add 2a

wtheo8.tex

@@ -54,7 +54,17 @@
 
 \begin{aufgabe}
     \begin{enumerate}[(a)]
-        \item a
+        \item Es gilt
+        \begin{align*}
+            \int_0^\infty \P(X > y) \d{y} &= \int_0^\infty \int_y^\infty \mathbbm{f}^X(x) \d{x} \d{y}\\
+            &= \int_0^\infty \int_0^\infty \mathbbm{f}^X(x)\mathbbm{1}_{x>y} \d{x} \d{y}\\
+            \intertext{Fubini}
+            &= \int_0^\infty \int_0^\infty \mathbbm{f}^X(x)\mathbbm{1}_{x>y} \d{y} \d{x}\\
+            &= \int_0^\infty \int_0^x \mathbbm{f}^X(x) \d{y} \d{x}\\
+            &= \int_0^\infty x\mathbbm{f}^X(x) \d{x}\\
+            &= \int_\Omega X(\omega) \mathbbm{f}(\omega) \d{\omega}\\
+            &= \E(X)
+        \end{align*}
         \item Es gilt
         \begin{align*}
             \E(X) &= \int_0^\infty \P(X > y) \d{y}\\