Under the regularity conditions for asymptotic normality with $\Theta \subseteq \mathbb{R}$, \begin{align*} \sqrt{n}(\hat{\theta}_n - \theta_0) \xrightarrow{d} \mathcal{N}(0,\, I(\theta_0)^{-1}), \end{align*} where $I(\theta_0) = \mathbb{E}_{\theta_0}\!\left[\left(\frac{d}{d\theta}\log f(X, \theta_0)\right)^{\!2}\right] = -\mathbb{E}_{\theta_0}\!\left[\frac{d^2}{d\theta^2}\log f(X, \theta_0)\right]$.