Suppose that \(\left\{W_{n}ight\}_{n=1}^{\infty}\) is a sequence of independent random variables such that \(W_{n}\) has a \(\mathrm{N}\left(\theta, \sigma^{2}ight)\) distribution for all \(n \in \mathbb{N}\) where \(\theta eq 0\). Define a sequence of random variables \(\left\{X_{n}ight\}_{n=1}^{\infty}\) where \(X_{n}=\bar{W}_{n}\) for all \(n \in \mathbb{N}\) so that \(\mathrm{N}\left(\theta, n^{-1} \sigma^{2}ight)\) distribution for all \(n \in \mathbb{N}\) and \(X_{n} \xrightarrow{p} \theta\) as \(n ightarrow \infty\). Find the asymptotic distribution of \(n^{1 / 2}\left[\exp \left(-X_{n}^{2}ight)-\exp \left(-\theta^{2}ight)ight]\).