Solution
= Solution
Since $\rho=\sigma^2$ and the reparametrization is one-to-one, invariance of the <maximum-likelihood estimator> gives
$$
\boxed{\widehat\rho_{\rm MLE}=\widehat\sigma_{\rm MLE}^{,2}
=\frac1n\sum_{i=1}^nX_i^2}.
$$
= Solution
Since $\rho=\sigma^2$ and the reparametrization is one-to-one, invariance of the <maximum-likelihood estimator> gives
$$
\boxed{\widehat\rho_{\rm MLE}=\widehat\sigma_{\rm MLE}^{,2}
=\frac1n\sum_{i=1}^nX_i^2}.
$$