The Central Limit Theorem
n are i.i.d. (independent and identically distributed) random variables having the same distribution with mean , variance ˙2, and moment generating function M X(t), then if n!1 the limiting distribution of the random variable Z= T n ˙ p n (where T= X 1 +X 2 + +X n) is the standard normal distribution N(0;1). Proof: M Z(t) = M T n ˙ p n (t ...
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