##### R-code for making Figure 7.2

x = seq(-3,3,0.1)+3
y = seq(-3,3,0.1)+3

n = length(x)

z1=matrix(0,n,n)
z2=matrix(0,n,n)

sigma11=1
sigma22=0.5
rho1=0
rho2=0.8


for(i in 1:n){
   for(j in 1:n){

      z1[i,j] =(1/(2*pi*sqrt(sigma11*sigma22*(1-rho1^2))))*
               exp(-(1/(2*(1-rho1^2)))*(((x[i]-3)/sqrt(sigma11))^2+
               ((y[j]-3)/sqrt(sigma22))^2-
               2*rho1*((x[i]-3)/sqrt(sigma11))*((y[j]-3)/sqrt(sigma22))))

      z2[i,j] =(1/(2*pi*sqrt(sigma11*sigma22*(1-rho2^2))))*
               exp(-(1/(2*(1-rho2^2)))*(((x[i]-3)/sqrt(sigma11))^2+
               ((y[j]-3)/sqrt(sigma22))^2-
               2*rho2*((x[i]-3)/sqrt(sigma11))*((y[j]-3)/sqrt(sigma22))))

}}

postscript("fig72.ps",width=4.5,height=5.0,horizontal=F)

con = (1/(2*pi*sqrt(sigma11*sigma22*(1-rho2^2))))*exp(-0.5*5.991465)

contour(x,y,z2,xlab=expression(x[1]),ylab=expression(x[2]),mgp=c(2,1,0),
        nlevels=1,drawlabels=F,levels=c(con), cex=0.6)
lines(rep(0.763523,2),c(1.881762,4.118239), lty=3, cex=0.6)
lines(rep(5.236477,2),c(1.881762,4.118239), lty=3, cex=0.6)
lines(c(0.763523,5.236477),rep(1.881762,2), lty=2, cex=0.6)
lines(c(0.763523,5.236477),rep(4.118239,2), lty=2, cex=0.6)

graphics.off()