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[PS] Start notes & remarks update

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janishutz
2026-06-15 13:46:28 +02:00
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semester4/ps/ps-jh/parts/06_estimators/02_max-likelihood.tex
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@@ -30,7 +30,7 @@ Einfacher: Statt maximieren, Nullstellen von Ableitung nach $\vartheta$.
% TODO: Maybe remark from slide 356 (= p33 in 7)
\shortexample \bi{Verteilungen}\\
\fbox{\bi{Bernoulli}} $\cX_i \sim \text{Ber}(p)$ i.i.d, hier $\vartheta = p$. Dabei:
\highlight{Bernoulli} $\cX_i \sim \text{Ber}(p)$ i.i.d, hier $\vartheta = p$. Dabei:
$p_\cX(x; \vartheta) = \P_\vartheta[\cX = x] = \vartheta^x (1 - \vartheta)^{1 - x}$ mit $x \in \{0, 1\}$. LH-Func:
\[
L(x_1, \ldots, x_n; \vartheta) = \vartheta^{\sum_{k = 1}^{n} x_k} (1 - \vartheta)^{n - \sum_{k = 1}^{n} x_k}