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." ] }, {