3.
Central Limit Theorem Let $X_1, X_2,...$ be a sequence of iid random variable
with finite mean $\mu$ and finite variance $\sigma^2$, and let $S_n$ be the sum of the first $n$ random
variables in the sequence:
$S_n = X_1 + X_2 + ... + X_n$.
(a) Let $X_i$ be a uniform continuous random variable taking values in the interval
$(0, 3)$. Write a MATLAB program to plot the pdf and cdf of $S_n$. Consider
$n = 1, 2, 3, 4, 5, 10, 20, 40$ and compare your results.
b Write a MATLAB program to generate a Gaussian random variable with the same
mean and variance as $S_n$. Superimpose this plot with the plots from part (a).
