Let \(\left\{X_{n}ight\}_{n=1}^{\infty}\) be a sequence of independent random variables where \(X_{n}\) has a \(\operatorname{GEOmetric}\left(\theta_{n}ight)\) distribution where \(\left\{\theta_{n}ight\}_{n=1}^{\infty}\) is described below. For each sequence determine whether \(X_{n}=O_{p}(1)\) as \(n ightarrow \infty\).

a. \(\theta_{n}=n(n+10)^{-1}\) for all \(n \in \mathbb{N}\).

b. \(\theta_{n}=n^{-1}\) for all \(n \in \mathbb{N}\).

c. \(\theta_{n}=n^{-2}\) for all \(n \in \mathbb{N}\).

d. \(\theta_{n}=\frac{1}{2}\) for all \(n \in \mathbb{N}\).