NSamp = seq(10,100,10) ## The sample sizes to consider
nrep = 1000            ## The number of data sets to generate

## A place to store the results.
V = NULL

## Vary the sample size over 10, 20, ..., 100.
for (k in 1:length(NSamp)) {

    ## The sample size to use in this iteration.
    nsamp = NSamp[k]

    ## Generate a 1000xnsamp array of standard normal draws.
    D = rnorm(nrep*nsamp)
    X = array(D, c(nrep,nsamp))

    ## Get the mean of each row of X.
    Y = apply(X, 1, mean)

    ## Calculate the sample variance of Y.
    V[k] = var(Y)
}


## Plot the simulation results.
plot(NSamp, V, t='b', xlab='Sample size', ylab='Variance of Xbar')

## Overplot the exact results.
lines(NSamp, 1/NSamp, t='b', col='red')

## Add a legend.
legend(x='topright', legend=c('Simulation', 'Theory'), 
       col=c('black', 'red'), lty=c(1,1))