nreps<-10
N<-1000000
plot(c(10000:N),c(10000:N)*0,ylim=range(-20,20),type="n",ylab=expression(hat(I)))

for(irep in 1:nreps){

	X<-runif(N)
	Ival<-sin(2*pi/X)/X
	Ihat<-cumsum(Ival)/c(1:N)
	lines(Ihat)

}
abline(h=0.1526,col="red") #truth
title('Ten Realizations')
plot(Ihat,type="l",ylim=range(-5,5),ylab=expression(hat(I)),xlab="N")
abline(h=0.1526,col="red")
dev.off()

set.seed(263411)
X<-runif(N)
Ival<-sin(2*pi/X)/X
Ihat2<-cumsum(Ival)/c(1:N)
plot(Ihat2,type="l",ylim=range(-5,5),ylab=expression(hat(I)),xlab="N")
abline(h=0.1526,col="red")

set.seed(2011)
X<-runif(N)
Ival<-sin(2*pi/X)/X
Ihat3<-cumsum(Ival)/c(1:N)
plot(Ihat3,type="l",ylim=range(-5,5),ylab=expression(hat(I)),xlab="N")
abline(h=0.1526,col="red")