Fix factorial symbol and change variable k to n

.latexmkrc

@@ -1,4 +1,3 @@
 $pdflatex="pdflatex -shell-escape -interaction=nonstopmode -synctex=1 %O %S";
 $out_dir = 'build';
 $pdf_mode = 1;
-

Makefile

@@ -1,19 +1,25 @@
 PRESENTATIONS := $(patsubst src/%/presentation.tex,build/presentation_%.pdf,$(wildcard src/*/presentation.tex))
 HANDOUTS := $(patsubst build/presentation_%.pdf,build/presentation_%_handout.pdf,$(PRESENTATIONS))
 
+RC_PDFLATEX := $(shell grep '$$pdflatex' .latexmkrc \
+	       | sed -e 's/.*"\(.*\)".*/\1/' -e 's/%S//' -e 's/%O//')
+
 .PHONY: all
 all: $(PRESENTATIONS) $(HANDOUTS)
 
 build/presentation_%.pdf: src/%/presentation.tex build/prepared
-	TEXINPUTS=./lib/cel-slides-template-2025:$$TEXINPUTS latexmk $<
+	TEXINPUTS=./lib/cel-slides-template-2025:$(dir $<):$$TEXINPUTS \
-	mv build/presentation.pdf $@
+		latexmk -outdir=build/$* $<
+	cp build/$*/presentation.pdf $@
 
 build/presentation_%_handout.pdf: src/%/presentation.tex build/prepared
-	TEXINPUTS=./lib/cel-slides-template-2025:$$TEXINPUTS latexmk -pdflatex='pdflatex %O "\def\ishandout{1}\input{%S}"' $<
+	TEXINPUTS=./lib/cel-slides-template-2025:$(dir $<):$$TEXINPUTS \
-	mv build/presentation.pdf $@
+		latexmk -outdir=build/$*_handout \
+		-pdflatex='$(RC_PDFLATEX) %O "\def\ishandout{1}\input{%S}"' $<
+	cp build/$*_handout/presentation.pdf $@
 
 build/prepared:
-	mkdir -p build
+	mkdir build
 	touch build/prepared
 
 .PHONY: clean

src/2025-12-19/presentation.tex

@@ -99,7 +99,7 @@
         \pause\column{\kitthreecolumns}
         \centering
         \begin{itemize}
-            \item Verteilungsfunktion $F_X(x)$ einer stetiger ZV
+            \item Verteilungsfunktion $F_X(x)$ einer stetigen ZV
                 \begin{gather*}
                     F_X(x) = P(X \le x)
                 \end{gather*}
@@ -107,7 +107,7 @@
         \pause\column{\kitthreecolumns}
         \centering
         \begin{itemize}
-            \item Wahrscheinlichkeitsdichte $f_X(x)$ einer stetiger ZV
+            \item Wahrscheinlichkeitsdichte $f_X(x)$ einer stetigen ZV
                 \begin{gather*}
                     F_X(x) = \int_{-\infty}^{x} f_X(u) du
                 \end{gather*}
@@ -154,7 +154,7 @@
     \end{minipage}
     \begin{minipage}{0.38\textwidth}
         \begin{lightgrayhighlightbox}
-            Erinnerung
+            Erinnerung: Diskrete Zufallsvariablen
             \begin{align*}
                 \text{\normalfont Erwartungswert: }& E(X) =
                 \sum_{n=1}^{\infty} x_n P_X(x) \\
@@ -171,7 +171,7 @@
     \begin{columns}[t]
         \column{\kitthreecolumns}
         \centering
-        \begin{greenblock}{Verteilungsfunktion (kontinuierlich)}
+        \begin{greenblock}{Verteilungsfunktion (stetige ZV)}
             \vspace*{-6mm}
             \begin{gather*}
                 F_X(x) = P(X \le x)\\[4mm]
@@ -270,9 +270,9 @@
                 \end{align*}
                 \pause\begin{gather*}
                     \int_{-\infty}^{\infty} f_X(x) dx
-                    = \int_{-\infty}^{\infty} C\cdot x e^{-ax^2} dx
+                    = \int_{0}^{\infty} C\cdot x e^{-ax^2} dx
-                    = \frac{C}{-2a} \int_{-\infty}^{\infty} (-2ax) e^{-ax^2} dx  \\
+                    = \frac{C}{-2a} \int_{0}^{\infty} (-2ax) e^{-ax^2} dx  \\
-                    = \frac{C}{-2a} \int_{-\infty}^{\infty} (e^{-ax^2})' dx
+                    = \frac{C}{-2a} \int_{0}^{\infty} (e^{-ax^2})' dx
                     = \frac{C}{-2a} \mleft[ e^{-ax^2} \mright]_0^{\infty} \overset{!}{=} 1 \hspace{10mm} \Rightarrow C = 2a
                 \end{gather*}
                 \centering
@@ -711,7 +711,7 @@
                     2 - 2\Phi\left(\frac{0{,}2}{\sigma'}\right) = 2{,}12\cdot 10^{-3} \\[2mm]
                     \Rightarrow \Phi\left(\frac{0{,}2}{\sigma'}\right) \approx 0{,}9989 \\[2mm]
                     \Rightarrow \sigma' \approx \frac{0{,}2}{\Phi^{-1}(0{,}9989)}
-                    \approx \frac{0{,}2}{3{,}08} \approx 0{,}65
+                    \approx \frac{0{,}2}{3{,}08} \approx 0{,}065
                 \end{gather*}
             \end{columns}
         \pause \vspace*{-5mm}\item Durch einen Produktionsfehler verschiebt sich der