02: TODO finish the derivation for the CLT

Exercise sheet 2/exercise_sheet_02.ipynb

@@ -707,8 +707,20 @@
     "\n",
     "\\begin{align}\n",
     "\\phi_{Z_n}(t) &= \\left( \\phi_X(cn^{-2/3}t) \\right)^n \\mathbb{E}\\left[ e^{itcn^{1/3}\\mathbb{E}[X])} \\right]\n",
-    "           \\\\ &= \\left( 1 + 3 i cn^{-2/3}t - (|cn^{-2/3}t|+i cn^{-2/3}t)\\,\\sqrt{2\\pi|cn^{-2/3}t|} \\right)^n e^{3itcn^{1/3}}\n",
-    "\\end{align}"
+    "           \\\\ &= \\left( 1 + 3 i cn^{-2/3}t - (|cn^{-2/3}t|+i cn^{-2/3}t)\\,\\sqrt{2\\pi|cn^{-2/3}t|} + \\mathcal{O}(t^2) \\right)^n e^{3itcn^{1/3}}\n",
+    "\\end{align}\n",
+    "\n",
+    "Taking the limit $n \\to \\infty$, the "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "4e36d50e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# TODO: Finish the derivation above and delete this cell."
    ]
   },
   {