##### R-code for Example 7.1. It writes the related data to 
##### the file "example71.dat." It also makes "fig73.ps".

#### Generate 30 random vectors from N_3(mu,Sigma)

library(MASS)   ### R package for generating multivariate normal random vectors.

set.seed(100)

mu1 = c(0,0,0)
mu2 = c(1,1,1)

Sigma = matrix(c(1,0.8,0.5,0.8,1,0.8,0.5,0.8,1),3,3)

x1 = mvrnorm(20,mu1,Sigma)
x2 = mvrnorm(10,mu2,Sigma)

x = rbind(x1,x2)
n = length(x[,1])

xbar = colMeans(x)
S2 = cov(x)

T12 = rep(0,n)

for(i in 1:n){
   T12[i] = t(x[i,]-xbar) %*% solve(S2) %*% (x[i,]-xbar)
}

write.table(round(cbind(x,xbar,T12),digits=3), 
            file="example71.dat",col.names=T, row.names=F)


postscript("fig73.ps",width=4.5,height=4.5,horizontal=F)

ii = seq(1,n)

plot(ii,T12,type="o",lty=1,pch=16,xlab="i",
     ylab=expression(T[list(1,i)]^{2}),mgp=c(2,1,0),xlim=c(0,31), 
     ylim=c(0,15),cex=0.8)
lines(ii,rep(10.77279,n),lty=2,cex=0.8)

graphics.off()