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Let X be a Bernoulli(1/3) random variable, that is, P(X = 0) = WIN and P(X = 1) = For every n 2 1, we define Xn = 1+- ) X. n Then the sequence (Xn)n21 converges in probability to the r.v. X.Let (Xn) n> 1 be a sequence of independent random variables, each uniformly distributed on (- 1, !), or Xn ~ U Find the limit in probability, if it exists, of the sequence Xn