{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 "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 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 15 "with(combinat):" }} {PARA 7 "" 1 "" {TEXT -1 67 "Warning, the protected name Chi has been \+ redefined and unprotected\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "6 \+ to the power of 10:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "6^10;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\")whYg" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "factorial:" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "5!;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$?\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "number o f combinations (say 20 'choose' 5):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "binomial(20,5);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#\"&/b\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 62 "numbe r of permutations (20 P 5) can be indirectly computed by:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "binomial(20,5)*5 !;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"(![g=" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 60 "the multinomial coefficient (say 20 'choose' 5,4,4,3 ,2,2):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "multinomial(20,5,4,4,3,2, 2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\".+!GJfm9" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 22 "DISCRETE DISTRIBUTIONS" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "values:=[-4,0,5,20]: pr:=[0. 43,0.31,0.23,0.03]:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "Mean, vari ance and standard deviation:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 83 "m:=add(values[i]*pr[i],i=1..4); add(values[i]^ 2*pr[i],i=1..4)-m^2; sigma:=sqrt(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG$\"\"$!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"'\"HY#!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&sigmaG$\"+.9xi\\!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "skewness and kurtosis" }{MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "add((values[i]-m)^3*pr[ i],i=1..4)/sigma^3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+v=Yb>!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "add((values[i]-m)^4*pr[i] ,i=1..4)/sigma^4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+YU+%G)!\"*" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "PGF:" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "PGF:=add(z^values[i]*pr[i],i =1..4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$PGFG,*$\"#J!\"#\"\"\"*&$ \"#VF(F)%\"zG!\"%F)*&$\"#BF(F))F-\"\"&F)F)*&$\"\"$F(F))F-\"#?F)F)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "m:=subs(z=1,diff(PGF,z)); \+ # getting mean and variance based on PGF\nsubs(z=1,diff(PGF,z,z))+m-m^ 2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG$\"\"$!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"'\"HY#!\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 80 "Probability that independent sum of 100 of these will have a value less than 50:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "aux:=expand(PGF^100): \nadd(coeff(aux,z,i),i=-400.. 49);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+hLYo#)!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "plotting the corresponding distribution: " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "with (plots): pointplot([seq([i,coeff(aux,z,i)],i=-140..150)]);" }} {PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been r edefined\n" }}{PARA 13 "" 1 "" {GLPLOT2D 495 224 224 {PLOTDATA 2 "6#-% 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\"F)$\"+pr!**G*FK7$$\"$4\"F)$\"+x\\\\^*)FK7$$\"$5\"F)$\"+iPRB')FK7$$\" $6\"F)$\"+13!\\I)FK7$$\"$7\"F)$\"+y+c&*zFK7$$\"$8\"F)$\"+o8a&p(FK7$$\" $9\"F)$\"+D/30uFK7$$\"$:\"F)$\"+fk'Q7(FK7$$\"$;\"F)$\"+()zE^oFK7$$\"$< \"F)$\"+iE+(e'FK7$$\"$=\"F)$\"+coCJjFK7$$\"$>\"F)$\"+&)G2%3'FK7$$\"$? \"F)$\"+eE3XeFK7$$\"$@\"F)$\"+[5v8cFK7$$\"$A\"F)$\"+qX#**Q&FK7$$\"$B\" F)$\"+xIut^FK7$$\"$C\"F)$\"+ng9l\\FK7$$\"$D\"F)$\"+\"*3rjZFK7$$\"$E\"F )$\"+U#G!pXFK7$$\"$F\"F)$\"+J&G5Q%FK7$$\"$G\"F)$\"+YLz*>%FK7$$\"$H\"F) $\"+^y;DSFK7$$\"$I\"F)$\"+D%\\n&QFK7$$\"$J\"F)$\"+4mB%p$FK7$$\"$K\"F)$ \"+>`gPNFK7$$\"$L\"F)$\"+BT(oQ$FK7$$\"$M\"F)$\"+4@$=C$FK7$$\"$N\"F)$\" +QQ7-JFK7$$\"$O\"F)$\"+nz`nHFK7$$\"$P\"F)$\"+$>n!QGFK7$$\"$Q\"F)$\"+() Qn8FFK7$$\"$R\"F)$\"+'4CTf#FK7$$\"$S\"F)$\"+$*>7zCFK7$$\"$T\"F)$\"+V]_ oBFK7$$\"$U\"F)$\"+zTKiAFK7$$\"$V\"F)$\"+!zQ/;#FK7$$\"$W\"F)$\"+rqji?F K7$$\"$X\"F)$\"+EWoo>FK7$$\"$Y\"F)$\"+Tl[y=FK7$$\"$Z\"F)$\"+5H-#z\"FK7 $$\"$[\"F)$\"+0`=4 " 0 "" {MPLTEXT 1 0 50 "add(bin omial(20,i)*(1/6.)^i*(5/6)^(20-i),i=4..20);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+FOaMV!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "NE GATIVE BINOMIAL (need more than 30 rolls to get the fourth six):" }} {PARA 0 "" 0 "" {TEXT -1 16 "Either directly:" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "1-add(binomial(i-1,4-1)*(1/6 .)^4*(5/6)^(i-4),i=4..30);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+h_>' R#!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 73 "Or through the binomial \+ formula (getting fewer than 4 sixes in 30 rolls):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "add(binomial(30,i)*(1/6.) ^i*(5/6)^(30-i),i=0..3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+q_>'R# !#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "Or by expanding the corres ponding PGF:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 182 "PGF:=(z/6./(1-5/6*z))^4: # use at least one decimal point !!!\naux:=series(PGF,z,75): # when expanding non-polynomial PDF, we have to use 'series'\n1-add(coeff(aux,z,i),i=4..30);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+h_>'R#!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "and plotting the distribution" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "with(plots): pointplot([seq([i,coeff(aux, z,i)],i=4..74)]);" }}{PARA 13 "" 1 "" {GLPLOT2D 495 223 223 {PLOTDATA 2 "6#-%'POINTSG6co7$$\"\"%\"\"!$\"+*Q\\gr(!#87$$\"\"&F)$\"+jk,sD!#77$$ \"\"'F)$\"+JwOe`F27$$\"\"(F)$\"+>FhI*)F27$$\"\")F)$\"+A5Q-8!#67$$\"\"* F)$\"+H!3lt\"FB7$$\"#5F)$\"+O]jq@FB7$$\"#6F)$\"+G$*3%e#FB7$$\"#7F)$\"+ *oN4'HFB7$$\"#8F)$\"+V&G**G$FB7$$\"#9F)$\"+b#*3kNFB7$$\"#:F)$\"+kY4!y$ FB7$$\"#;F)$\"+4')fPRFB7$$\"#F)F]p7$$\"#?F)$\"+G;2WSFB7$$\"#@F)$\"+1hxkRFB7$$\"#AF)$\"+OMkaQFB7$$ \"#BF)$\"+*y#R>PFB7$$\"#CF)$\"+*3=Wc$FB7$$\"#DF)$\"+&*Qo%R$FB7$$\"#EF) $\"+zFm9KFB7$$\"#FF)$\"+S5#FB7$$ \"#LF)$\"+v2tM>FB7$$\"#MF)$\"+6K]tW;KsF27$$\"#WF)$\"+fR\")ykF27$$\"#XF)$\"+k71%z&F27$$\"#YF)$ \"+')*oK<&F27$$\"#ZF)$\"+T*G=h%F27$$\"#[F)$\"+>lA0TF27$$\"#\\F)$\"+R-4 \\OF27$$\"#]F)$\"+a'G#RKF27$$\"#^F)$\"+4mlrGF27$$\"#_F)$\"+AEhUDF27$$ \"#`F)$\"+')*o&[AF27$$\"#aF)$\"+PfB')>F27$$\"#bF)$\"+@6c_\"F27$$\"#fF)$\"+ZaR^5 F27$$\"#gF)$\"+$p,5B*F,7$$\"#hF)$\"+1*pt4)F,7$$\"#iF)$\"+@G$o4(F,7$$\" #jF)$\"+11u9iF,7$$\"#kF)$\"+I!)*yV&F,7$$\"#lF)$\"+ljWaZF,7$$\"#mF)$\"+ %=]P:%F,7$$\"#nF)$\"+V)*GEOF,7$$\"#oF)$\"+],cjJF,7$$\"#pF)$\"+:b(zv#F, 7$$\"#qF)$\"+*p\"y-CF,7$$\"#rF)$\"+;T(>4#F,7$$\"#sF)$\"+wDA?=F,7$$\"#t F)$\"+SA!Ge\"F,7$$\"#uF)$\"+=0`v8F," 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "HYPERGEOMETRIC (getting at least 4 spades when dealt 10 cards):" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "add(bin omial(13,i)*binomial(39,10-i)/binomial(52,10.),i=4..10);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"+ygrU?!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 103 "POISSON (getting at least 8 arrivals during the next 15 minute s, when the arrival rate is 27 per hour):" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "L:=27*15/60.: 1-add(L^i/i! *exp(-L),i=0..7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+l$=4k$!#5" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 62 "MULTINOMIAL (getting exactly 3 si xes and 2 fives in 20 rolls):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "multinomial(20,3,2,15)*(1/6.)^3*(1/6)^2*(4/6) ^15;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+n)>Kb%!#6" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 77 "PGF of W=2X-3Y+4, where X is the number \+ of sixes and Y is the number of ones" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "P:=add(add(multinomial(20,i,j,20-i -j)*(1/6.)^i*(1/6)^j*(4/6)^(20-i-j)*z^(2*i-3*j+4),j=0..20-i),i=0..20): " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Probability that W>5:" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "add(coe ff(P,z,i),i=6..20);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+GTHXB!#5" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 90 "MULTIVARIATE HYPERGEOMETRIC (get ting exactly 4 spades and 3 diamonds when dealt 10 cards):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "binomial(13,4)*b inomial(13,3)*binomial(26,3)/binomial(52,10.);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+IgwgL!#6" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 79 "PG F of W=2X-3Y+4, where X is the number of spades and Y the number of di amonds:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "P:=add(add(bino mial(13,i)*binomial(13,j)*binomial(26,10-i-j)/binomial(52,10.)*z^(2*i- 3*j+4),j=0..10-i),i=0..10):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Pr obability of W>5:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "add(coeff(P,z,i),i=6..24);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+\\\"feD#!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "UNIVARIATE CONTINUOUS DISTRIBUTIONS" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "Given f(x)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "f:=piecewise(x<-1,0, x<1,c*(x+1), \+ x<3,c*(3-x), 0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG-%*PIECEWI SEG6&7$\"\"!2%\"xG!\"\"7$*&%\"cG\"\"\",&F+F0F0F0F02F+F07$*&F/F0,&\"\"$ F0F+F,F02F+F67$F)%*otherwiseG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "f ind c:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "int(f,x=-1..3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"%\"\"\" %\"cGF&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "c:=1/4:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "plot(f,x=-2..4);" }}{PARA 13 "" 1 "" {GLPLOT2D 495 163 163 {PLOTDATA 2 "6%-%'CURVESG6$7Y7$$!\"# \"\"!$F*F*7$$!3!******\\2<#p=!#7$$!3M++]i83V()FK$\"3:***\\Pf'HUJFN7$ $!3B******\\V'zV(FK$\"3%>++]7*30kFN7$$!3%)*****\\d;%)G'FK$\"3S++]i&e*y #*FN7$$!3#*)*****\\!)H%*\\FK$\"3E++]([D9D\"FK7$$!3Q+++]d'[p$FK$\"3!*** **\\iNGw:FK7$$!3/******\\>iUCFK$\"3C++]7XM*)=FK7$$!3B++]7YY08FK$\"3%** *\\(o%Qjt@FK7$$\"3%z-+++XDn%!#?$\"32++]i8o6DFK7$$\"3C++++y?#>\"FK$\"31 +++]>0)z#FK7$$\"3h****\\(3wY_#FK$\"3!***\\(=-p68$FK7$$\"3F)******HOTq$ 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0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "find F (y):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 " F:=int(f,x=-infinity..y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG-%* PIECEWISEG6&7$\"\"!1%\"yG!\"\"7$,(*&#\"\"\"\"\")F1*$)F+\"\"#F1F1F1*&#F 1\"\"%F1F+F1F1F0F11F+F17$,(*&#\"\"$F8F1F+F1F1*&#F1F2F1F3F1F,#F1F2F,1F+ F>7$F12F>F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "plot(F,y=-2. .4);" }}{PARA 13 "" 1 "" {GLPLOT2D 495 170 170 {PLOTDATA 2 "6%-%'CURVE SG6$7S7$$!\"#\"\"!$F*F*7$$!3!******\\2<#p=!#!#?7$$!3B******\\V'zV(FH$\"3od'Q)RL.0#)FK7$$!3%)***** \\d;%)G'FH$\"3'4%=4S9)>s\"!#>7$$!3#*)*****\\!)H%*\\FH$\"3)pAH:]J@8$FV7 $$!3Q+++]d'[p$FH$\"3]\"Q:)Q(R$p\\FV7$$!3/******\\>iUCFH$\"3tEx#QPX#RrF V7$$!3B++]7YY08FH$\"3Y@7c+#o$\\%*FV7$$\"3%z-+++XDn%FK$\"3[rfM`'3\"FH$\"3gg(zH%*=ec\"FH7$$\"3h****\\(3wY_#FH$\"3))G*4()) Q%3'>FH7$$\"3F)******HOTq$FH$\"3_?Ah'*=aZBFH7$$\"3I,+](3\">)*\\FH$\"37 cXr)p@=\"GFH7$$\"3_,+]isVIiFH$\"3%oN\\;nQGH$FH7$$\"3&=++](o:;vFH$\"3pA ,(e*o>NQFH7$$\"3#>++v$)[op)FH$\"3skSlb>lpVFH7$$\"3W*****\\i%Qq**FH$\"3 Ka/)eF._)\\FH7$$\"3&****\\(QIKH6F/$\"3r#e5Lj4di&FH7$$\"3#****\\7:xWC\" F/$\"3ubeR4WnZhFH7$$\"37++]Zn%)o8F/$\"3ESLdLQB,.)FH7$$\"3!*****\\A))oz=F/$\"3#Hqg>eG6V)FH7$$\"3e* *****Hk-,?F/$\"3M<=0eZc_()FH7$$\"36+++D-eI@F/$\"3K(o[&ol8b!*FH7$$\"3u* **\\(=_(zC#F/$\"3-iB[5M2$H*FH7$$\"3M+++b*=jP#F/$\"3lOYjUux8&*FH7$$\"3g ***\\(3/3(\\#F/$\"3#e;@f&)RQo*FH7$$\"33++vB4JBEF/$\"3i.Czu;jA)*FH7$$\" 3u*****\\KCnu#F/$\"3z>mc!H9)>**FH7$$\"3s***\\(=n#f(GF/$\"35B)*4wsv!)** FH7$$\"3P+++!)RO+IF/$\"\"\"F*7$$\"30++]_!>w7$F/F`w7$$\"3O++v)Q?QD$F/F` w7$$\"3G+++5jypLF/F`w7$$\"3<++]Ujp-NF/F`w7$$\"3++++gEd@OF/F`w7$$\"39++ v3'>$[PF/F`w7$$\"37++D6EjpQF/F`w7$$\"\"%F*F`w-%'COLOURG6&%$RGBG$\"#5! \"\"F+F+-%+AXESLABELSG6$Q\"y6\"Q!Fey-%%VIEWG6$;F(Fhx%(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 "" {TEXT -1 5 "mean:" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "m:=int(x*f,x=-1..3);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG\"\"\"" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 9 "variance:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 23 "int(x^2*f,x=-1..3)-m^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "MGF: " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "M:=s implify(int(f*exp(x*t),x=-1..3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %\"MG,$*&#\"\"\"\"\"%F(*(,(-%$expG6#,$*&F)F(%\"tGF(F(F(*&\"\"#F(-F-6#, $*&F3F(F1F(F(F(!\"\"F(F(F(-F-6#,$F1F8F(F1!\"#F(F(" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 7 "median:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "fsolve(F=1/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#$\"+++++5!\"*" }}}}{MARK "48 0 0" 77 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }