eth-janishutz/eth-summaries
1
0
Fork 0
mirror of https://github.com/janishutz/eth-summaries.git synced 2026-07-27 21:29:09 +02:00
Code Issues Packages Projects Releases Wiki Activity

[PS] Start rewrite of max likelihood section

Browse Source 
Also adds various small quality of life improvements and simpler
explanations
This commit is contained in:
janishutz
2026-07-11 17:28:42 +02:00
parent d75e317fd4
commit 793401968b
19 changed files with 94 additions and 86 deletions
Download Patch File Download Diff File Expand all files Collapse all files
semester4/ps/ps-jh/parts/04_joint-distribution/00_discrete.tex
+2 -2
View File
@@ -40,7 +40,7 @@ $\forall k \in \{ 1, \ldots, n \}$ und $\forall x \in W_k$ gilt:
F_{\cX_k}(x) = \lim_{\elementstack{x_l \rightarrow \8}{l \in \{ 1, \ldots, n \} \backslash \{ k \}}} F(x_1, \ldots, x_{k - 1}, x, x_{k + 1}, \ldots, x_n)
\]
\shorttheorem[Erwartungswert Bild] (Solange Summe wohldefiniert ist, summieren über $x_1 \in W_1, \ldots, x_n \in W_n$)
\shorttheorem[Erwartungswert Bild] (Solange $\Sigma$ wohldef, summieren über $x_1 \in W_1, \ldots, x_n \in W_n$), siehe rechts für details
\[
\E[\varphi(\cX_1, \ldots, \cX_n)] = \sum_{x_1, \ldots, x_n} \varphi(x_1, \ldots, x_n) p(x_1, \ldots, x_n)
\]
@@ -49,5 +49,5 @@ $\forall k \in \{ 1, \ldots, n \}$ und $\forall x \in W_k$ gilt:
\begin{itemize}
\item $\cX_1, \ldots, \cX_n$ sind unabhängig
\item $\forall x_1 \in W_1, \ldots, x_n \in W_n$ gilt (prod. Randv. von $\cX_i$)
\[ p(x_1, \ldots, x_n) = \P[\cX_1 = x_1] \cdot \ldots \cdot \P[\cX_n = x_n] \]
\[ p(x_1, \ldots, x_n) = \P[\cX_1 = x_1] \cdot \ldots \cdot \P[\cX_n = x_n] \]
\end{itemize}