(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 13.2' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 157224, 2835] NotebookOptionsPosition[ 154608, 2790] NotebookOutlinePosition[ 155036, 2807] CellTagsIndexPosition[ 154993, 2804] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ RowBox[{"ClearAll", "[", "\"\\"", "]"}]], "Input", CellChangeTimes->{{3.92615667517485*^9, 3.926156686424818*^9}}, CellLabel->"In[1]:=",ExpressionUUID->"c22a04d7-f3c4-4738-819c-f8ab099b7991"], Cell[CellGroupData[{ Cell["Einf\[UDoubleDot]hrung in die Computer Algebra - 2024 - \ \[CapitalUDoubleDot]bungsblatt 5", "Chapter", CellChangeTimes->{{3.9270239720010033`*^9, 3.927024011562078*^9}, { 3.927277035400279*^9, 3.927277036245101*^9}, {3.9289036792676163`*^9, 3.928903680025075*^9}, {3.929435678614498*^9, 3.929435679603327*^9}}, TextAlignment->Center,ExpressionUUID->"9549d516-5ace-4b64-ab57-b4c23eb0b6cc"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["3. 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Vergleichen Sie grafisch die Verteilung von q mit einer ", Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["\[Chi]", "2"], "-", "Verteilung"}], TraditionalForm]], ExpressionUUID->"bee64699-b40a-45b6-b310-08cd37bf8e0b"], " mit 2 Freiheitsgraden." }], "Text", CellChangeTimes->{{3.929429966736289*^9, 3.929429973728672*^9}, { 3.929430040735958*^9, 3.929430054964446*^9}, {3.9294304818969812`*^9, 3.929430525024475*^9}, {3.929430564227847*^9, 3.929430632262744*^9}, { 3.929430830492697*^9, 3.929430849241171*^9}, {3.929437335160636*^9, 3.929437335549252*^9}, {3.9297863793782682`*^9, 3.9297863807642736`*^9}, { 3.929786458219371*^9, 3.929786467957387*^9}, {3.930021324605966*^9, 3.930021338439274*^9}, {3.9300237487405233`*^9, 3.930023768665547*^9}}, Background->RGBColor[ 0.94, 0.88, 0.94],ExpressionUUID->"707f6808-59bf-4ab7-9927-27cdb3f79406"], Cell[TextData[StyleBox["Hinweis: ParallelTable[ ], ChiSquareDistribution[ ]", FontWeight->"Bold"]], "Text", CellChangeTimes->{{3.929436888285372*^9, 3.929436930159102*^9}, { 3.9294371835309772`*^9, 3.929437195504073*^9}, {3.929771307000428*^9, 3.929771317529364*^9}, {3.929776499449049*^9, 3.929776690401609*^9}, { 3.9297774197557077`*^9, 3.929777469783823*^9}, {3.9300237444057703`*^9, 3.930023744858857*^9}}, Background->RGBColor[ 0.87, 0.94, 1],ExpressionUUID->"31ac254d-9b58-4077-b62f-2b4168e86063"], Cell[TextData[{ StyleBox["6. ", FontWeight->"Bold"], " Importieren Sie nun den Datensatz \[OpenCurlyDoubleQuote]data.dat\ \[CloseCurlyDoubleQuote], der auf ILIAS zur Verf\[UDoubleDot]gung steht. \ Bestimmen Sie die Anzahl Ereignisse in jedem der zehn Bins. Berechnen Sie \ daraus durch Maximierung der Likelihood-Funktion die Werte von a und b." }], "Text", CellChangeTimes->{{3.929430965032612*^9, 3.929430994292651*^9}, { 3.9294310487469807`*^9, 3.929431067831378*^9}, {3.929783678499864*^9, 3.929783716646359*^9}, {3.9297856348906927`*^9, 3.929785636598433*^9}, { 3.930021351050953*^9, 3.930021351451796*^9}, {3.930022215661895*^9, 3.93002227619706*^9}}, Background->RGBColor[ 0.94, 0.88, 0.94],ExpressionUUID->"eafd119a-68e2-4bfc-a5c7-eca87e28d1f7"], Cell[TextData[{ StyleBox["Hinweis: ", FontWeight->"Bold"], "N\[UDoubleDot]tzliche Befehle: ", StyleBox["Import[], Flatten[], BinCounts[ ]", FontWeight->"Bold"] }], "Text", CellChangeTimes->{{3.929436888285372*^9, 3.929436930159102*^9}, { 3.9294371835309772`*^9, 3.929437195504073*^9}, {3.929771307000428*^9, 3.929771317529364*^9}, {3.929776499449049*^9, 3.929776690401609*^9}, { 3.9297774197557077`*^9, 3.929777469783823*^9}, {3.930022289857053*^9, 3.9300223155342627`*^9}}, Background->RGBColor[ 0.87, 0.94, 1],ExpressionUUID->"98c8ed7e-9f7f-4282-af74-07264da8b2cc"], Cell[TextData[{ StyleBox["7. ", FontWeight->"Bold"], StyleBox["(Optional)", FontSlant->"Italic"], StyleBox[" \n", FontWeight->"Bold"], "Stellen Sie grafisch den Konfidenzbereich f\[UDoubleDot]r die Parameter a \ und b dar, welcher gegeben ist durch\n", StyleBox[" - 2 (log L (a, b) - log L_max) < \ InverseCDF[ChiSquareDistribution[2], CL]", FontWeight->"Bold"], " mit CL = 0.68 f\[UDoubleDot]r 68 % Konfidenz und CL = 0.95 f\[UDoubleDot]r \ 95 % Konfidenz . 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