Let \(X_{1}, \ldots, X_{n}\) be a set of independent and identically distributed random variables from a shifted exponential density of the form

\[f(x)= \begin{cases}\exp [-(x-\theta)] & \text { for } x \geq \theta \\ 0 & \text { for } x<\theta\end{cases}\]

Let \(X_{(1)}=\min \left\{X_{1}, \ldots, X_{n}ight\}\). Prove that \(X_{(1)} \xrightarrow{p} \theta\) as \(n ightarrow \infty\).