[See] Let (X_i) be r.v.'s with E X_i=0 and E X_i X_j ≤q r(j-i), 1 ≤q i ≤q
Question: Let \(\left(X_{i}\right)\) be r.v.'s with \(E X_{i}=0\) and \(E X_{i} X_{j} \leq r(j-i), 1 \leq\) \(i \leq j<\infty\), where \(r(n)\) is a deterministic sequence with \(r(n) \rightarrow 0\) as \(n \rightarrow \infty\) Prove that \(n^{-1} \sum_{i=1}^{n} X_{i} \rightarrow 0\) in probability.
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![[Solution Library] Suppose events A_n satisfy P(A_n)](/images/solutions/MC-solution-library-69380.jpg "[Solution Library] Suppose events A_n satisfy P(A_n) \rightarrow")
[Solution Library] Suppose events A_n satisfy P(A_n) \rightarrow
![[See Solution] (a) Let Z have standard](/images/solutions/MC-solution-library-69381.jpg "[See Solution] (a) Let Z have standard Normal distribution. Show")
[See Solution] (a) Let Z have standard Normal distribution. Show
[See] Let (X_n) be i.i.d. with
(See Steps) Let 0 ≤q X_1 ≤q X_2 ≤q ... be r.v.'s such
(Solved) Prove that the following are equivalent. X_n \rightarrow
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