Statistics Graduate Level Quiz
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CONVERGENCE & LIMIT THEOREMS
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For n≥3, let Xn have probability 1/2−1/n at 0, probability 2/n at 1, and probability 1/2−1/n at 2. Let qn=inf{x:Fn(x)≥1/2} be its lower median. If X assigns probability 1/2 to each of 0 and 2 and has lower median q, which statement is correct?
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