Let (left{X_{n}ight}_{n=1}^{infty}) and (left{Y_{n}ight}_{n=1}^{infty}) be sequences of random variables. Suppose that (X_{n}=o_{p}left(Y_{n}ight)) as (n ightarrow infty). Prove
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Let \(\left\{X_{n}ight\}_{n=1}^{\infty}\) and \(\left\{Y_{n}ight\}_{n=1}^{\infty}\) be sequences of random variables. Suppose that \(X_{n}=o_{p}\left(Y_{n}ight)\) as \(n ightarrow \infty\). Prove that \(X_{n}=O_{p}\left(Y_{n}ight)\) as \(n ightarrow \infty\).
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