problem-6.7
problem-6.7
The central limit theorem says that the sampling distribution of
the sample average of a large number of independent, identically
distributed random numbers is approximately normal. This indicates
that the chi-squared distribution should become bell-shaped for
large values of n. The following simulation shows that this
happens by n=100 or so.
> res = c()
> n = 4; for(i in 1:500) res[i] = sum(rnorm(n)^2); qqnorm(res)
> n = 10; for(i in 1:500) res[i] = sum(rnorm(n)^2); qqnorm(res)
> n = 25; for(i in 1:500) res[i] = sum(rnorm(n)^2); qqnorm(res)
> n = 50; for(i in 1:500) res[i] = sum(rnorm(n)^2); qqnorm(res)
> n = 100; for(i in 1:500) res[i] = sum(rnorm(n)^2); qqnorm(res)