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b) Assume now that (Xn, n 1) is a sequence of bounded, uncorrelated and identically distributed random variables such that E(X1) = 0 and

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b) Assume now that (Xn, n 1) is a sequence of bounded, uncorrelated and identically distributed random variables such that E(X1) = 0 and Var(X1) = 1. That said, under this more general assumption, Kolmogorov's 0-1 law may not necessarily hold. Prove it by exhibiting a sequence of random variables (Xn, n 1) satisfying these assumptions and an event B = T such that 0 < P(B) < 1.

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