(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 5298, 180] NotebookOptionsPosition[ 4172, 136] NotebookOutlinePosition[ 4657, 155] CellTagsIndexPosition[ 4614, 152] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Exercise 1.51 (* Mathematica 7.0.0 *)", "Subsubtitle", CellChangeTimes->{{3.570276674092516*^9, 3.570276713488222*^9}, { 3.571146091744033*^9, 3.571146092795353*^9}}], Cell[CellGroupData[{ Cell["(b) Calculating P[N(1)<5 | N (0.5) > 2]", "Subsection", CellChangeTimes->{{3.571146103816606*^9, 3.571146126871756*^9}, { 3.57114618812582*^9, 3.571146194075267*^9}, {3.571146311670328*^9, 3.571146355075485*^9}, {3.571147219123814*^9, 3.5711472214115267`*^9}}], Cell["Denominator: P[N (0.5) > 2]=", "Text", CellChangeTimes->{{3.571146103816606*^9, 3.571146126871756*^9}, { 3.571146358851479*^9, 3.571146366923181*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"1", "-", RowBox[{"CDF", "[", RowBox[{ RowBox[{"PoissonDistribution", "[", "2.5", "]"}], ",", "2"}], "]"}]}]], "Input", CellChangeTimes->{{3.571146134156057*^9, 3.571146148412551*^9}}], Cell[BoxData["0.4561868841166703`"], "Output", CellChangeTimes->{{3.571146145377923*^9, 3.571146148894524*^9}, 3.571146378881734*^9}] }, Open ]], Cell["Numerator: P[N (0.5) > 2, N(1)<5]=", "Text", CellChangeTimes->{{3.571146103816606*^9, 3.571146126871756*^9}, { 3.57114618812582*^9, 3.571146194075267*^9}, {3.571146371197826*^9, 3.571146374251277*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"PDF", "[", RowBox[{ RowBox[{"PoissonDistribution", "[", "2.5", "]"}], ",", "3"}], "]"}], "\[Times]", RowBox[{"CDF", "[", RowBox[{ RowBox[{"PoissonDistribution", "[", "2.5", "]"}], ",", "1"}], "]"}]}], "+", RowBox[{ RowBox[{"PDF", "[", RowBox[{ RowBox[{"PoissonDistribution", "[", "2.5", "]"}], ",", "4"}], "]"}], "\[Times]", RowBox[{"CDF", "[", RowBox[{ RowBox[{"PoissonDistribution", "[", "2.5", "]"}], ",", "0"}], "]"}]}]}]], "Input", CellChangeTimes->{{3.5711462034573298`*^9, 3.571146271413261*^9}}], Cell[BoxData["0.07238029002923842`"], "Output", CellChangeTimes->{3.571146272096201*^9, 3.5711463801684303`*^9}] }, Open ]], Cell["P[N(1)<5 | N (0.5) > 2]=", "Text", CellChangeTimes->{{3.571146103816606*^9, 3.571146126871756*^9}, { 3.57114618812582*^9, 3.571146194075267*^9}, {3.571146311670328*^9, 3.571146317587344*^9}}], Cell[CellGroupData[{ Cell[BoxData[ FractionBox["%", "%%"]], "Input", CellChangeTimes->{{3.571146281026572*^9, 3.571146284837302*^9}}], Cell[BoxData["0.1586636804988174`"], "Output", CellChangeTimes->{3.571146285806944*^9, 3.571146382423438*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ (c) largest \[Lambda]: P[N(1)\[GreaterEqual]8]\[LessEqual]0.1 or P[N(1)\ \[LessEqual]7]\[GreaterEqual]0.9\ \>", "Subsection", CellChangeTimes->{{3.571146103816606*^9, 3.571146126871756*^9}, { 3.57114618812582*^9, 3.571146194075267*^9}, {3.571146311670328*^9, 3.571146355075485*^9}, {3.5711463991892023`*^9, 3.571146399595553*^9}, { 3.571147212632084*^9, 3.57114728889163*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FindRoot", "[", RowBox[{ RowBox[{ RowBox[{"CDF", "[", RowBox[{ RowBox[{"PoissonDistribution", "[", "\[Lambda]", "]"}], ",", "7"}], "]"}], "==", "0.9"}], ",", RowBox[{"{", RowBox[{"\[Lambda]", ",", "0.001"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.571147291382193*^9, 3.571147333310253*^9}, { 3.5711475123619432`*^9, 3.5711475292691174`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"\[Lambda]", "\[Rule]", "4.656118176898001`"}], "}"}]], "Output", CellChangeTimes->{ 3.571147334652072*^9, {3.571147514956462*^9, 3.571147529775435*^9}}] }, Open ]] }, Open ]] }, Open ]] }, WindowSize->{640, 750}, WindowMargins->{{4, Automatic}, {Automatic, 4}}, PrintingCopies->1, PrintingPageRange->{1, Automatic}, PrivateNotebookOptions->{"VersionedStylesheet"->{"Default.nb"[8.] -> True}}, FrontEndVersion->"9.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (January 25, \ 2013)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[567, 22, 175, 2, 27, "Subsubtitle"], Cell[CellGroupData[{ Cell[767, 28, 273, 3, 35, "Subsection"], Cell[1043, 33, 160, 2, 26, "Text"], Cell[CellGroupData[{ Cell[1228, 39, 223, 6, 28, "Input"], Cell[1454, 47, 138, 2, 28, "Output"] }, Open ]], Cell[1607, 52, 214, 3, 26, "Text"], Cell[CellGroupData[{ Cell[1846, 59, 621, 20, 44, "Input"], Cell[2470, 81, 113, 1, 28, "Output"] }, Open ]], Cell[2598, 85, 203, 3, 26, "Text"], Cell[CellGroupData[{ Cell[2826, 92, 114, 2, 47, "Input"], Cell[2943, 96, 110, 1, 28, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[3102, 103, 394, 7, 35, "Subsection"], Cell[CellGroupData[{ Cell[3521, 114, 413, 11, 28, "Input"], Cell[3937, 127, 195, 4, 28, "Output"] }, Open ]] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)