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[PS] Layout fixes, new remarks
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@@ -16,6 +16,8 @@ Dabei $T \sim \cN(n \E_\vartheta[\cY_k], n \V_\vartheta[\cY_k])$ unter $\P_\vart
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\shortremark $\cX_k \sim \cN(0, 1)$ i.i.d: $\displaystyle \left( \sum_{k = 1}^{m} \cX_k^2 \right) \sim \chi^2_m$.
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$\chi^2_2 = \text{Exp}(\frac{1}{2})$
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\shortremark Allgemein: $\cX_k \sim \cN(\mu, \sigma^2)$, dann $\frac{n - 1}{\sigma^2} S^2 \sim \chi_{n - 1}^2$, mit $S$ eine Summe wie oberhalb
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\shortdefinition[Studentsche $t$-Verteilung] $\cX \sim t_m$ falls Dichte
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\[
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f_\cX(x) = \frac{\Gamma\left( \frac{m + 1}{2} \right)}{\sqrt{m \pi} \Gamma \left( \frac{m}{2} \right)} \left( 1 + \frac{x^2}{m} \right)^{-\frac{m + 1}{2}}
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