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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 815 "restart:\nwith(Stat
istics):\npoisson_:=RandomVariable(Poisson(lambda)):\npdf:=subs(u=n,Pr
obabilityFunction(poisson_,u));\ncdf:=simplify(subs(u=n,CDF(poisson_,u
)));\nmu_:=Mean(poisson_);\nvar_:=Variance(poisson_);\nskew_:=simplify
(convert(Skewness(poisson_),GAMMA),symbolic);\nkurt_:=simplify(convert
(Kurtosis(poisson_),GAMMA),symbolic);\nqdf:=simplify(Quantile(poisson_
,q));\nqdf2:=solve(cdf=q,K);\npdfgr:=[factor(diff(pdf, lambda))];\ncdf
gr:=[diff(cdf, lambda)];\nvalnum:=lambda=10:\nevalf(subs(valnum,n=12,p
df));\nevalf(subs(valnum,n=12,cdf));\nevalf(subs(valnum,n=12,pdfgr));
\nevalf(subs(valnum,n=12,cdfgr));\nq:=evalf(Quantile(Poisson(subs(valn
um,lambda)),0.95));\nevalf(subs(valnum,n=q,cdf));\nevalf(subs(valnum,m
u_));\nevalf(subs(valnum,sqrt(var_)));\nevalf(subs(valnum,skew_));\nev
alf(subs(valnum,kurt_));\nevalf(subs(valnum,var_));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%$pdfG-%*PIECEWISEG6$7$\"\"!2%\"nGF)7$*()%'lambdaGF+
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"" 1 "" {XPPMATH 20 "6#>%$cdfG*&-%&GAMMAG6$,&-%&floorG6#%\"nG\"\"\"F.F
.%'lambdaGF.-F'6#F)!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$mu_G%'l
ambdaG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%var_G%'lambdaG" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%&skew_G*&\"\"\"F&*$%'lambdaG#F&\"\"#!\"\"
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&kurt_G*&%'lambdaG!\"\",&*&\"\"$
\"\"\"F&F+F+F+F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$qdfG-%'RootOf
G6#,&-%&floorG6#%#_ZG\"\"\"-F&6#,(*&-%&GAMMAG6$,&F,F-F-F-%'lambdaGF-F,
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{XPPMATH 20 "6#>%%qdf2G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&pdfgr
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1 "" {XPPMATH 20 "6#>%&cdfgrG7#,$*()%'lambdaG-%&floorG6#%\"nG\"\"\"-%$
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{XPPMATH 20 "6#$\"+4I.y%*!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+kZ
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"" 1 "" {XPPMATH 20 "6#7#$!+4I.y%*!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 
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{XPPMATH 20 "6#$\"+gwFiJ!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+gw
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" 1 "" {XPPMATH 20 "6#$\"#5\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 61 "fsolve(subs(lambda=0.2,GAMMA(n+1,lambda)/GAMMA(n+1))=
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5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "plot(map(_x->subs(lam
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bda),n)]),n=0..100);" }}{PARA 13 "" 1 "" {GLPLOT2D 446 446 446 
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F(-%+AXESLABELSG6$Q\"n6\"Q!Fhgl-%%VIEWG6$;F(Fj\\l%(DEFAULTG" 1 2 0 1 
10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 161 "cdf:=convert(CDF(Gamma(1,
lambda),n),GAMMA);\ncdf2:=1-GAMMA(lambda,n)/GAMMA(lambda);\ncdf3:=GAMM
A(n,lambda)/GAMMA(n);\nevalf(subs(lambda=100,n=100,[cdf,cdf2,cdf3]));
" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$cdfG-%*PIECEWISEG6$7$\"\"!2%\"n
GF)7$*,-%$expG6#,$*&\"\"#!\"\"F+\"\"\"F4F5,(*&-F/6#,$*&F3F4F+F5F5F5,(-
%&GAMMAG6#,&F3F5%'lambdaGF5F4-F>6$,&F5F5FAF5F+F5*&FBF5FAF5F5F5F4*&)F+,
&*&F3F4FAF5F5F5F4F5-%+WhittakerMG6%,&*&F3F4FAF5F5F5F5,&*&F3F4FAF5F5#F5
F3F5F+F5F5*(FGF5FJF5FAF5F5F5-F>6#FAF4FAF4FDF41F)F+" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%%cdf2G,&\"\"\"F&*&-%&GAMMAG6$%'lambdaG%\"nGF&-F)6#F
+!\"\"F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%cdf3G*&-%&GAMMAG6$%\"nG
%'lambdaG\"\"\"-F'6#F)!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%$\"+&
)z)H8&!#5$\"+#)z)H8&F&$\"+=?,n[F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 51 "with(plots):\nseries(diff(GAMMA(n,x)/GAMMA(n),x),n);
" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#+/%\"nG,$*&%\"xG!\"\"-%$expG6#,$F'
F(\"\"\"F(F-,&*(F'F(-%#lnG6#F'F-F)F-F(*(F'F(F)F-%&gammaGF-F(\"\"#,(*&#
F-F5F-*(F'F(F0F5F)F-F-F(*(F'F(F)F-,&*&\"#7F(%#PiGF5F-*&F5F(F4F5F-F-F-*
*F)F-,&F0F-F4F-F-F'F(F4F-F(\"\"$,***F)F-FAF-F'F(F;F-F-*(F'F(F)F-,(*&#F
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AMMA(n+1,x)-x*GAMMA(n,x)))/x^(1/4),x=1..10);" }}{PARA 13 "" 1 "" 
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" {MPLTEXT 1 0 126 "for i from 0 to 99 do\n  level:=(0.5+i)/100.0;\n  \+
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q]);\nod:\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+++++]!#7$\"\"$\"
\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+++++:!#6$\"\"%\"\"!" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+++++D!#6$\"\"%\"\"!" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#7$$\"+++++N!#6$\"\"&\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7$$\"+++++X!#6$\"\"&\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#7$$\"+++++b!#6$\"\"&\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$
\"+++++l!#6$\"\"&\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+++++v!
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\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+++++&*!#6$\"\"'\"\"!" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"++++]5!#5$\"\"'\"\"!" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#7$$\"++++]6!#5$\"\"'\"\"!" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#7$$\"++++]7!#5$\"\"'\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7$$\"++++]8!#5$\"\"(\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#7$$\"++++]9!#5$\"\"(\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$
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{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"++++]>!#5$\"\"(\"\"!" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#7$$\"++++]?!#5$\"\"(\"\"!" }}{PARA 11 "" 1 "" 
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{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"++++]F!#5$\"\")\"\"!" }}{PARA 11 
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{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"++++]N!#5$\"\"*\"\"!" }}{PARA 11 
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\"++++]R!#5$\"\"*\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"++++]S!
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\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"++++]U!#5$\"\"*\"\"!" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"++++]V!#5$\"\"*\"\"!" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#7$$\"++++]W!#5$\"\"*\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7$$\"++++]X!#5$\"\"*\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#7$$\"++++]Y!#5$\"#5\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$
\"++++]Z!#5$\"#5\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"++++][!#
5$\"#5\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"++++]\\!#5$\"#5\"
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