Write a program in \(\mathrm{R}\) that simulates 1000 samples of size \(n\) from an EXPONENTIAL(1) distribution. On each sample compute \(n^{1 / 2}\left(\bar{X}_{n}-1ight)\) and \(n^{1 / 2}\left(\bar{X}_{n}^{2}-1ight)\). Make a density histogram of the 1000 values of \(n^{1 / 2}\left(\bar{X}_{n}-1ight)\), and on a separate plot make a histogram with the same scale of the 1000 values of \(n^{1 / 2}\left(\bar{X}_{n}^{2}-1ight)\). Compare the variability of the two histograms with what is predicted by theory, and describe how the transformation changes the variability of the sequences. Repeat the experiment for \(n=5,10,25\), 100 and 500 and describe how both sequences converge to a NORmaL distribution.