{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 "" 0 1 0 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 "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "L:=(2*pi*sigma^2)^( -(n+m)/2)*exp(-(sum((x[i]-theta)^2,i=1..n)+sum((y[j]-theta)^2,j=1..m)) /(2*sigma^2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG*&),$*&%#piG\" \"\")%&sigmaG\"\"#F*F-,&%\"nG#!\"\"F-*&#F*F-F*%\"mGF*F1F*-%$expG6#,$*& ,**&F/F*)%&thetaGF-F*F*-%$sumG6$,&*$)&%\"xG6#%\"iGF-F*F**(F-F*FDF*F=F* F1/FG;F*F/F**&F4F*F " 0 "" {MPLTEXT 1 0 39 "th etahat:=solve(diff(L,theta)=0,theta);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)thetahatG,$*&,&-%$sumG6$,$&%\"xG6#%\"iG!\"#/F/;\"\"\"%\"nGF3-F)6 $,$&%\"yG6#%\"jGF0/F;;F3%\"mGF3F3,&F4F3F>F3!\"\"#F@\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&-%$sumG6$&%\"xG6#%\"iG/F+;\"\"\"%\"nGF.-F&6$&%\"yG6 #%\"jG/F5;F.%\"mGF.F.,&F/F.F8F.!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "3 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }