Let $X_{1}, \cdots, X_{n}$ be a random c.i.i.d sample such as, given $\theta$, $X_{1} \sim \mathcal{N}(0,\theta)$. Construct a confidence interval for $\theta$ using asymptotic results.
This question is asking to use Fisher information to find an approximated confidence interval for $\theta$. I already found that $\hat{\theta}_{\text{MLE}}$ is
$$ \frac{\sum_{i=1}^n X_{i}^2}{n}$$
But, I can't find theta's Fisher information because I don't know the expected value of $\sum_{i=1}^n X_{i}^2$. Could someone help me to fully solve this question?