Let \(\left\{X_{n}ight\}_{n=1}^{\infty}\) be a sequence of independent random variables where \(X_{n}\) has a \(\operatorname{GAmma}\left(\alpha_{n}, \beta_{n}ight)\) distribution for all \(n \in \mathbb{N}\) and \(\left\{\alpha_{n}ight\}_{n=1}^{\infty}\) and \(\left\{\beta_{n}ight\}_{n=1}^{\infty}\) are bounded sequences of positive real numbers. That is, there exist real numbers \(\alpha\) and \(\beta\) such that \(0<\alpha_{n} \leq \alpha\) and \(0<\beta_{n} \leq \beta\) for all \(n \in \mathbb{N}\). Prove that \(X_{n}=O_{p}(1)\) as \(n ightarrow \infty\).