Extreme value investigation. This (dicult!) question aims to teach the essence of an extreme value distribution! An interesting extreme valuedistributionisgivenbyPevsner(2003, p.103). Takethemaximum of a sample (with size 1000) from the standard normal distribution and repeat this 1000 times. So that you sampled 1000 maxima. Next, subtract from these maxima an and divide by bn, where

an <- sqrt(2*log(n)) - 0.5*(log(log(n))+log(4*pi))*(2*log(n))^(-1/2) bn <- (2*log(n))^(-1/2)

Now plot the density from the normalized maxima and add the extreme value function f(x) from Pevsner his book, and add the density (dnorm) from the normal distribution. What do you observe?