Suppose that n = 16 and that Xi takes the value 0 with probability 0.5 and the value 1 with probability 0.5. Compare with the results in Exercise 1.
The Central Limit Theorem does not work if random variables are not independent. The simplest case to compute is where they are perfectly correlated with each other. In particular, suppose the random variables X1, X2 ... Xn are all equal, and consider the sum

Find the mean and variance of Sn, and sketch its probability distribution.

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S, =EX1.