m$\"1+++/(p3-\"F@7$Fd[mF]g[lFf[mFf[m7$Fd[m$\"
1*****>VPv%))F[s7$F[\\mFag[lF]\\mF]\\m7$F[\\m$\"1+++jTi)=(F[s7$Fb\\mFe
g[lFd\\mFd\\m7$Fb\\m$\"1+++%=$=(\\&F[s7$Fj\\mFig[lF\\]mF\\]m7$Fj\\m$\"
1+++by=qRF[s7$Fb]mF]h[lFd]mFd]m7$Fb]m$\"1+++BVW;FF[s7$Fi]mFah[lF[^mF[^
m7$Fi]m$\"1+++4))ol<F[s7$Fa^mFeh[lFc^mFc^m7$Fa^m$\"1+++`a/$4\"F[s7$Fi^
mFih[lF[_mF[_m7$Fi^m$\"1+++^\\!*ekF`t7$F`_mF]i[lFb_mFb_m7$F`_m$\"1+++2
ao]OF`t7$Fh_mFai[lFj_mFj_m7$Fh_m$\"1+++'fau(>F`t7$F_`mFei[lFa`mFa`m7$F
_`m$\"1+++!Rw#G5F`t7$Fg`mFii[lFi`mF2-F:6$7en7$F-$\"1\"fG?c0Nm\"Fju7$FQ
$\"1/eeLW6OGFju7$Fen$\"1l*=V]m%GWFju7$Fjo$\"1)pE[5/-;(Fju7$F^q$\"1J4$*
*3Cg8\"F`t7$Fbr$\"1#)3\"=#HIf<F`t7$F]s$\"18&**fvBye#F`t7$Fgs$\"1aSZ_@(
Hy$F`t7$F\\u$\"1p'pp?1W[&F`t7$Ffu$\"1gzWk-VsxF`t7$F\\v$\"1Db(3Bpy3\"F[
s7$Fbv$\"1#*G7$R;bV\"F[s7$Fhv$\"1neT*z,0#>F[s7$F^w$\"1srGu'o^^#F[s7$Fd
w$\"1\\w;#4+I>$F[s7$Fjw$\"1B(Gr&*yU*QF[s7$F`x$\"1-&*G1'*o@[F[s7$Ffx$\"
1I[IL&>)ocF[s7$F\\y$\"1y2wcx*Rp'F[s7$Fby$\"1pz()\\u?.wF[s7$Fhy$\"1RDk,
=ae&)F[s7$F_z$\"1@!*3<)HDQ*F[s7$Fez$\"1C]%pY61,\"F@7$F[[l$\"1^lX:(G61
\"F@7$F^dw$\"1UI$*>w-\"3\"F@7$Fa[l$\"1%>InG_`4\"F@7$$\"1U5Spcai7Fjy$\"
1>39aH^+6F@7$Ffdw$\"1H%Gs7%3/6F@7$$\"1#z>h&\\5!H\"Fjy$\"1l/j1-016F@7$F
g[l$\"1tq&)*e-k5\"F@7$$\"1]7`>)zeJ\"Fjy$\"1B-)o=%R06F@7$F^ew$\"1q&3H.l
J5\"F@7$$\"1<ajf-()R8Fjy$\"1ZP_;Ds*4\"F@7$F]\\l$\"1eiWG!y]4\"F@7$Fa\\z
$\"1n,ca7-\"3\"F@7$Fc\\l$\"1R!o*y\"[;1\"F@7$Fi\\l$\"1t8dC%=h+\"F@7$F_]
l$\"1&\\8z'zaW$*F[s7$Fe]l$\"1lQ**H8!o_)F[s7$F[^l$\"11m$HK!>EvF[s7$Fa^l
$\"1W/Sl$e$*e'F[s7$Fg^l$\"1>%H6>)o%f&F[s7$F]_l$\"1l\"e[B+7t%F[s7$Fc_l$
\"1>xz44$o&QF[s7$Fi_l$\"1`\"\\/'G&*=JF[s7$F_`l$\"1v#*ydVjYCF[s7$Fe`l$
\"1,o!3![P!*=F[s7$F[al$\"1V^uP0\">T\"F[s7$Faal$\"1d\"fOXHP/\"F[s7$Fgal
$\"1Y_#okD3](F`t7$F]bl$\"1M$>/Nc5H&F`t7$Fcbl$\"1L?hus6oPF`t7$Fibl$\"1(
*)RH)e*y\\#F`t7$F_cl$\"1moV%)o5&p\"F`t7$Fecl$\"1xXb%o/\")4\"F`t7$F[dl$
\"1#ywF8\"4.rFju7$Fadl$\"1O_L52E^VFjuFfdl-F(6%F*%.Lambda~is~13.GF2Fj\\
pF`am7'-F:6$7en7$F-$\"1W9f/0lA(*F`v7$FQ$\"1ChdC(p*e;Fju7$Fen$\"1F3-g+p
&f#Fju7$Fjo$\"1'*)es7-F@%Fju7$F^q$\"1*>QJiw(>nFju7$Fbr$\"1.4ht&zy/\"F`
t7$F]s$\"1U!**4\"RX`:F`t7$Fgs$\"1yTOkAf#H#F`t7$F\\u$\"1%=^F$omhLF`t7$F
fu$\"1Dzz0qvD[F`t7$F\\v$\"1P\"yEGp_&oF`t7$Fbv$\"1h*fg'4Cx\"*F`t7$Fhv$
\"1@5&HWJ(\\7F[s7$F^w$\"1@)>(o6xo;F[s7$Fdw$\"1cZJAJyh@F[s7$Fjw$\"1Wi%[
1H*)o#F[s7$F`x$\"1NKx'4@NT$F[s7$Ffx$\"1_Cx$z%p/TF[s7$F\\y$\"1m!ybGiN)
\\F[s7$Fby$\"1byO*z)e4eF[s7$Fhy$\"1'>4qi:\"RnF[s7$F_z$\"1!pKJ.cPh(F[s7
$Fez$\"1OXL@+tv%)F[s7$F[[l$\"1W$)fmki&=*F[s7$Fa[l$\"1\\F!p&f'e#)*F[s7$
Fg[l$\"1e2`fQhJ5F@7$F^ew$\"1HiYA@fY5F@7$F]\\l$\"19l^*zJu0\"F@7$$\"1UN'
fk?[O\"Fjy$\"1s$>$ee^h5F@7$Fa\\z$\"1v67j*QV1\"F@7$$\"1Dc^y4t!R\"Fjy$\"
1Z,i')4*e1\"F@7$Fc\\l$\"1x2h`j;m5F@7$$\"1](=#*4qqT\"Fjy$\"1Y2Z'34^1\"F
@7$Fi\\z$\"1%Hc4G#pi5F@7$$\"1<H23!QQW\"Fjy$\"1Q&*f&>D*e5F@7$Fi\\l$\"1A
^oLA#Q0\"F@7$Fa]z$\"1L7$4Z_+/\"F@7$F_]l$\"1^e]dpW@5F@7$Fe]l$\"1fzi=4dF
(*F[s7$F[^l$\"1(G(4/4?=!*F[s7$Fa^l$\"1Tct1')3k#)F[s7$Fg^l$\"1$f\"yL;=y
tF[s7$F]_l$\"1lI\")[T6RlF[s7$Fc_l$\"1z'**G/0'>cF[s7$Fi_l$\"1/YR1zx#y%F
[s7$F_`l$\"1E#*\\`3ejRF[s7$Fe`l$\"1nn*>2%3OKF[s7$F[al$\"1KD!=gsYc#F[s7
$Faal$\"12B%R:S.,#F[s7$Fgal$\"1#=XgMSj`\"F[s7$F]bl$\"1#R4b**4O:\"F[s7$
Fcbl$\"1%oCj$\\%Gr)F`t7$Fibl$\"1&o6jK\"*y='F`t7$F_cl$\"1#>zhCvDZ%F`t7$
Fecl$\"1d_%3@BN5$F`t7$F[dl$\"1!R&RwI5Z@F`t7$Fadl$\"1;uf'HLgT\"F`tFfdl-
F:6$7dqF]el7$F^el$\"1+++\">(G:$)F\\w7$FdelF`a]lFfelFfel7$Fdel$\"1+++2-
9k6F`v7$FhelFda]lFjelFjel7$Fhel$\"1*****pW\")*[\")F`v7$F_flFha]lFaflFa
fl7$F_fl$\"1+++3!eG!QFju7$FfflF\\b]lFhflFhfl7$Fffl$\"1+++..+J8F`t7$F]g
lF`b]lF_glF_gl7$F]gl$\"1+++\\3!os$F`t7$FdglFdb]lFfglFfgl7$Fdgl$\"1****
*pkoep)F`t7$F[hlFhb]lF]hlF]hl7$F[hl$\"1+++HP<R<F[s7$FbhlF\\c]lFdhlFdhl
7$Fbhl$\"1+++ESbVIF[s7$FihlF`c]lF[ilF[il7$Fihl$\"1+++utTMZF[s7$F`ilFdc
]lFbilFbil7$F`il$\"1+++CV=GmF[s7$FfilFhc]lFhilFhil7$Ffil$\"1*****R&4(e
V)F[s7$F^jlF\\d]lF`jlF`jl7$F^jl$\"1*****zW\\=%)*F[s7$FejlF`d]lFgjlFgjl
7$Fejl$\"1+++z9*)f5F@7$F\\[mFdd]lF^[mF^[mFfd]l7$Fd[mFdd]lFf[mFf[m7$Fd[
m$\"1+++s/K#*)*F[s7$F[\\mFid]lF]\\mF]\\m7$F[\\m$\"1+++:/yb')F[s7$Fb\\m
F]e]lFd\\mFd\\m7$Fb\\m$\"1+++`(*GGrF[s7$Fj\\mFae]lF\\]mF\\]m7$Fj\\m$\"
1+++j`AWbF[s7$Fb]mFee]lFd]mFd]m7$Fb]m$\"1+++*o=_3%F[s7$Fi]mFie]lF[^mF[
^m7$Fi]m$\"1+++#3`'fGF[s7$Fa^mF]f]lFc^mFc^m7$Fa^m$\"1+++)QNk!>F[s7$Fi^
mFaf]lF[_mF[_m7$Fi^m$\"1+++ch=87F[s7$F`_mFef]lFb_mFb_m7$F`_m$\"1+++&Q6
YQ(F`t7$Fh_mFif]lFj_mFj_m7$Fh_m$\"1+++u**o2VF`t7$F_`mF]g]lFa`mFa`m7$F_
`m$\"1+++'Q1BT#F`t7$Fg`mFag]lFi`mF2-F(6%F*%.Lambda~is~14.GF2Fj`mF`am7'
-F(6%F*%.Lambda~is~15.GF2-F:6$7Y7$F-$\"1YF9mf7(p&F`v7$FQ$\"1WB2Ra%ys*F
`v7$Fen$\"1?b<QruC:Fju7$Fjo$\"13o9)y&p#[#Fju7$F^q$\"1kH3XjnyRFju7$Fbr$
\"1%4&R\"yJ;C'Fju7$F]s$\"1PORn%=fJ*Fju7$Fgs$\"1!G,t:CiQ\"F`t7$F\\u$\"1
ki^)yXF0#F`t7$Ffu$\"1Uu,GdyzHF`t7$F\\v$\"1)=Ltd.xG%F`t7$Fbv$\"1Bwlxs67
eF`t7$Fhv$\"1(zZz\\1t.)F`t7$F^w$\"1&3$RBoU\"4\"F[s7$Fdw$\"1Q7'**es)Q9F
[s7$Fjw$\"1CLW7w\\?=F[s7$F`x$\"1r)=\\Eh;O#F[s7$Ffx$\"1lIw]/&e*GF[s7$F
\\y$\"1j>G-Zd,OF[s7$Fby$\"1.#euZRUH%F[s7$Fhy$\"1SNGzuy7^F[s7$F_z$\"1=(
G_+l!HfF[s7$Fez$\"1+l'=6j:z'F[s7$F[[l$\"1$[;[LE^c(F[s7$Fa[l$\"1KS%y=Vi
M)F[s7$Fg[l$\"1*[tiX271*F[s7$F]\\l$\"1[l?I%*3u&*F[s7$Fc\\l$\"1u@Yy5,()
**F[s7$Fi\\z$\"1D+ud3f85F@7$Fi\\l$\"1D8J0/!Q-\"F@7$$\"1]7y]bJq9Fjy$\"1
Nht\\M/F5F@7$Fa]z$\"1v(p]')>\"H5F@7$$\"1]PMFF]'\\\"Fjy$\"1H;9WD-I5F@7$
F_]l$\"1B)pUR[(H5F@7$$\"1](oavL\\`\"Fjy$\"1lYjfG)e-\"F@7$Fe]l$\"106.$)
pm<5F@7$$\"1]PM-TS)e\"Fjy$\"1e&e+*od.5F@7$F[^l$\"12yUJntW)*F[s7$Fa^l$
\"1njiS\"R_Q*F[s7$Fg^l$\"145q)G!4_()F[s7$F]_l$\"1N:y&*Gly!)F[s7$Fc_l$
\"1vwHN.pnsF[s7$Fi_l$\"1n*=N*3elkF[s7$F_`l$\"1*fu*peI>cF[s7$Fe`l$\"1_U
F*RQD\"[F[s7$F[al$\"1g9gwW=:SF[s7$Faal$\"1^Vaw[N6LF[s7$Fgal$\"1T@Zm^2p
EF[s7$F]bl$\"1ZbxE3p:@F[s7$Fcbl$\"1*=R&=WR\"o\"F[s7$Fibl$\"1,[lRWjn7F[
s7$F_cl$\"1FEiaD=x'*F`t7$Fecl$\"1d%G%Gf;FrF`t7$F[dl$\"10'R!phcE_F`t7$F
adl$\"1HT=]:luOF`tFfdl-F:6$7dqF]el7$F^el$\"1+++0K-fIF\\w7$FdelF_c^lFfe
lFfel7$Fdel$\"1+++3[`)e%Ffv7$FhelFcc^lFjelFjel7$Fhel$\"1+++16STMF`v7$F
_flFgc^lFaflFafl7$F_fl$\"1+++`0q?<Fju7$FfflF[d^lFhflFhfl7$Fffl$\"1+++t
qi_kFju7$F]glF_d^lF_glF_gl7$F]gl$\"1+++A\")yN>F`t7$FdglFcd^lFfglFfgl7$
Fdgl$\"1+++0.ZR[F`t7$F[hlFgd^lF]hlF]hl7$F[hl$\"1+++^$Hq.\"F[s7$FbhlF[e
^lFdhlFdhl7$Fbhl$\"1+++L+VW>F[s7$FihlF_e^lF[ilF[il7$Fihl$\"1+++@nrSKF[
s7$F`ilFce^lFbilFbil7$F`il$\"1+++%3v5'[F[s7$FfilFge^lFhilFhil7$Ffil$\"
1+++](Q(GmF[s7$F^jlF[f^lF`jlF`jl7$F^jl$\"1,++OM#fG)F[s7$FejlF_f^lFgjlF
gjl7$Fejl$\"1,++*)3og&*F[s7$F\\[mFcf^lF^[mF^[m7$F\\[m$\"1+++n'eV-\"F@7
$Fd[mFgf^lFf[mFf[mFif^l7$F[\\mFgf^lF]\\mF]\\m7$F[\\m$\"1+++,DO.'*F[s7$
Fb\\mF\\g^lFd\\mFd\\m7$Fb\\m$\"1+++Y^bt%)F[s7$Fj\\mF`g^lF\\]mF\\]m7$Fj
\\m$\"1,++bfHhqF[s7$Fb]mFdg^lFd]mFd]m7$Fb]m$\"1+++MtqubF[s7$Fi]mFhg^lF
[^mF[^m7$Fi]m$\"1++++0.\"=%F[s7$Fa^mF\\h^lFc^mFc^m7$Fa^m$\"1+++d.X')HF
[s7$Fi^mF`h^lF[_mF[_m7$Fi^m$\"1+++`h@O?F[s7$F`_mFdh^lFb_mFb_m7$F`_m$\"
1+++cq'zK\"F[s7$Fh_mFhh^lFj_mFj_m7$Fh_m$\"1,+++Tz*H)F`t7$F_`mF\\i^lFa`
mFa`m7$F_`m$\"1+++gk()z\\F`t7$Fg`mF`i^lFi`mF2Fj`mF`am-%&TITLEG6#Q[oNor
mal~Approx.~to~the~Poisson.~Lambda~is~increasing~from~1~to~15F^am" 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 11 "Indeed, as " }
{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 30 " becomes larger , t
he Poisson(" }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 35 ") dis
tribution becomes increasingly" }}{PARA 0 "" 0 "" {TEXT -1 32 "well ap
proximated by the Normal(" }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }
{TEXT -1 1 "," }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 15 ") d
istribution." }}{PARA 0 "" 0 "" {MPLTEXT 0 21 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 10 "Si
mulation" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 290 0 "" }
{MPLTEXT 0 21 0 "" }}{PARA 0 "" 0 "" {TEXT -1 284 "We will now simulat
e some data from a poisson distribution in order to compare the sampli
ng distribution to the theoretical distribution.  The next bit of code
 will simulate a random sample of size 500 from a Poisson(5) distribut
ion, but you are invited to change the value of lambda." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart: with(plots):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "lambda:=5: numsim:=500:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "sample:=PoissonS(lambda,nums
im):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "a:=Histogram(sample
,-0.5..15+0.5,16):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "b:=Pr
obHist(PoissonPDF(lambda,x),0..16,17):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 60 "display([a,b],title=\"Simulated(red) vs. Theoretical(
blue)\");" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6'-%'
CURVESG6%7\\o7$$!1+++++++]!#;\"\"!7$F($\"1+++++++!)!#=7$$\"1+++++++]F*
F-7$F1F+F37$F1$\"1+++++++M!#<7$$\"1+++++++:!#:F57$F9F+F<7$F9$\"1++++++
+'*F77$$\"1+++++++DF;F>7$FAF+FC7$FA$\"1++++++S8F*7$$\"1+++++++NF;FE7$F
HF+FJ7$FH$\"1++++++?=F*7$$\"1+++++++XF;FL7$FOF+FQ7$FO$\"1++++++g;F*7$$
\"1+++++++bF;FS7$FVF+FX7$FV$\"1++++++?9F*7$$\"1+++++++lF;FZ7$FgnF+Fin7
$Fgn$\"1++++++g6F*7$$\"1+++++++vF;F[o7$F^oF+F`o7$F^o$\"1+++++++cF77$$
\"1+++++++&)F;Fbo7$FeoF+Fgo7$Feo$\"1+++++++GF77$$\"1+++++++&*F;Fio7$F
\\pF+F^p7$F\\p$\"1+++++++;F77$$\"1++++++]5!#9F`p7$FcpF+FfpFbp7$$\"1+++
+++]6FepF`p7$FhpF+Fjp7$Fhp$\"1+++++++gF/7$$\"1++++++]7FepF\\q7$F_qF+Fa
qFaq7$$\"1++++++]8FepF+FbqFbqFbq7$$\"1++++++]9FepF+FeqFeqFeq7$$\"1++++
++]:FepF+Fhq-%'COLOURG6&%$RGBG$\"*++++\"!\")F+F+-%*LINESTYLEG6#\"\"$-F
$6$7`oF'7$F($\"1+++**p%zt'F/7$F1FjrF3F37$F1$\"1++++N(*oLF77$F9F^sF<F<7
$F9$\"1+++\\PVA%)F77$FAFbsFCFC7$FA$\"1+++e*QPS\"F*7$FHFfsFJFJ7$FH$\"1+
++)ptYv\"F*7$FOFjsFQFQF\\t7$FVFjsFXFX7$FV$\"1+++\"3GAY\"F*7$FgnF_tFinF
in7$Fgn$\"1+++H'[W/\"F*7$F^oFctF`oF`o7$F^o$\"1+++NR!y_'F77$FeoFgtFgoFg
o7$Feo$\"1+++UxbEOF77$F\\pF[uF^pF^p7$F\\p$\"1+++q)yK\"=F77$FcpF_uFfpFf
p7$Fcp$\"1,++(ow@C)F/7$FhpFcuFjpFjp7$Fhp$\"1+++'GSUV$F/7$F_qFguFaqFaq7
$F_q$\"1+++\\;'3K\"F/7$FcqF[vFbqFbq7$Fcq$\"1+++IIO<Z!#>7$FfqF_vFeqFeq7
$Ffq$\"1+++VVXs:Fav7$FiqFdvFhqFhq7$Fiq$\"1+++A)>R\"\\!#?7$$\"1++++++];
FepFhv7$F\\wF+-F\\r6&F^rF+F+F_r-%&TITLEG6#QESimulated(red)~vs.~Theoret
ical(blue)6\"-%+AXESLABELSG6$%!GFiw-%%VIEWG6$%(DEFAULTGF]x" 1 2 0 1 0 
2 9 1 4 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 63 "Now let's compare the sim
ulated mean to the theoretical mean.  " }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "theo_mean:=lambda;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*theo_meanG\"\"&" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 30 "sim_mean:=evalf(Mean(sample));" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%)sim_meanG$\"++++e\\!\"*" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 47 "relative_error:=(sim_mean-theo_mean)/theo_me
an;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%/relative_errorG$!+++++%)!#7
" }}}}}{MARK "1" 0 }{VIEWOPTS 1 1 0 1 1 1803 }