Let X1, X2, ..., Xn be independent and identically distributed random variables such that P(X1 = 1) = P(X1 =-1) = }. Derive the moment generating function of the random variable Yn = E;=1ª;Xj, where a1, a2, . , an are constants. In the special case a¡ = 2-) for j > 1, show that Yn converges in distribution as n → ∞ to the uniform distribution on the interval (–1, 1).

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