# 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.