EXERCISE 9- Find a sequence of random variables which converge in L1 b.docx
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A sequence of random variables that converges in L1 but not almost surely is a sequence of Bernoulli random variables where the probability of success goes to 0 at a slow enough rate. Specifically, let Xn be a Bernoulli random variable with P(Xn = 1) = 1/n, then Xn converges to 0 in L1 but with positive probability Xn does not converge to 0.
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