Question: Given a sample (x_{1}, ldots, x_{n}) from a (mathrm{N}left(mu, sigma^{2} ight)) distribution, determine the method of moments estimate and the MLE of (sigma^{2}).

Given a sample $x_{1}, \ldots, x_{n}$ from a $\mathrm{N}\left(\mu, \sigma^{2}\right)$ distribution, determine the method of moments estimate and the MLE of $\sigma^{2}$.

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