Let S_n = X₁ +...+X_n, where X’s are independent and uniform on [0,1]. Consider S^∗_n = (S_n − n/2)/√n/12. Explain why it makes sense to consider this r.v. Using software, for n = 5, 10, 20, simulate a number of values (say, 1000) of S^∗_n, and make histograms (see Section 7.5). Compare these histograms and provide recommendations regarding the application of the CLT in this case. (Advice: If we use Excel, then, say for n = 5, we should arrange 5 consecutive columns with 1000 generated (from [0,1]) numbers in each. For each row (of five numbers), we compute the value of S^∗_n; the results may be placed into a separate column.)