Let (left{X_{n}ight}_{n=1}^{infty}) and (left{Y_{n}ight}_{n=1}^{infty}) be sequences of independent random variables, where (X_{n}) has a (operatorname{Uniform}(0, n)) distribution

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Let \(\left\{X_{n}ight\}_{n=1}^{\infty}\) and \(\left\{Y_{n}ight\}_{n=1}^{\infty}\) be sequences of independent random variables, where \(X_{n}\) has a \(\operatorname{Uniform}(0, n)\) distribution and \(Y_{n}\) has a \(\operatorname{Uniform}\left(0, n^{2}ight)\) distribution for all \(n \in \mathbb{N}\). Prove that \(X_{n}=o_{p}\left(Y_{n}ight)\) as \(n ightarrow \infty\).

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