{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 "" {TEXT -1 8 "binomial" }{MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "f:=binomial(n,i)*p^i*(1-p)^(n-i):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "simplify(sum(f,i=0..n),sy mbolic);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "simplify(sum(i*f,i=0..n),symbolic); # mean, computed directly through the usual sum" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"nG\"\"\"%\"pGF%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "simplify(sum((i-n*p)^2*f,i=0..n),symbolic); # variance(Maple has d ifficulty fully simplifying)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*,)! \"\"%\"nG\"\"\"%\"pGF(F'F(),&F(F&F)F(,&F'F&F(F(F(),&F(F(F)F&F'F(F&" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "n:=18: p:=1/6: with(plots) :" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has b een redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "pointplo t([seq([i,f],i=0..9)]);" }}{PARA 13 "" 1 "" {GLPLOT2D 494 494 494 {PLOTDATA 2 "6#-%'POINTSG6,7$$\"\"!F($\"+wO5cP!#67$$\"\"\"F($\"+Bt>_8! #57$$\"\"#F($\"+]at)H#F17$$\"\"$F($\"+![%)>X#F17$$\"\"%F($\"+g$))*Q=F1 7$$\"\"&F($\"+\"[L)H5F17$$\"\"'F($\"+` " 0 " " {MPLTEXT 1 0 39 "evalf(add(f,i=7..18)); # Pr(7<=X<=18)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+NO*Q1#!#6" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "geometric" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f:=p*(1-p)^(i-1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "sum(f ,i=1..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "MGF:=sum(exp(i*t)*f,i=1..infinity); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$MGFG*(-%$expG6#%\"tG\"\"\"%\"pG F*,(F*F*F&!\"\"*&F&F*F+F*F*F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "simplify(series(MGF,t,3)); # expanding moment generating functi on" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#++%\"tG\"\"\"\"\"!*&F%F%%\"pG!\" \"F%,$*(\"\"#F),&F(F%F,F)F%F(!\"#F)F,-%\"OG6#F%\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "negative binomial" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 37 "f:=binomial(i-1,k-1)*p^k*(1-p)^(i-k):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "sum(f,i=k..infinity);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "sum(i*f,i=k..infinity); # mean, the old-fashioned wa y" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"kG\"\"\"%\"pG!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "sum((i-k/p)^2*f,i=k..infinit y); # variance" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(%\"kG\"\"\",&F &!\"\"%\"pGF&F&F)!\"#F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " k:=3: p:=1/6.: with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning , the name changecoords has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "pointplot([seq([i,f],i=k..50)]);" }}{PARA 13 "" 1 "" {GLPLOT2D 494 494 494 {PLOTDATA 2 "6#-%'POINTSG6R7$$\"\"$\"\"!$\" +K'H'HY!#77$$\"\"%F)$\"+3uSd6!#67$$\"\"&F)$\"+YB,H>F27$$\"\"'F)$\"+9Q= zEF27$$\"\"(F)$\"+o(z*[LF27$$\"\")F)$\"+iI92RF27$$\"\"*F)$\"+p+FTVF27$ $\"#5F)$\"+!zg8l%F27$$\"#6F)$\"+([n^%[F27$$\"#7F)$\"+7G*[$\\F27$$\"#8F )$\"+5G*[$\\F27$$\"#9F)$\"+3<7g[F27$$\"#:F)$\"+D$=^s%F27$$\"#;F)$\"+2I QVXF27$$\"#F)$\"+\\dAJQF27$$ \"#?F)$\"+#\\)HoNF27$$\"#@F)$\"+%3!)RI$F27$$\"#AF)$\"+^&RJ/$F27$$\"#BF )$\"+)eW&*y#F27$$\"#CF)$\"+>H,YDF27$$\"#DF)$\"+(>dXJ#F27$$\"#EF)$\"+-# >l4#F27$$\"#FF)$\"+X4p#*=F27$$\"#GF)$\"+^=U.rG:F27$$ \"#IF)$\"+J:Ho8F27$$\"#JF)$\"+n))o@7F27$$\"#KF)$\"+ggG)3\"F27$$\"#LF)$ \"+gQlt'*F,7$$\"#MF)$\"+PrY\"e)F,7$$\"#NF)$\"+FS<)f(F,7$$\"#OF)$\"+]yb :nF,7$$\"#PF)$\"+@A\\DfF,7$$\"#QF)$\"+zk2?_F,7$$\"#RF)$\"+RRt\"f%F,7$$ \"#SF)$\"+6)zK.%F,7$$\"#TF)$\"+[Z'z`$F,7$$\"#UF)$\"+J!*\\*4$F,7$$\"#VF )$\"+_;17FF,7$$\"#WF)$\"+&y(HqBF,7$$\"#XF)$\"+!f2$p?F,7$$\"#YF)$\"+7(G Y!=F,7$$\"#ZF)$\"+3W@s:F,7$$\"#[F)$\"+P)3%o8F,7$$\"#\\F)$\"+G2#**=\"F, 7$$\"#]F)$\"+xjzL5F," 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 " sum(f,i=40..infinity); # Pr(X>=40)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #$\"+#)oWQJ!#6" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "hypergeometric " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "resta rt:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "f:=binomial(K,i)*bin omial(N-K,n-i)/binomial(N,n):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "N:=52: K:=13: n:=5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "add(f,i=0..5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "add(i*f,i=0..5); # mean (ol d-fashioned way)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"&\"\"%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "add((i-5/4)^2*f,i=0..5); # \+ variance " }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"$N#\"$s#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "n*K/N*(N-K)/N*(N-n)/(N-1); # agre es with our formula" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"$N#\"$s#" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "with(plots): pointplot([ seq([i,f],i=0..5)]);" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}{PARA 13 "" 1 "" {GLPLOT2D 494 494 494 {PLOTDATA 2 "6#-%'POINTSG6(7$$\"\"!F($\"+MhL:A!#57$$\"\"\"F($ \"+yc>9TF+7$$\"\"#F($\"+>rzUFF+7$$\"\"$F($\"+0&\\!#8" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "evalf(add(f,i=2..4)); # Pr(2<=X<=4)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+1i^lO!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "poisson" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "f:=lambda^ i/i!*exp(-lambda):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "sum(f ,i=0..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "sum(i*f,i=0..infinity); # mean, t he old way" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%'lambdaG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "sum((i-lambda)^2*f,i=0..infinity); \+ # variance" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%'lambdaG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "sum(exp(i*t)*f,i=0..infinity); # \+ MGF" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$expG6#,&%'lambdaG!\"\"*&-F$6 #%\"tG\"\"\"F'F-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "serie s(%,t,3); # first two simple moments (agrees with 'old way')" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#++%\"tG\"\"\"\"\"!%'lambdaGF%,&*&#F%\" \"#F%F'F%F%*&F*F%*$)F'F+F%F%F%F+-%\"OG6#F%\"\"$" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 25 "lambda:=3.8: with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "pointplot([seq([i,f],i=0..11 )]);" }}{PARA 13 "" 1 "" {GLPLOT2D 494 494 494 {PLOTDATA 2 "6#-%'POINT SG6.7$$\"\"!F($\"+'=xqB#!#67$$\"\"\"F($\"+2L*3])F+7$$\"\"#F($\"+G(p^h \"!#57$$\"\"$F($\"+c;)e/#F67$$\"\"%F($\"+tveV>F67$$\"\"&F($\"+cl7x9F67 $$\"\"'F($\"+_[8b$*F+7$$\"\"(F($\"+w<]y]F+7$$\"\")F($\"+W$)G7CF+7$$\" \"*F($\"+X<_=5F+7$$\"#5F($\"+LEQqQ!#77$$\"#6F($\"+t7/P8Fin" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "sum(f,i=9..infinity); # Pr(X>=9) " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*T\\%)f\"!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "multinomial" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "restart: with(combinat):" }}{PARA 7 "" 1 "" {TEXT -1 67 "Warning, the protected name Chi has been redefi ned and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "f: =multinomial(n,i,j,n-i-j)*pW^i*pL^j*(1-pW-pL)^(n-i-j):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "pW:=0.40: pL:=0.55: n:=10:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "add(add(f,j=0..n-i),i=0..n); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+++++5!\"*" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 68 "add(add(f,j=0..min(i-1,n-i)),i=0..n); # pro b. of winning the series" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+I7N%R# !#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "add(add((i-n*pW)*(j- n*pL)*f,j=0..n-i),i=0..n); # Cov. between # wins & losses (old way)" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+++++A!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "-n*pW*pL; # agrees with our formula" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!&+?#!\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "multivariate hypergeometric" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 71 "f:=binomial(K1,i)*binomial(K2,j)*binomial(N-K1-K2,n -i-j)/binomial(N,n):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "K1: =13: K2:=13: N:=52: n:=5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "add(add(f,j=0..5-i),i=0..5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# \"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "evalf(add(add(f,j =0..min(i-1,5-i)),i=0..5)); # prob. more spades than diamonds" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+;&*yBP!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "add(add((i-5/4)*(j-5/4)*f,j=0..5-i),i=0..5); # C ov between # spades & diamonds (old way)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##!$N#\"$;)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "-n*K1/N *K2/N*(N-n)/(N-1); # agrees with our formula" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##!$N#\"$;)" }}}}{MARK "59 0 0" 88 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }