{VERSION 5 0 "IBM INTEL NT" "5.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 
2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Text Output" -1 6 
1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 2 1 3 1 }1 1 
0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 
-1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 
0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 
1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "\"t distribution\":
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "f:=(1+x^2/m)^(-(m+1)/2)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG),&\"\"\"F'*&%\"xG\"\"#%\"m
G!\"\"F',&F+#F,F*#F'F*F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 
"plot(subs(m=3,f),x=-4..4);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 
{PLOTDATA 2 "6%-%'CURVESG6$7bo7$$!\"%\"\"!$\"3!ywVAzuI\\#!#>7$$!3ommmm
FiDQ!#<$\"3iyFape#Q*GF-7$$!35LLLo!)*Qn$F1$\"387.Juix1LF-7$$!3nmmmwxE.N
F1$\"3eh*[dhQ$eQF-7$$!3YmmmOk]JLF1$\"3mTp95\">w_%F-7$$!3_LLL[9cgJF1$\"
3[]HK;aMM`F-7$$!3smmmhN2-IF1$\"38G()\\,f0PiF-7$$!3!******\\`oz$GF1$\"3
U_hT?eVltF-7$$!3!omm;)3DoEF1$\"3=rg^8he)y)F-7$$!3?+++:v2*\\#F1$\"3+Rd`
nA\"H0\"!#=7$$!3BLLL8>1DBF1$\"3)em4BR;PF\"Ffn7$$!3kmmmw))yr@F1$\"3M8Q>
jCT6:Ffn7$$!3;+++S(R#**>F1$\"3/T7x68LQ=Ffn7$$!30++++@)f#=F1$\"32\\n$o#
e9VAFfn7$$!3-+++gi,f;F1$\"3F$eN?w2*>FFfn7$$!3qmmm\"G&R2:F1$\"3%pV93N:y
B$Ffn7$$!3XLLLtK5F8F1$\"3'pE;\"=*p,(RFfn7$$!3eLLL$HsV<\"F1$\"3y\"=IBWK
Jp%Ffn7$$!3+-++]&)4n**Ffn$\"3\"zV2\"QA_VcFfn7$$!3cpmmT<z!=*Ffn$\"3-s[
\"pN/W4'Ffn7$$!37PLLL\\[%R)Ffn$\"3Ab0k_WcdlFfn7$$!3qnmmT<yJvFfn$\"3'*)
zPdcJC2(Ffn7$$!3G)*****\\&y!pmFfn$\"3mduhQ:V%e(Ffn7$$!3'))******4\"eZe
Ffn$\"3E9xqsJKe!)Ffn7$$!3Y******\\O3E]Ffn$\"3'=P[*>R,2&)Ffn7$$!3NKLLL3
z6LFfn$\"3y@neoB.2$*Ffn7$$!3/LLLeGmCDFfn$\"3+=m&yUS#)e*Ffn7$$!3sLLL$)[
`P<Ffn$\"39a)=$=%H<!)*Ffn7$$!39nm;aH-88Ffn$\"3i$G)QOz/'))*Ffn7$$!3m0++
]-6&)))F-$\"3!oJ[a*odZ**Ffn7$$!3wsm;/1binF-$\"3%)))3E7:ep**Ffn7$$!3')R
LLe4**RYF-$\"3iQ)o^Uic)**Ffn7$$!3'p++DJJu^#F-$\"37$R%zkjx&***Ffn7$$!3g
Snmmmr[R!#?$\"3uT;s^g*)****Ffn7$$\"3n=L$3Fr)4=F-$\"3q%)ef,m\"y***Ffn7$
$\"3S6LL3Uh9SF-$\"3]@O.,RE*)**Ffn7$$\"38/L$e9d$>iF-$\"3!\\$eJ^GEu**Ffn
7$$\"3'oHLL3+TU)F-$\"3!>hZQ.dG&**Ffn7$$\"3AGL$efeLG\"Ffn$\"3u!G4/-(4\"
*)*Ffn7$$\"3yELL$=2Vs\"Ffn$\"3Oe;$Hc#p/)*Ffn7$$\"3Khmmm7+#\\#Ffn$\"35q
&>(fW])f*Ffn7$$\"3)e*****\\`pfKFfn$\"3=u:W*[evK*Ffn7$$\"3]imm\"*f#))3%
Ffn$\"3yit$H$>8s*)Ffn7$$\"36HLLLm&z\"\\Ffn$\"3SX!e'Qu`j&)Ffn7$$\"3;jmm
;(HXx&Ffn$\"3=2i:HOU*4)Ffn7$$\"3>(******z-6j'Ffn$\"3@rMY*p@ng(Ffn7$$\"
3W%*****\\C4puFfn$\"3p<wslx')4rFfn7$$\"3q\"******4#32$)Ffn$\"3WsORj%\\
&4mFfn7$$\"3q#****\\<!)y6*Ffn$\"3a2QAyF3JhFfn7$$\"3r$*****\\#y'G**Ffn$
\"3]tmb.&*=lcFfn7$$\"3K****\\FJ*G3\"F1$\"3IQu%[\"\\7p^Ffn7$$\"3G******
H%=H<\"F1$\"3g6+X\\cX+ZFfn7$$\"3qKLLo,\"QD\"F1$\"3SM23Y*)[0VFfn7$$\"35
mmm1>qM8F1$\"33b6_mAlORFfn7$$\"3%)*******HSu]\"F1$\"3(=z*fb'[wB$Ffn7$$
\"3'HLL$ep'Rm\"F1$\"3/Xo$H$pT/FFfn7$$\"3')******R>4N=F1$\"3V)eC@A4(>AF
fn7$$\"3#emm;@2h*>F1$\"3\"ePoa[D\\%=Ffn7$$\"3]*****\\c9W;#F1$\"3a%[D6
\"o,C:Ffn7$$\"3Lmmmmd'*GBF1$\"3)y7X.9G#o7Ffn7$$\"3j*****\\iN7]#F1$\"3_
+N'Qke/0\"Ffn7$$\"3aLLLt>:nEF1$\"3+snf8*y()z)F-7$$\"35LLL.a#o$GF1$\"3M
APj#>)3utF-7$$\"3ammm^Q40IF1$\"3%ouO0#yD=iF-7$$\"3y******z]rfJF1$\"3R/
Nr'yT(Q`F-7$$\"3gmmmc%GpL$F1$\"3pN&o&)='[/XF-7$$\"3/LLL8-V&\\$F1$\"3%*
[SksJ?')QF-7$$\"3=+++XhUkOF1$\"3&GhgS&y\"[L$F-7$$\"3=+++:o<EQF1$\"35;w
8Y]V#*GF-7$$\"\"%F*F+-%'COLOURG6&%$RGBG$\"#5!\"\"$F*F*Fial-%+AXESLABEL
SG6$Q\"x6\"Q!F^bl-%%VIEWG6$;F(F`al%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 
1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 32 "c:=int(f,x=-infinity..infinity);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"cG**-%&GAMMAG6#,&%\"mG#\"\"\"\"\"#F+F,!\"\"*&F,F,
F*F.#F.F-%#PiGF+-F'6#,$F*F+F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 7 "f:=f/c:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "var:=simpli
fy(int(x^2*f,x=-infinity..infinity));" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%$varG*&%\"mG\"\"\",&F&F'\"\"#!\"\"F*" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 27 "int(subs(m=3,f),x=-1..1.0);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"+5y(**3'!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 17 "\"F distribution\":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
33 "f:=x^(n/2-1)/(1+n/m*x)^((n+m)/2):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "plot(subs(\{n=3,m=6\},f),x=0..7);" }}{PARA 13 "" 1 "
" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7co7$$\"\"!F)F(7$$
\"39L$eRZF\"oZ!#?$\"3FB%[S_l:$o!#>7$$\"3Emm\"z%\\DO&*F-$\"3+\"QR+'Gce&
*F07$$\"3%**\\(=U#Q/V\"F0$\"3M,8VP9Ee6!#=7$$\"3DLLe*)4D2>F0$\"3VuuZr2H
B8F;7$$\"3))**\\P%[w3'GF0$\"3!QX5YS!p'e\"F;7$$\"3]mm;z>]9QF0$\"3g!RLy#
4*Qz\"F;7$$\"3[L$eRZF\"oZF0$\"3EWcfc.%R'>F;7$$\"3v***\\(oHv@dF0$\"3(>v
?k(R(o5#F;7$$\"3/m;aj%y`n'F0$\"3M:8Z$y7)GAF;7$$\"3+LLLeR+HwF0$\"3&ofo=
H\\QL#F;7$$\"3&pm;z%\\DO&*F0$\"3Mn\\3^U8/DF;7$$\"3&****\\Pf]V9\"F;$\"3
Y6vd&=SNj#F;7$$\"3?L$3Fpv]L\"F;$\"3bf.Awa*=t#F;7$$\"3gmmm\"z+e_\"F;$\"
3=$=h$)Hme!GF;7$$\"3QL3Fp&)pd=F;$\"3-P#y//K+*GF;7$$\"3;+](oM'f*=#F;$\"
3)o)4,W*p=$HF;7$$\"3S$3xcBXbN#F;$\"3E9%***R[nSHF;7$$\"3lm\"zW7%\\@DF;$
\"3/tj^zr!H%HF;7$$\"3!*\\7G8IW(o#F;$\"3_7.b]SZRHF;7$$\"3sLL3->R`GF;$\"
3R*4CQhZ6$HF;7$$\"3=+]7G%**)*f$F;$\"3;*Q\"H=x%*[GF;7$$\"3mmm;apSYVF;$
\"3T]B\"3,#4@FF;7$$\"3Gnmm;G'y4&F;$\"3)o1/@0\"=qDF;7$$\"3Onm;z'=$\\eF;
$\"35#[%Q`/$3T#F;7$$\"3i+]7.I?(f'F;$\"3y)*Gxn/#>D#F;7$$\"3!RL$3Ft3XtF;
$\"31\\#y#=sP(4#F;7$$\"3J++DJ=ZQ!)F;$\"3M$=j$G5Kg>F;7$$\"3tmmTNj&=t)F;
$\"3(e?\"eBRUI=F;7$$\"33+](=`xn,\"!#<$\"3uG=U[***fe\"F;7$$\"3#omT&y/Gl
6Fft$\"3'e>%)R39xO\"F;7$$\"3++]PurI88Fft$\"3)GSICii?=\"F;7$$\"3aLL$e#3
dl9Fft$\"3!zd[IX@,-\"F;7$$\"3ymm\"Ht%o*f\"Fft$\"3]]!3w`TQ)*)F07$$\"3K+
+]F_m]<Fft$\"3J`D<n]w6yF07$$\"32++]icE->Fft$\"3&32A5(358oF07$$\"3;++]s
2O[?Fft$\"3w2oT([P@*fF07$$\"3um;aG\"H5=#Fft$\"3Y7FbE$**zM&F07$$\"3^LL$
ej%yQBFft$\"3)))zg.m\\yo%F07$$\"3mLLLVUUsCFft$\"3PHY*e@u[?%F07$$\"35+]
(o()yyi#Fft$\"3^Q#>r$RA<PF07$$\"3GLLLoD[lFFft$\"3v>F.fSDULF07$$\"3P+](
oibk\"HFft$\"37IU0/t#G)HF07$$\"3a+]i!o<-1$Fft$\"3!4SVb[(z$o#F07$$\"3qL
L3-$=-@$Fft$\"3([%Rr`j=5CF07$$\"3kL$3xplzM$Fft$\"3)f4cE/_')=#F07$$\"3g
mm\"H([a'\\$Fft$\"3)4_e#)o*>x>F07$$\"3wm;ayo(3l$Fft$\"3-EEs:3m$y\"F07$
$\"3?+]7VLA&y$Fft$\"3uVFaA_&Rj\"F07$$\"3'pm;a?@.$RFft$\"3_ewv#)3N*[\"F
07$$\"3)******\\\\@-3%Fft$\"33i$\\qO\\iN\"F07$$\"3Q++v$opoA%Fft$\"3i#z
<B#\\-S7F07$$\"3c+](oMf(oVFft$\"3SoGA/U6R6F07$$\"3#)***\\ii.j_%Fft$\"3
;MY#RPL(Q5F07$$\"3%GLL$oT'ym%Fft$\"31)*>Y`Z`x&*F-7$$\"3'3++DE5!>[Fft$
\"3[B&4S&Qn(z)F-7$$\"3Mm;a)3rf&\\Fft$\"3#H)3*f:2\"e\")F-7$$\"3*4++vW0d
5&Fft$\"3))o[e>CoBvF-7$$\"3;L$3-\"QfY_Fft$\"3I1\"\\&)*)e=)pF-7$$\"3C+]
PWF'QR&Fft$\"3YTQrOoTmkF-7$$\"3[LL$e/Xy`&Fft$\"3Ws%oLg)[2gF-7$$\"3m**
\\(=<\"e)o&Fft$\"3!*H;p,YmpbF-7$$\"3%ymmm(zvLeFft$\"3M6>o3t$\\=&F-7$$
\"3-nm\"zAAA)fFft$\"3vANq\\28D[F-7$$\"3LM$3-7d%HhFft$\"3)fmNAd8&)\\%F-
7$$\"3#4++]p]ZE'Fft$\"3=*R+SsPBA%F-7$$\"3$QL$e*R7)>kFft$\"3evPF.=HJRF-
7$$\"3'pmmmV,&elFft$\"3[+%Q!p%z=p$F-7$$\"3<+](o(GP1nFft$\"3'[4jmr(HcMF
-7$$\"3g+]78Z!z%oFft$\"3w()R-G&=\"[KF-7$$\"\"(F)$\"3Dnd\"pAM:/$F--%'CO
LOURG6&%$RGBG$\"#5!\"\"F(F(-%+AXESLABELSG6$Q\"x6\"Q!Fabl-%%VIEWG6$;F(F
bal%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 
0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "c:=int(f,x=0
..infinity);" }}{PARA 6 "" 1 "" {TEXT -1 68 "Definite integration: Can
't determine if the integral is convergent." }}{PARA 6 "" 1 "" {TEXT 
-1 34 "Need to know the sign of --> 1/2*n" }}{PARA 6 "" 1 "" {TEXT -1 
57 "Will now try indefinite integration and then take limits." }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG**)*&%\"nG\"\"\"%\"mG!\"\",$F(#F
+\"\"#F)-%&GAMMAG6#,$F*#F)F.F)-F06#,$F(F3F)-F06#,&F(F3*&F3F)F*F)F)F+" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f:=f/c:" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 37 "mu:=simplify(int(x*f,x=0..infinity));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG*&%\"mG\"\"\",&F&F'\"\"#!\"\"F*
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "v:=simplify(int(x^2*f,x
=0..infinity)-mu^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG,$*,%\"m
G\"\"#,(F'\"\"\"F(!\"\"%\"nGF*F*F,F+,&F'F*\"\"%F+F+,&F'F*F(F+!\"#F(" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "int(subs(\{n=3,m=6\},f),x=
2.3..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"++#z?x\"!#5" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "\"chi-square distribution\":
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "f:=x^(m/2-1)*exp(-x/2):
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "plot(subs(m=4,f),x=0..1
4);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVES
G6$7`o7$$\"\"!F)F(7$$\"3+LLLeR+Hw!#>$\"3fwCC5eZVtF-7$$\"3gmmm\"z+e_\"!
#=$\"3N)*\\\\0os89F37$$\"3!*****\\(=,()G#F3$\"33Xi^'fB7/#F37$$\"3?LLL$
e,;0$F3$\"3v)3$z#))p(>EF37$$\"3wm;aQrR:PF3$\"3I%*f;lh]&3$F37$$\"3I++v$
p#>zVF3$\"3ru?*GgU!=NF37$$\"3JL$e*[#))H/&F3$\"3i'ft>[]!>RF37$$\"3Unm;/
Qy1dF3$\"3Is[/^t7!H%F37$$\"3!RL3-L\"H`kF3$\"3k%Q#e5;etYF37$$\"3Q++Dc))
z*>(F3$\"3x'H&GL(zJ-&F37$$\"3'om\"H#Q1j%zF3$\"3UZ;O4y)3M&F37$$\"3KLLL3
R\"Gp)F3$\"3rRgD4LdGcF37$$\"3YLLLjDd>5!#<$\"3*e0+Mz'zBhF37$$\"3YLL$etj
)p6Feo$\"3BQ\"4`]By^'F37$$\"38+]i+1W>8Feo$\"3F_r\"R/a9#oF37$$\"3ymmTlu
,p9Feo$\"3G=\"GiG![ZqF37$$\"31++DmVp2;Feo$\"3;1'Q7T)4'>(F37$$\"3MLL3n7
PY<Feo$\"3o&3Cu.zJH(F37$$\"3+++D;s;==Feo$\"3\"pwh[At_K(F37$$\"3'om;a;j
**)=Feo$\"3Y\"p%Q9g.YtF37$$\"3_LLe9\"f<'>Feo$\"3uolp?mActF37$$\"3<++vj
]bL?Feo$\"3mFnr0[cctF37$$\"3VLL3Pl!y5#Feo$\"3Si#[jJwsM(F37$$\"39nmT5!e
?=#Feo$\"3SWa;#e$*)GtF37$$\"3S++v$[4jD#Feo$\"3MBn\\?=4-tF37$$\"3mLL3d4
cIBFeo$\"3M]IQ6\"4vE(F37$$\"3imm\"Hl(eyCFeo$\"3#G&f#QT3x<(F37$$\"3+++v
[VhEEFeo$\"37NM8\\EtjqF37$$\"32nmm^;9JHFeo$\"3u;\"3&G!e$pnF37$$\"3eLL$
eYp$*>$Feo$\"3GKrW6BXhkF37$$\"3i+++b/L,NFeo$\"3EP(R1%QN!3'F37$$\"38+++
D8`/QFeo$\"3uI.&G22vn&F37$$\"3I+++X:s'4%Feo$\"33n+%*fFc#G&F37$$\"3]LL3
d#e?O%Feo$\"3V^Q4ja'e#\\F37$$\"3-nmmr#pvn%Feo$\"3l;AE8:F6XF37$$\"3Knmm
'[[[%\\Feo$\"31`<LxdYsTF37$$\"3?++v`xvb_Feo$\"3'Re2<G8jz$F37$$\"3cmmmO
^'4`&Feo$\"3!H)RcHc]\"[$F37$$\"3u++v`7\"H$eFeo$\"3'Q&=\"y:uq:$F37$$\"3
5,+Dh`V?hFeo$\"3#=b]9Y1\"pGF37$$\"3Rnm;/mV?kFeo$\"3#*RuI'>00f#F37$$\"3
EnmT&RJfp'Feo$\"3G'\\_x<3SN#F37$$\"3?LL$eu*3$*pFeo$\"3s9M!*Q!R!>@F37$$
\"3_LL3dPv,tFeo$\"3g\"G>U![9'*=F37$$\"3Q++D'oY/d(Feo$\"3r[\"\\$H%y(=<F
37$$\"3#RLL3TU1'yFeo$\"3AI\"eg&HiV:F37$$\"3'********)HWg\")Feo$\"3!)Qk
\\F&=%z8F37$$\"3w++]n$RPX)Feo$\"3+G\"3P=ySB\"F37$$\"37,+v$p=vt)Feo$\"3
z)QiUywn5\"F37$$\"3k****\\_sg_!*Feo$\"3c#[J#)\\jaz*F-7$$\"3olmmO$GdL*F
eo$\"35XExpSSo()F-7$$\"3t,++D0-Q'*Feo$\"3)o]v#3[[#y(F-7$$\"3qKL3x@%>\"
**Feo$\"3?FY]rcBzpF-7$$\"3?++]*3T6-\"!#;$\"3_NHc8&>->'F-7$$\"3km;/i(=$
\\5Fc\\l$\"3$zgQ&eq5DbF-7$$\"31+]()[Dxy5Fc\\l$\"3KaB=D%eB!\\F-7$$\"3qm
m;4!pv5\"Fc\\l$\"3gnKwB7GeVF-7$$\"3%***\\PMirP6Fc\\l$\"3'f#))>yqZ]QF-7
$$\"3eLLL&f^n;\"Fc\\l$\"3%y\\NG\"y9:MF-7$$\"3SLLeXWW'>\"Fc\\l$\"3iZH9j
S))=IF-7$$\"3(omTSU\"*eA\"Fc\\l$\"3+B&*ym3qpEF-7$$\"3?+++R,&HD\"Fc\\l$
\"3CnT0)>YLQ#F-7$$\"3ymm\"*zC'RG\"Fc\\l$\"3k\\fYKe_\"4#F-7$$\"3RLLL(G+
<J\"Fc\\l$\"3!GaTy$H+g=F-7$$\"3/+]PvXFT8Fc\\l$\"3'o7TMt-0k\"F-7$$\"37+
]iU4ep8Fc\\l$\"3aNF\"oz`SX\"F-7$$\"#9F)$\"3sAjx^Zjw7F--%'COLOURG6&%$RG
BG$\"#5!\"\"F(F(-%+AXESLABELSG6$Q\"x6\"Q!Fbal-%%VIEWG6$;F(Fc`l%(DEFAUL
TG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" 
}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "c:=int(f,x=0..infinity);
" }}{PARA 6 "" 1 "" {TEXT -1 68 "Definite integration: Can't determine
 if the integral is convergent." }}{PARA 6 "" 1 "" {TEXT -1 34 "Need t
o know the sign of --> 1/2*m" }}{PARA 6 "" 1 "" {TEXT -1 57 "Will now \+
try indefinite integration and then take limits." }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"cG*&)\"\"#,$%\"mG#\"\"\"F'F+-%&GAMMAG6#F(F+" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f:=f/c:" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 27 "mu:=int(x*f,x=0..infinity);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%#muG%\"mG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 45 "var:=simplify(int(x^2*f,x=0..infinity)-mu^2);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%$varG,$%\"mG\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "int(subs(m=4,f),x=2.0..4.0);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"+E.`(H$!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 14 "\"convolution\":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "
\"two standardized normal RVs\":" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "f:=x->exp(-x^2/2)/sqrt(2*Pi): " }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 39 "int(f(x)*f(y-x),x=-infinity..infinity);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&-%$expG6#,$*$)%\"yG\"\"#\"\"\"#!\"
\"\"\"%F-%#PiG#F/F,#F-F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 
"\"two exponential RVs\":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
27 "f:=x->exp(-x/beta)/beta:   " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 45 "L:=0:  H:=infinity:  max(L,y-H);  min(H,y-L);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#-%$maxG6$\"\"!,&%\"yG\"\"\"%)infinityG!\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"yG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "int(f(x)*f(y-x),x=0..y);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*(%\"yG\"\"\"%%betaG!\"#-%$expG6#,$*&F&!\"\"F$F%F-F%" }
}}}{MARK "31" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 
33 1 1 }