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Sharp EL-9900 operation manual Freedom of denominator

Models: EL-9900

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Chapter 10: Statistics & Regression Calculations

08 pdfF( pdfF(value, degree of freedom of numerator, degree of

freedom of denominator)

Finds the probability density of a specified value x for the F distribution that possesses two independent degrees of freedom, m and n. A list cannot be used.

Limitations: Degree of freedom ≤ 70

•Degree of freedom is a positive real number.

•An error may occur when an extremely large number is entered for degrees of freedom.

Example

Find the probability density for the F distribution generated with degrees of freedom 15 and 10 when x = 3.

09 cdfF( cdfF(lower limit, upper limit, degree of freedom of numerator,

degree of freedom of denominator)

Finds the F distribution probability of a specified range x for the F distribution with two independent degrees of freedom, m and n. A list cannot be used.

Limitations:

Degree of freedom ≤ 670

•Degree of freedom is a positive real number.

•An error may occur when an extremely large number is entered for degree of freedom.

Example

Find the probability of the range x = 0 to 2.5 for the F distribution generated with degrees of freedom 15 and 10.

180

Image 190

Sharp EL-9900 operation manual Freedom of denominator

Contents

EL-9900 For Your Records Introduction Their respective holdersBasic Mode Reversible KeyboardAdvanced Mode Default mode Contents Chapter Matrix Features 120 Chapter Slide Show Feature 115Chapter Chapter Solver Feature 194 Chapter List Features 131Chapter Financial Features 183 Chapter Statistics & Regression Calculations 145Chapter Option Menu 222 Chapter Programming Features 202Appendix 228 Index 265Caring for Your Calculator Getting Started Before UseCalculator OFF Automatic power off function Using the Hard CoverAdjusting Display contrastPart Names and Functions Main UnitPower ON/OFF key Display screenReversible Keyboard Basic Operation keysGetting Started Basic Key Operations ExampleChanging the Keyboard To change KeyboardBasic → Advanced Quick Run-through Basic ModeAdvanced → Basic Set up the calculator before calculation Enter fractions Change answer 1. Press @ Mode from Fractions to Decimals Basic / Advanced Keyboard How to switch the keyboardOperating the Graphing Calculator Basic Key Operations Standard Calculation KeysEntering a Entering numbersNumber entry Example Negative valueCursor Basics Performing standard math calculationsMethod Tion Editing EntriesCursor naviga About the InsertSecond Function Key Alpha Key Math Function keys for Basic keyboard Math Function KeysMath Function keys for Advanced keyboard Common Math Function Keys for both keyboards Examples MATH, STAT, and Prgm Menu Keys Setup Menu Calculator’s then . configurationSetup Menu Items Operating the Graphing Calculator Precedence of Calculations Error Messages 10 +Resetting the Calculator Using the reset switchSelecting the Reset within the Option menu Basic Calculations Basic Keyboard Try itProcedure ConceptAddition Arithmetic KeysPerforming SubtractionWhen to leave out the ⋅ sign Entering a number with a negative valueCalculations Using Various Function Keys Specifying no common factorSpecifying a common factor Example RAA E RAB E AA +AB E Second FunctionsRAC E Example Radians Calculations Using Math Menu ItemsDegrees CalcNUM Abs absvalueFpart fpart value Round roundvalue , digit number of decimalsIpart ipart value Int int valueLcm lcmnatural number, natural number Min minlistMax maxlist Gcd gcdnatural number, natural numberRandom random number of trial Remain natural number remain natural numberProb RndInt rndIntminimum value, maximum value , number of trialRndCoin rndCoin number of trial RndDice rndDice number of trialConv Angle Basic Graphing Features Basic Keyboard = 3.5 +Basic Graphing Features Basic Keyboard Explanations of Various Graphing Keys Graph BasicsZoom To select a box area to zoom Factor Factor menu, press Eto activate the setup toolPower EXPSTO TrigRCL Basic Graphing Features Basic Keyboard Other Useful Graphing Features Following illustration shows these relationships Basic Graphing Features Basic Keyboard Basic Graphing Features Basic Keyboard Basic Graphing Features Basic Keyboard Substitution feature Example Basic Graphing Features Basic Keyboard Advanced Calculations Advanced Keyboard Various Calculation Keys Example Calculate arctangent @t1 E Calculations Using Math Menu 01 log2 log2 valueDxequation, value of x , tolerance Fminequation, lower limit of x, upper limitFmaxequation, lower limit of x, upper limit Equation, lower limit, upper limit , tolerance dxCsc value ∑ expression, initial value, end value , incrementSec value Cot valueCosh-1cosh-1value Sinh-1sinh-1valueTanh-1tanh-1value →dms value degrees →dms Rectangular/polar coordinate conversionRθ→x rθ→xr coordinate, θ coordinate Xy→r xy→rx coordinate, y coordinateXy→θ xy→θx coordinate, y coordinate Rθ→y rθ→yr coordinate, θ coordinateAdvanced Calculations Advanced Keyboard Or value a or value B Value a and value BNot not value Xnor value a xnor value B Neg neg valueXor value a xor value B Conj conjcomplex numberImage imagecomplex number Calculations using complex numbersReal realcomplex number Abs abscomplex numberFunctions available for complex number calculations More Variables Single Value Variables and List VariablesAbs, round, ipart, fpart, int Tool Menu Advanced Calculations Advanced Keyboard Setup Menu Advanced Graphing Features Advanced Keyboard Un = un-1⋅ 1 0.6 +Advanced Graphing Features Advanced Keyboard Advanced Graphing Features Advanced Keyboard Use 3 in or 4 OUT of the a Zoom to adjust the drawing size Graphing Parametric EquationsPolar Graphing Draw a graph r = 16cosθsinθGraphing Sequences Based TimeBased Web Phase-based uv, uw, or vwExample 1 n-based Graphing Time Example 2 Phase-based Graphing uv Example 3 n-1-based Graphing Web Calc Function Advanced Specific sub Menus InflecFormat Setting Advanced keyboard specific sub-menusZoom Functions Specific sub Menu items MenusHYP Parametric coordinate system Setting a WindowRectangular coordinate system Polar coordinate systemTables Setting a table 101 Draw Function Line Draw menu104 HLine y-value HlineVline HLine ExampleTlineequation, x-value TlineVLine Example Tline ExampleShade DrawDraw equation Shadeequation1, equation2 , lower value, upperDrawInv DrawInv equation Circle ExampleText Textcolumn, row, strings Column and row definitions for text inputPntCHGx-coordinate, y-coordinate PntON PntONx-coordinate, y-coordinatePntOFFx-coordinate, y-coordinate PxlONcolumn, rowDrawON DrawON equation number 1, .... or DrawON PxlTST PxlTSTcolumn, rowDrawOFF DrawOFF equation number 1, .... or DrawOFF StoGD StoGD number 0-9Saves the graph data Example RclGD RclGD numberStoPict StoPict number 0-9Saves the pixel data Example Substitution Feature Create a new Slide Show FeatureSlide Show Enter x 3x 1x + 2 at the first equation Playing back the newly created Slide Show Select a file Select an imageRearranging the captured images Insertion point Slide Show menuSpecify MoveDEL RenameMatrix Features 3x + 2y + z = 2x + 3y + z = 34 x + 2y + 3z =Select a matrix DimensionsProblem To editEntering and Viewing a Matrix Enter elements Editing keys and functionsMatrix Normal Matrix Operations Matrix + Matrix Matrix Matrix Matrix ⋅ Matrix SquareDim dimmatrix name Calculations using OPE menusSpecial Matrix Operations Fill fillvalue, matrix nameAugment augmentmatrix name, matrix name Identity identity dimension valueCumul cumul matrix name Rndmat rndmatnumber of row, number of columnRowplus rowplusmatrix name, row number, row number Rowswap rowswapmatrix name, row number, row numberRowmult rowmultmultiplied number, matrix name, row number Mat→listmatrix name, column number, list name Mat→listmatrix name, list name 1, ..., list name nList→mat list→matlist 1, .... list n, matrix name Trans trans matrix name Calculations using Math menusDet det matrix name RowEF rowEF matrix nameUse of menus An expressionConcept Procedure List FeaturesEnter each speed value in the list Store the list Equation usingEnter Creating a list Normal List OperationsCalculate Press @+@ Root of L2 SortA sortAlist name Calculations using the OPE menu functionsSpecial List Operations SortD sortDlist nameNatural number ⇒ dimlist name Dim dimlistFill fillvalue, list Cumul cumul list Dflist dflist listAugment augmentlist 1, list List→mat list→matlist 1, ..., list n, matrix nameMean meanlist , frequency list Sum sumlist , start number, end number Median medianlist , frequency listProd prodlist , start number, end number StdDv stdDvlist , frequency list Drawing multiple graphs using the list functionStandard deviation and variance Varian varianlist , frequency listUsing Ldata functions StoLD StoLD natural numberHow to enter the list Using List Table to Enter or Edit ListsRclLD RclLD natural number How to edit the list Opening the list Press S Table to enter Statistics & Regression CalculationsData Statistics & Regression Calculations Selecting SettingGraph drawing Whether148 Statistics Features Stat menusStatistical evaluations available under the C Calc menu Statistical calculations using the Sunday data L2 Statistical calculations using the Monday data L3152 Graph Types Statistical graph types overview chartGraphing the statistical data HistogramNormal probability plot N.P Normal distribution plot N.D Box plot Box Modified box plot MBox Pie chart PIE Scatter diagram S.D XY Line Xyline Statistical plotting on/off function Specifying statistical graph and graph functionsPress DD Limit and press 22 LimON Tracing Trace function of statistical graphsGraph SortD sortDlist Data list operationsSortA sortAlist SetList SetList list name 1 , list nameRegression Calculations 161 162 15 x’ value or list x’ Using Regression Functions16 y’ value or list y’ Press #CSD0404 Rgx2 Residual list Statistical Hypothesis TestingAbout Start a statisti Cal test Press see TestZint1prop and 15 Zint2prop 167 168 169 170 171 172 Ztest1prop Tests the success probability P0 of a population 174 175 176 Distribution functions InvNorm InvNormprobability , mean, standard deviation CdfT cdfTlower limit, upper limit, degree of freedom 07 cdfχ2 cdfχ2lower limit, upper limit, degree of freedomFreedom of denominator 181 Cdfpoi cdfpoimean, value Cdfgeo cdfgeosuccess probability, valueDraw a cash Financial FeaturesFlow diagram on PaperPayment due at the end of the period Payment due at the beginning of the periodSetting the payment due time Press CC Period Press 11 PmtEnd and press ESimple interest and compound interest Set the TAB FSE 2 and FIX Respectively 188 SlvI% N, PV, PMT, FV, P/Y, C/Y Calc functionsSolvpmt N, I%, PV, FV, P/Y, C/Y SlvPV N, I%, PMT, FV, P/Y, C/Y190 Example using the 08 Calculations Bal Bal number of payments , decimal place to round11 →Apr →Apr effective interest rate, number of settlements Conversion functions12 →Eff →Eff nominal interest rate, number of settlements Vars Menu Three Analysis Methods Equation, Newton, and Graphic Solver FeatureEquation Solver Feature Newton’s 197 198 199 Saving/Renaming Equations for Later Use Recalling a Previously Saved Equation Program Programming FeaturesCreating a new ExecProgramming Features Programming Hints Program line by Command orStoring a Blank lineOperands Setting a variableVariables Comparison operandsPrgm menu PA Programming commandsCommand strings Print character stringsIs set to the corresponding numeric value as specified Rem Rem commentsKey variable Following tableScrn menu PC Brnch menu PBO menu PD Setup menu PE Tab integer 0 to Format menu PF06 Y’ OFF Y’OFF 212 Splot menu PG Plt1graph type, X list name , Y list name, frequency listFlow control tools If If conditional statements Goto label nameNext WEndOther menus convenient for programming Copy menu PHVars menu Value Debugging Sample programs When an infinite Loop occursMatfill 221 Option Menu Accessing the Option MenuAdjusting the screen contrast Checking the memory usageCreated Deleting files Linking to another EL-9900 or PC225 226 Reset function Transmission between the ELReplacing Batteries AppendixHandling Replacing unit Procedures forOperation 230 Saved calculator configurations are not retained Troubleshooting GuideCalculator’s power won’t turn on Graph cannot be seenScreen images cannot be stored Slide Show Specifications Program features Substitution featuresSlide Show features Power supplyError Codes and Error Messages Break % calculation Error Conditions Relating to Specific TasksFinancial PV calculationFV calculation PMT calculationError conditions during financial calculations Distribution functionDf = However Γs = 0 x s 1 e x dx Df Degree of freedom Arithmetic calculation Calculation RangeFunction calculation Function Calculation range ⋅ 10-99≤ x 1 ⋅ Ln x = loge Log Xy → θ = tan-1 Function Calculation range Σx 1 ⋅ Complex number calculation Catalog Feature Math menus List of Menu/Sub-menu ItemsMcalc Mconv MnumMprob MangleMlogic List menusMineq Mcomplex@lMATH @lLDATAScalc SEDIT/OPESreg Stest SdistriStat Plot menus Stat Plot mode HIST/B.L./N.P./N.D./BOX/PIE/S.D./XYLINEPLOT1/PLOT2/PLOT3/LIMIT/ON/OFF Draw menus @dDRAW@dON/OFF/LINE/GDATA/PICT/SHADE Zoom menus@dPOINT ZzoomFACTOR/POWER ZHYP/STO/RCL Calc menus@kCALC Slide Show menus Pin the Prgramming mode PrgmPin the Prgramming mode Brnch Prgm menusPin the Prgramming mode I/O Pin the Prgramming mode ScrnPin the Prgramming mode Setup Pin the Prgramming mode Format Pin the Prgramming mode Splot@mNAME Pin the Prgramming mode CopyMatrix menus @mEDIT@mMATH Finance menus@gSOLVER/CALC @gVARS Tool menus@gPERIOD @VN BASE/SYSTEM/POLY@in the Solver mode METHOD/EQTN/SAVE/RENAME Solver menusIndex 266 267 268 269 270 271 272 Europe Sharp Corporation