##### R-code for making Figure 5.2. It reads data
##### from "example51.dat".

x <- scan("example51.dat")

mu0=10
sigma=2
lambda=0.1
rho=2.703

En=rep(0,length(x))
U=rep(0,length(x))
L=rep(0,length(x))

En[1] = lambda*x[1]+(1-lambda)*mu0
for(i in 2:length(x)){
   En[i] = lambda*x[i]+(1-lambda)*En[i-1]
}

for(i in 1:length(x)){
   U[i] = mu0+rho*sqrt(lambda/(2-lambda)*(1-(1-lambda)^(2*i)))*sigma
   L[i] = mu0-rho*sqrt(lambda/(2-lambda)*(1-(1-lambda)^(2*i)))*sigma
}

ii <- seq(1,length(x))

postscript("fig52.ps",width=4.5,height=4.5,horizontal=F)

plot(ii,En,type="o",lty=1,pch=16,xlab="n",ylab=expression(E[n]),
     mgp=c(2,1,0),xlim=c(0,31),ylim=c(7.5,12.5),cex=0.8)
lines(ii,U,lty=2,cex=0.8)
lines(ii,rep(mu0,length(ii)),lty=3,cex=0.8)
lines(ii,L,lty=2,cex=0.8)

graphics.off()