Let \(\left\{X_{n}ight\}_{n=1}^{\infty}\) be a sequence of independent random variables where \(X_{n}\) has an \(\operatorname{ExpONEntial}\left(\theta_{n}ight)\) distribution for all \(n \in \mathbb{N}\), and \(\left\{\theta_{n}ight\}_{n=1}^{\infty}\) is a sequence of real numbers such that \(\theta_{n}>0\) for all \(n \in \mathbb{N}\). Find the necessary properties for the sequence \(\left\{\theta_{n}ight\}_{n=1}^{\infty}\) that will ensure that \(\left\{X_{n}ight\}_{n=1}^{\infty}\) is uniformly integrable.