Add gen_histogram.py and finish theory for exercise 2

.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
@@ -487,11 +487,16 @@
             $x$ & $\Phi(x)$ & $x$ & $\Phi(x)$ & $x$ & $\Phi(x)$ \\
             \hline
             \hline
-            0{,}00 & 0{,}500000 & 0{,}10 & 0{,}539828 & 0{,}20 & 0{,}579260 \\
+            $0{,}00$ & $0{,}500000$ & $0{,}10$ & $0{,}539828$ &
-            0{,}02 & 0{,}507978 & 0{,}12 & 0{,}547758 & 0{,}22 & 0{,}587064 \\
+            $0{,}20$ & $0{,}579260$ \\
-            0{,}04 & 0{,}515953 & 0{,}14 & 0{,}555670 & 0{,}24 & 0{,}594835 \\
+            $0{,}02$ & $0{,}507978$ & $0{,}12$ & $0{,}547758$ &
-            0{,}06 & 0{,}523922 & 0{,}16 & 0{,}563559 & 0{,}26 & 0{,}602568 \\
+            $0{,}22$ & $0{,}587064$ \\
-            0{,}08 & 0{,}531881 & 0{,}18 & 0{,}571424 & 0{,}28 & 0{,}610261 \\
+            $0{,}04$ & $0{,}515953$ & $0{,}14$ & $0{,}555670$ &
+            $0{,}24$ & $0{,}594835$ \\
+            $0{,}06$ & $0{,}523922$ & $0{,}16$ & $0{,}563559$ &
+            $0{,}26$ & $0{,}602568$ \\
+            $0{,}08$ & $0{,}531881$ & $0{,}18$ & $0{,}571424$ &
+            $0{,}28$ & $0{,}610261$ \\
             \hline
         \end{tabular}\\
     \end{minipage}
@@ -565,16 +570,16 @@
             & $\Phi(x)$ \\
             \hline
             \hline
-            1{,}40 & 0{,}919243 & 2{,}80 & 0{,}997445 & 3{,}00 &
+            $1{,}40$ & $0{,}919243$ & $2{,}80$ & $0{,}997445$ &
-            0{,}998650 & 4{,}20 & 0{,}999987 \\
+            $3{,}00$ & $0{,}998650$ & $4{,}20$ & $0{,}999987$ \\
-            1{,}42 & 0{,}922196 & 2{,}82 & 0{,}997599 & 3{,}02 &
+            $1{,}42$ & $0{,}922196$ & $2{,}82$ & $0{,}997599$ &
-            0{,}998736 & 4{,}22 & 0{,}999988 \\
+            $3{,}02$ & $0{,}998736$ & $4{,}22$ & $0{,}999988$ \\
-            1{,}44 & 0{,}925066 & 2{,}84 & 0{,}997744 & 3{,}04 &
+            $1{,}44$ & $0{,}925066$ & $2{,}84$ & $0{,}997744$ &
-            0{,}998817 & 4{,}24 & 0{,}999989 \\
+            $3{,}04$ & $0{,}998817$ & $4{,}24$ & $0{,}999989$ \\
-            1{,}46 & 0{,}927855 & 2{,}86 & 0{,}997882 & 3{,}06 &
+            $1{,}46$ & $0{,}927855$ & $2{,}86$ & $0{,}997882$ &
-            0{,}998893 & 4{,}26 & 0{,}999990 \\
+            $3{,}06$ & $0{,}998893$ & $4{,}26$ & $0{,}999990$ \\
-            1{,}48 & 0{,}930563 & 2{,}88 & 0{,}998012 & 3{,}08 &
+            $1{,}48$ & $0{,}930563$ & $2{,}88$ & $0{,}998012$ &
-            0{,}998965 & 4{,}28 & 0{,}999991 \\
+            $3{,}08$ & $0{,}998965$ & $4{,}28$ & $0{,}999991$ \\
             \hline
         \end{tabular}
         % \cdots
@@ -706,7 +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

src/2026-01-30/gen_correlated_data.py

@@ -0,0 +1,38 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from numpy.typing import NDArray
+import argparse
+
+
+def twodim_array_to_pgfplots_table_string(a: NDArray):
+    return (
+        " \\\\\n".join([" ".join([str(vali) for vali in val]) for val in a]) + "\\\\\n"
+    )
+
+
+def main():
+    # Parse command line arguments
+
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--correlation", "-c", type=np.float32, required=True)
+    parser.add_argument("-N", type=np.int32, required=True)
+    parser.add_argument("--plot", "-p", action="store_true")
+
+    args = parser.parse_args()
+
+    # Generate & plot data
+
+    means = np.array([0, 0])
+    cov = np.array([[1, args.correlation], [args.correlation, 1]])
+
+    x = np.random.multivariate_normal(means, cov, size=args.N)
+
+    print(twodim_array_to_pgfplots_table_string(x))
+
+    if args.plot:
+        plt.scatter(x[:, 0], x[:, 1])
+        plt.show()
+
+
+if __name__ == "__main__":
+    main()

src/2026-01-30/gen_histogram.py

@@ -0,0 +1,40 @@
+import argparse
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.special import binom
+
+
+def array_to_pgfplots_table_string(a):
+    return " ".join([f"({k}, {val})" for (k, val) in enumerate(a)]) + f" ({len(a)}, 0)"
+
+
+def P_binom(N, p, k):
+    return binom(N, k) * p**k * (1 - p) ** (N - k)
+
+
+def main():
+    # Parse command line arguments
+
+    parser = argparse.ArgumentParser()
+    parser.add_argument("-N", type=np.int32, required=True)
+    parser.add_argument("-p", type=np.float32, required=True)
+    parser.add_argument("--show", "-s", action="store_true")
+
+    args = parser.parse_args()
+
+    # Generate and show data
+
+    N = args.N
+    p = args.p
+
+    bars = np.array([P_binom(N, p, k) for k in range(N + 1)])
+
+    print(array_to_pgfplots_table_string(bars))
+
+    if args.show:
+        plt.stem(bars)
+        plt.show()
+
+
+if __name__ == "__main__":
+    main()