Suppose that $\theta \in \mathbb{R}^{d}$ is the parameter of a non-degenerate exponential family. Derive the asymptotic distribution of the maximum-likelihood estimator $\hat{\theta}_{n}$ of $\theta$ based on a sample of size $n$. [You may assume that the density is infinitely differentiable with respect to the parameter, and that differentiation with respect to the parameter commutes with integration.]

Part II 2004