Statistics Graduate Level Quiz
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CONVERGENCE & LIMIT THEOREMS
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For random variables XnX_n and XX on a common probability space, suppose that for every ε>0\varepsilon>0 and every positive integer nn, P(∣Xn−X∣>ε)≤1/(n2ε2)P(|X_n-X|>\varepsilon)\leq 1/(n^2\varepsilon^2).
Which convergence conclusion follows from this bound without any independence assumption?
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