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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> par20 = ''
> par19 = ''
> par18 = ''
> par17 = ''
> par16 = ''
> par15 = ''
> par14 = ''
> par13 = ''
> par12 = ''
> par11 = ''
> par10 = ''
> par9 = ''
> par8 = ''
> par7 = ''
> par6 = ''
> par5 = ''
> par4 = ''
> par3 = ''
> par2 = '0.5'
> par1 = '500'
> ylab = ''
> xlab = ''
> main = ''
> 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/freestat/rcomp/tmp/1jkgj1228761978.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   0   1   2   3   4   5   6   5   6   5   6   5   4   3
 [19]   2   1   2   3   4   5   4   3   4   5   6   5   6   7   6   5   4   5
 [37]   6   7   6   5   6   7   6   5   4   3   4   5   4   5   4   5   6   5
 [55]   4   5   6   7   8   7   8   9   8   9  10   9  10   9   8   9   8   9
 [73]  10   9  10  11  10  11  10   9   8   9   8   7   6   7   6   5   4   3
 [91]   2   1   0  -1  -2  -1  -2  -3  -4  -5  -6  -7  -8  -9  -8  -9 -10 -11
[109] -12 -11 -10  -9  -8  -9  -8  -9 -10  -9  -8  -9  -8  -9  -8  -7  -8  -7
[127]  -6  -7  -6  -5  -6  -5  -4  -5  -6  -5  -4  -3  -4  -5  -4  -3  -4  -5
[145]  -4  -3  -2  -1  -2  -3  -4  -5  -4  -5  -6  -7  -6  -5  -6  -7  -6  -5
[163]  -4  -5  -4  -5  -4  -5  -4  -5  -6  -5  -6  -5  -4  -3  -2  -3  -4  -5
[181]  -4  -5  -6  -7  -8  -7  -8  -7  -6  -5  -6  -7  -8  -9  -8  -9  -8  -9
[199]  -8  -7  -6  -5  -6  -7  -8  -7  -8  -7  -6  -7  -6  -5  -6  -5  -4  -5
[217]  -6  -7  -8  -7  -8  -7  -6  -5  -6  -7  -6  -5  -6  -5  -6  -5  -4  -3
[235]  -2  -3  -4  -3  -2  -3  -2  -1  -2  -3  -4  -3  -2  -3  -4  -3  -2  -1
[253]  -2  -1   0   1   2   3   2   3   2   3   2   1   2   1   0   1   2   3
[271]   2   1   2   1   2   3   4   5   6   7   6   7   8   7   6   5   4   3
[289]   4   5   4   5   4   3   4   5   4   3   2   3   2   1   2   3   4   3
[307]   2   3   4   3   2   3   4   3   2   3   4   3   2   1   0  -1   0  -1
[325]  -2  -1   0   1   0  -1  -2  -1  -2  -3  -2  -1   0   1   0   1   2   3
[343]   2   1   0   1   0   1   0  -1   0   1   2   3   4   3   4   5   6   5
[361]   4   5   4   3   2   3   4   5   6   5   6   5   4   3   2   1   0  -1
[379]  -2  -3  -4  -3  -4  -5  -6  -5  -4  -3  -4  -5  -6  -7  -8  -9  -8  -7
[397]  -6  -5  -4  -3  -2  -3  -2  -1  -2  -1   0   1   2   3   2   1   2   3
[415]   2   3   2   1   0   1   0  -1  -2  -1   0   1   2   3   4   3   4   3
[433]   2   3   4   3   4   5   4   5   4   3   2   1   2   1   2   1   2   3
[451]   2   1   2   1   0  -1  -2  -1  -2  -1   0  -1  -2  -3  -2  -1   0  -1
[469]  -2  -3  -2  -3  -2  -1   0  -1   0   1   2   1   0  -1   0  -1   0  -1
[487]  -2  -3  -2  -1   0  -1   0  -1   0  -1  -2  -3  -2  -3
> par1 <- as.numeric(12)
> x <- as.array(b)
> n <- length(x)
> sx <- sort(x)
> 
> #Note: the /var/www/html/freestat/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/freestat/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/freestat/rcomp/tmp/2mja51228761978.tab") 
> 
> system("convert tmp/1jkgj1228761978.ps tmp/1jkgj1228761978.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.648   0.296   0.746