{VERSION 3 0 "IBM INTEL LINUX" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {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 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 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 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 102 "This worksheet is for che cking whether the nth and n+1th entries are really independently distr ibuted." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 64 "N:=10000: Digits:=30: A:=[seq(evalf(frac(i^2*sqrt (2))),i=1..N)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "B:=sort( A):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "C:=[seq([N*(B[i+1]-B [i]),N*(B[i+2]-B[i+1])],i=1..N-2)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "C[15];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"9+!454' *f:Bh$QU!#C$\"9+g5PXpf)Gzf!GF&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 167 "f:=proc(xpos,ypos,steps) j:=0:for i from 1 to N-2 do if (C[i] [1]<(xpos+steps) and C[i][2]<(ypos+steps) and C[i][1]>=xpos and C[i][2 ]>=ypos) then j:=j+1 fi; od; j; end:" }}{PARA 7 "" 1 "" {TEXT -1 41 "W arning, `j` is implicitly declared local" }}{PARA 7 "" 1 "" {TEXT -1 41 "Warning, `i` is implicitly declared local" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "f(1 ,1,1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#G" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 101 "M:=matrix(3,3,[f(0,0,1),f(0,1,1),f(0,2,1),f(1 ,0,1), f(1,1,1), f(1,2,1), f(2,0,1),f(2,1,1),f(2,2,1)]);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"MG-%'matrixG6#7%7%\"%2S\"%%[\"\"$5&7%\"%m9\" $t&\"$#>7%\"$6&\"$'>\"#a" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "F(x,y):=exp(-x)*exp(-y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"FG6$ %\"xG%\"yG*&-%$expG6#,$F'!\"\"\"\"\"-F+6#,$F(F.F/" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 38 "evalf(int(int(F(x,y),x=1..2),y=0..1));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"?ne>noy!)33mI%f*p9!#I" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "evalf(M[2,1]/N);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$ \"?+++++++++++++m9!#I" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "ev alf(int(int(F(x,y),x=0..1),y=0..1000));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"?R)HiZ/%ywbG)e07K'!#I" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "evalf((474+103+54)/1000);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$ \"?+++++++++++++5j!#I" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "ev alf(int(int(F(x,y),x=0..1000),y=0..1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"?y'fC&*3oN:rl<6Ck#!#I" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "T stands for \"Test function\" in the following" }{TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "T:=proc(x,y) if (abs(x-y)<2) then j:=1 else j:=0 fi; j; end:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 7 "" 1 "" {TEXT -1 41 "Warning, `j` is implicitly declare d local" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "tanswer:=0: for \+ k from 1 to N-2 do tanswer:=tanswer+sum('T(N*B[k],N*B[l])','l'=k+1..N- 2) od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "tanswer/(N-2);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6##\"%K6\"$*\\" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "2241/998;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"% TA\"$)**" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 11 " " 1 "" {TEXT -1 0 "" }}}{MARK "0 0 0" 102 }{VIEWOPTS 1 1 0 1 1 1803 }