source('https://myweb.uiowa.edu/pbreheny/7110/f20/notes/fun.R')

# Convergence of x^2
n <- 100
N <- 1000
col <- alphaCol('gray40', 0.2)
ylim <- c(-1.5, 1.5)
at <- seq(4, 10, 2)
lab <- 2^at

x <- rasym(n, N, 100, mean=TRUE)
matplot(log2(as.numeric(rownames(x))), sqrt(1)*x^2, type='l', col=col, lty=1, xaxt='n', bty='n', las=1, xlab='n', ylab=expression(bar(X)^2 - mu^2), ylim=ylim)
axis(1, at=at, label=lab)
mtext(expression(mu==0))

x <- rasym(n, N, 100, mu=1, mean=TRUE)
nn <- as.numeric(rownames(x))
matplot(log2(nn), sqrt(1)*(x^2-1), type='l', col=col, lty=1, xaxt='n', bty='n', las=1, xlab='n', ylab=expression(bar(X)^2 - mu^2), ylim=ylim)
axis(1, at=at, label=lab)
mtext(expression(mu==1))