Suppose $X_1,...,X_n$ are random samples from $N(\mu, \sigma^2)$, where both $\mu$ and $\sigma \gt 0$ are unknown, and let $\theta = \sigma^p$ for some $p \gt 0$. I want to find the Fisher Information of $\theta$, and the Cramér-Rao lower bound for the variance of any unbiased estimator for $\theta$.
I am kind of confused of this assumption $\theta = \sigma^p$, and I don't quite know how to deal with it. Any help is welcome