From f07d6a69d5b8861b6296378daebe073ef5690ec5 Mon Sep 17 00:00:00 2001
From: Kees van Kempen <k.vankempen@student.science.ru.nl>
Date: Mon, 19 Sep 2022 15:58:58 +0200
Subject: [PATCH] 02: TODO finish the derivation for the CLT

---
 Exercise sheet 2/exercise_sheet_02.ipynb | 16 ++++++++++++++--
 1 file changed, 14 insertions(+), 2 deletions(-)

diff --git a/Exercise sheet 2/exercise_sheet_02.ipynb b/Exercise sheet 2/exercise_sheet_02.ipynb
index 9005f67..95bfd86 100644
--- a/Exercise sheet 2/exercise_sheet_02.ipynb	
+++ b/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."
    ]
   },
   {