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SOLVED: Let U1, U2, ... be i.i.d. Uni(0, 1) random variables. -log U is distributed as exp(1). (2) Find the limit of the random sequence (U1U2 · · · Un)^2, as n → ∞. (3) Describe what happens to the sequence of random variables e^(Vn) (U1U2 · · · Un)'/√n. (1) Show that Xn converges to 0 as n → ∞.
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