Mathematische Statistik - Übung 6.2

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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} \,