problem-6.2
problem-6.2
A few simulations using steps of size 50 produce an answer.
> data(lawsuits)
> res = c()
> n = 5
> for(i in 1:300) res[i] = mean(sample(lawsuits,n,replace=TRUE))
> plot(density(scale(res)), xlim=c(-4,4)) # xlim= sets plot window
> n = 50
> for(i in 1:300) res[i] = mean(sample(lawsuits,n,replace=TRUE))
> lines(density(scale(res)), lty=2)
> n = 150
> for(i in 1:300) res[i] = mean(sample(lawsuits,n,replace=TRUE))
> lines(density(scale(res)), lty=3)
> n = 350
> for(i in 1:300) res[i] = mean(sample(lawsuits,n,replace=TRUE))
> lines(density(scale(res)), lty=5)
> n = 500
> for(i in 1:300) res[i] = mean(sample(lawsuits,n,replace=TRUE))
> lines(density(scale(res)), lty=10)
> qqnorm(res)
The use of xlim=c(-4,4) with plot() gives a
symmetric plot window for the subsequent density estimates. We see
by n=350 that the shape of the density becomes roughly
symmetric. A q-q plot shows the approximate normality of the
sample.