R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> par2 = '0.5'
> par1 = '500'
> n <- as.numeric(par1)
> p <- as.numeric(par2)
> heads=rbinom(n-1,1,p)
> a=2*(heads)-1
> b=diffinv(a,xi=0)
> c=1:n
> pheads=(diffinv(heads,xi=.5))/c
> postscript(file="/var/www/html/rcomp/tmp/1c6611228167409.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op=par(mfrow=c(2,1))
> plot(c,b,type='n',main='Law of Averages',xlab='Toss Number',ylab='Excess of Heads',lwd=2,cex.lab=1.5,cex.main=2)
> lines(c,b,col='red')
> lines(c,rep(0,n),col='black')
> plot(c,pheads,type='n',xlab='Toss Number',ylab='Proportion of Heads',lwd=2,cex.lab=1.5)
> lines(c,pheads,col='blue')
> lines(c,rep(.5,n),col='black')
> par(op)
> dev.off()
null device 
          1 
> b
  [1]  0  1  0 -1 -2 -1  0 -1  0  1  2  3  4  5  6  7  6  7  8  7  8  9 10  9 10
 [26] 11 12 13 14 13 14 15 16 15 16 17 18 19 20 21 20 19 18 19 18 17 16 17 18 19
 [51] 20 21 20 21 20 19 18 17 18 17 18 19 18 19 18 17 16 17 18 17 18 17 16 15 14
 [76] 15 16 17 18 17 16 17 16 15 16 17 18 17 16 17 16 17 16 17 18 19 20 21 22 23
[101] 24 25 24 23 24 23 22 21 20 21 20 21 22 21 22 21 22 21 22 21 20 21 20 21 20
[126] 21 20 19 20 21 22 21 20 19 18 17 16 17 18 17 16 15 14 15 14 15 14 15 14 15
[151] 14 15 14 15 16 17 18 17 18 17 18 17 16 15 16 17 18 17 18 17 18 19 18 19 18
[176] 17 16 15 14 15 16 15 14 13 12 11 12 13 14 13 12 11 10  9 10 11 10  9  8  7
[201]  8  9 10  9 10  9  8  7  6  7  8  9 10 11 12 13 12 11 12 13 14 15 16 17 16
[226] 17 18 17 18 19 20 19 20 21 20 21 20 21 20 19 18 17 16 17 16 17 16 15 16 17
[251] 16 17 16 17 16 15 14 15 14 13 14 15 14 15 16 15 14 15 16 17 18 17 16 17 18
[276] 19 20 19 18 19 18 19 18 19 20 21 22 23 22 21 20 19 18 19 18 17 16 17 18 17
[301] 16 15 14 13 14 15 14 13 12 11 10 11 10  9 10 11 12 13 12 11 12 13 14 15 16
[326] 15 14 13 14 13 14 15 16 17 18 19 18 17 16 17 18 19 18 19 18 17 16 15 14 15
[351] 14 13 12 11 12 11 10 11 12 11 10 11 10 11 12 13 12 11 10  9  8  7  6  5  4
[376]  5  4  5  6  5  4  3  4  3  4  5  4  3  2  3  2  3  4  5  6  5  4  3  2  1
[401]  2  3  2  1  0  1  0 -1  0  1  0  1  0 -1  0  1  0  1  0 -1  0 -1 -2 -1  0
[426] -1  0 -1  0  1  0  1  2  3  4  3  2  3  2  1  0 -1  0 -1  0 -1 -2 -3 -4 -5
[451] -4 -3 -2 -3 -2 -1  0  1  2  1  2  1  0 -1 -2 -1  0  1  0 -1 -2 -1  0 -1 -2
[476] -3 -2 -1 -2 -1  0  1  0  1  2  1  0 -1  0 -1  0  1  2  1  0 -1 -2 -3 -4 -3
> par1 <- as.numeric(12)
> x <- as.array(b)
> n <- length(x)
> sx <- sort(x)
> 
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Variance Reduction Matrix',6,TRUE)
> a<-table.row.end(a)
> for (bigd in 0:2) {
+ for (smalld in 0:3) {
+ mylabel <- 'V(Y[t],d='
+ mylabel <- paste(mylabel,as.character(smalld),sep='')
+ mylabel <- paste(mylabel,',D=',sep='')
+ mylabel <- paste(mylabel,as.character(bigd),sep='')
+ mylabel <- paste(mylabel,')',sep='')
+ a<-table.row.start(a)
+ a<-table.element(a,mylabel,header=TRUE)
+ myx <- x
+ if (smalld > 0) myx <- diff(x,lag=1,differences=smalld)
+ if (bigd > 0) myx <- diff(myx,lag=par1,differences=bigd)
+ a<-table.element(a,var(myx))
+ a<-table.element(a,'Range',header=TRUE)
+ a<-table.element(a,max(myx)-min(myx))
+ a<-table.element(a,'Trim Var.',header=TRUE)
+ smyx <- sort(myx)
+ sn <- length(smyx)
+ a<-table.element(a,var(smyx[smyx>quantile(smyx,0.05) & smyx<quantile(smyx,0.95)]))
+ a<-table.row.end(a)
+ }
+ }
> a<-table.end(a)
> table.save(a,file="/var/www/html/rcomp/tmp/29if71228167409.tab") 
> 
> system("convert tmp/1c6611228167409.ps tmp/1c6611228167409.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.497   0.256   0.564