[PS] Analysis stuff, fixes

2026-07-27 21:29:09 +02:00 · 2026-07-22 16:11:11 +02:00
parent 5c56561acc
commit 45075d2952
4 changed files with 27 additions and 2 deletions
@@ -78,6 +78,12 @@ $\cX_i \sim \cN(\mu, \sigma^2)$ i.i.d. und $\vartheta = (\mu, \sigma^2) = (\mu,
 \[
    l(\vartheta) = -\frac{1}{2} n(\log(2 \pi) + \log(v)) - \sum_{k = 1}^{n} \frac{(x_k - \mu)^2}{2v}
 \]
+
+\[
+    \partial_{\mu} l = 2 \sum_{k = 1}^{n} \frac{x_k - \mu}{2 v}
+    \quad
+    \partial_v l = -\frac{n}{2v} + 2v^{-2}\sum_{k = 1}^{n} (x_k - \mu)^2
+\]
 Der \bi{Momentschätzer} ist $T = (T_1, T_2) = (E_\vartheta[\cX], \V_\vartheta[\cX])$:
 \[
    T_1 = \overline{\cX}_n \qquad