Question: Let S = n i=1 Xi, where Xi is a uniform random variable on the interval (0,1). Find the moment generating function for Z =

Let S =

Σn i=1 Xi, where Xi is a uniform random variable on the interval (0,1). Find the moment generating function for Z = S−????

????

where ???? and ???? are the mean and standard deviation, respectively, of S. Then show that this moment generating function approaches the moment generating function for a standard normal random variable as n → ∞.

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