# Fisher-Information for Normal Distribution with $N(0,\sigma^2) \,$

$f(\underline{x}; \sigma^2) = \left( \frac{1}{\sqrt{2 \pi \sigma^2}} \right)^2 \exp \left( - \frac{\sum_{i=1}^n x_i^2}{2 \sigma^2} \right) \,$

$\log f(\underline{x}; \sigma^2) = - \frac{n}{2} \log 2 \pi \sigma^2 - \frac{\sum_{i=1}^n x_i^2}{2 \sigma^2} \,$

$\frac{\partial}{\partial \sigma^2} \log f(\underline{x}; \sigma^2) = -\frac{n}{2 \sigma^2} + \frac{\sum_{i=1}^n x_i^2}{2 \sigma^4} \,$