diff --git a/semester4/ps/ps-jh/parts/03_expected-value/02_cont.tex b/semester4/ps/ps-jh/parts/03_expected-value/02_cont.tex index 0974e88..dc3c96a 100644 --- a/semester4/ps/ps-jh/parts/03_expected-value/02_cont.tex +++ b/semester4/ps/ps-jh/parts/03_expected-value/02_cont.tex @@ -6,8 +6,6 @@ \shortlemma[Int über gauss. Glockenk.] $\int_{-\8}^{\8} e^{\frac{-x^2}{2\sigma^2}} \dx x = \sqrt{2 \pi \sigma^2}$ \subsubsection{Beispiele} -% TODO: Consider if need derivation of them here and prev section as well -% TODO: Also add the ones proven in exercises \begin{itemize} \item $\cX \sim \cU([a, b])$, $a < b$: $\E[\cX] = \frac{a + b}{2}$ \item $\cX \sim \text{Exp}(\lambda)$, $\lambda > 0$: $\E[\cX] = \frac{1}{\lambda}$ diff --git a/semester4/ps/ps-jh/parts/06_estimators/02_max-likelihood.tex b/semester4/ps/ps-jh/parts/06_estimators/02_max-likelihood.tex index 23a1e22..7091bcb 100644 --- a/semester4/ps/ps-jh/parts/06_estimators/02_max-likelihood.tex +++ b/semester4/ps/ps-jh/parts/06_estimators/02_max-likelihood.tex @@ -40,7 +40,7 @@ Meistens sind $\cX_k$ i.i.d. unter $\P_\vartheta$, dann $L$ produkt, also besser \begin{enumerate} \item log-LH-Funk. bestimmen ($x_i$ statt $\cX_i$ verwenden) \item Nach $\vartheta$ ableiten (oder wodurch $\vartheta$ ersetzt wurde) - \item Nullstelle davon berechnen + \item Nullstelle davon berechnen (für Max (via e.g. $f'' < 0$)) \item ML-Schätzer ist dann Nullstelle von Ableitung (mit $x_i$ wieder durch $\cX_i$ ersetzt) \end{enumerate} diff --git a/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf b/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf index 85966bc..fbe238b 100644 Binary files a/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf and b/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf differ