Finish theory for exercise 2

src/2026-01-30/presentation.tex

@@ -515,7 +515,7 @@
         \begin{greenblock}{Kovarianz}
             \vspace*{-8mm}
             \begin{align*}
-                \text{cov}(X,Y) = E(X,Y) - E(X)E(Y)
+                \text{cov}(X,Y) = E(XY) - E(X)E(Y)
             \end{align*}
         \end{greenblock}
     \end{columns}
@@ -855,7 +855,7 @@
             wenn $Np(1-p) \ge 9$:
             \vspace{-2mm}
             \begin{align*}
-                P_X(a < S_N \le b) = \nsum_{k=a}^{b} \binom{N}{k} p^k(1-p)^{N-k}
+                P_{S_N}(a < S_N \le b) = \nsum_{k=a}^{b} \binom{N}{k} p^k(1-p)^{N-k}
                 \hspace{5mm}\approx\hspace{5mm}
                 \Phi\left(\frac{b - Np}{\sqrt{Np(1-p)}}\right) -
                 \Phi\left(\frac{a - Np}{\sqrt{Np(1-p)}}\right)
@@ -1037,7 +1037,7 @@
             \end{gather*}
             \vspace*{-7mm}
             \begin{align*}
-                P_X(a < S_N \le b) &= \nsum_{k=a}^{b} \binom{N}{k}
+                P_{S_N}(a < S_N \le b) &= \nsum_{k=a}^{b} \binom{N}{k}
                 p^k(1-p)^{N-k} \\
                 & \approx
                 \Phi\left(\frac{b - Np}{\sqrt{Np(1-p)}}\right) -