Chi-square distribution, F distribution | HP 50g manual

The Chi-square distribution

The Chi-square (χ2) distribution has one parameter ν, known as the degrees of freedom. The calculator provides for values of the upper-tail

(cumulative) distribution function for the χ2-distribution using UTPC given the value of x and the parameter ν. The definition of this function is, therefore, UTPC(ν,x) = P(X>x) = 1 - P(X<x). For example, UTPC(5, 2.5) = 0.776495…

The F distribution

The F distribution has two parameters νN = numerator degrees of freedom, and νD = denominator degrees of freedom. The calculator provides for values of the upper-tail (cumulative) distribution function for the F distribution, function UTPF, given the parameters νN and νD, and the value of F. The definition of this function is, therefore, UTPF(νN,νD,F) = P(ℑ>F) = 1 - P(ℑ<F). For example, to calculate UTPF(10,5, 2.5) = 0.1618347…

Reference

For additional probability distributions and probability applications, refer to Chapter 17 in the calculator’s user’s guide.

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HP 50g manual Chi-square distribution, F distribution

Contents

User’s manual HP 50g graphing calculator Printing History Preface Table of Contents Calculations with real numbers Algebraic and arithmetic operations Calculations with complex numbers Operations with lists Solution to equations Matrices and linear algebra Vectors Calculus Applications Graphics Probability Distributions Multi-variateCalculus ApplicationsVector Analysis Applications Differential Equations Equation Library Using SD cardsStatistical Applications Numbers in Different Bases Batteries Chapter Getting startedBasic Operations Page Tool menu Contents of the calculator’s displayMenus Introducing the calculator’s keyboard Setting time and date ALPHA-Left-Shift function, to enter the lower-case letter p Selecting calculator modes √ 3.*5.-1/3.*3./23.3+EXP2.5 Operating ModePage Lets try now the expression proposed earlier Fixed format with decimals Number Format and decimal dot or commaStandard format Scientific format Engineering format Decimal comma vs. decimal point Coordinate System Angle Measure Selecting CAS settings Explanation of CAS settings Selecting Display modes Selecting properties of the line editor Selecting the display font Selecting properties of the Stack Selecting properties of the equation writer EQW References Creating arithmetic expressions Chapter Introducing the calculatorCalculator objects Editing expressions in the stackPage Page 2L 1 + + 2 L + y Creating algebraic expressions Using the Equation Writer EQW to create expressions + 2 ⋅ 5 + ⎛ x + 2 ∝ ⋅ ∆y ⎞ Home directory Organizing data in the calculator Typing variable names VariablesSubdirectories Creating variables Algebraic mode RPN mode Page Checking variables contents Deleting variables Listing the contents of all variables in the screenUsing function Purge in the stack in Algebraic mode Using function Purge in the stack in RPN mode Choose boxes vs. Soft Menu Undo and CMD functions @@OK@@ References Examples of real number calculations Chapter Calculations with real numbersPage Using powers of 10 in entering data Page Hyperbolic functions and their inverses Using calculator menusReal number functions in the MTH menu Page Units menu Operations with unitsPage Attaching units to numbers Available units Unit prefixes Operations with units Unit conversions Quit Physical constants in the calculatorPage Defining and using functions Reference Definitions Setting the calculator to Complex modeChapter Calculations with complex numbers Entering complex numbers Polar representation of a complex number Cmplx menu through the MTH menu Simple operations with complex numbersCmplx menus Forms the complex number x,y out of real numbers x Cmplx menu in keyboard Functions applied to complex numbers Function Droite equation of a straight line Page Entering algebraic objects Chapter Algebraic and arithmetic operations Simple operations with algebraic objects Functions in the ALG menu Collect Operations with transcendental functions Expansion and factoring using log-exp functions Expansion and factoring using trigonometric functions FACTORSSIMP2 Functions in the Arithmetic menu Pcoef function PolynomialsHorner function Variable Peval function FractionsProot function Quot and Remainder functions Fcoef function SIMP2 functionPropfrac function Partfrac function − 5X 2 + 3X − Step-by-step operations with polynomials and fractionsFroots function Reference Function Isol Chapter Solution to equationsSymbolic solution of algebraic equations Function Solve Page Function Zeros Function Solvevx Numerical solver menu Polynomial Equations Finding the solutions to a polynomial equation Enter vector of roots Generating an algebraic expression for the polynomial Financial calculations Function Steq Solving equations with one unknown through Solution to simultaneous equations with Mslv Reference Page Changing sign Chapter Operations with listsCreating and storing lists Operations with lists of numbers Addition, subtraction, multiplication, division Page Functions applied to lists Lists of complex numbers MTH/LIST menu Lists of algebraic objectsPage MAP function SEQ functionPage Typing vectors in the stack Chapter VectorsEntering vectors Storing vectors into variables in the stack Moving to the right vs. moving down in the Matrix Writer Using the Matrix Writer Mtrw to enter vectors Press @GOTO@ 3@@OK@@ 3@@OK@@ @@OK@@ to move to position 3,3 Addition, subtraction Simple operations with vectors Absolute value function MTH/VECTOR menuMultiplication by a scalar, and division by a scalar Cross product MagnitudeDot product Reference Entering matrices in the stack Using the Matrix WriterChapter Matrices and linear algebra Typing in the matrix directly into the stack Operations with matrices Multiplication by a scalar Addition and subtractionMultiplication Cij = ∑aik ⋅ bkj , for i = 1,2,K, m j = 1,2,K, n Matrix-vector multiplicationMatrix multiplication Term-by-term multiplication Raising a matrix to a real power Inverse matrix Identity matrix TrA = ∑aii Characterizing a matrix The matrix Norm menuFunction DET Function Trace Using the numerical solver for linear systems Solution of linear systems ⎢x2 = ⎢1 Solution by division of matrices Solution with the inverse matrix References Graphs options in the calculator Chapter Graphics = 1 exp− x Plotting an expression of the form y = fxPage Generating a table of values for a function Fast 3D plots Keep the default plot window ranges to read Reference Page Function lim Chapter Calculus ApplicationsCalc Calculus menu Limits and derivatives Lim f Xdx = F x + C Anti-derivatives and integralsFunctions Deriv and Dervx Functions INT, INTVX, RISCH, Sigma and Sigmavx Definite integrals = ∑ Infinite seriesFunctions TAYLR, TAYLR0, and Series Reference Partial derivatives Chapter Multi-variate Calculus Applications Multiple integrals Gradient Chapter Vector Analysis ApplicationsDel operator Curl Divergence Function Ldec Solution to linear and non-linear equationsChapter Differential Equations CALC/DIFF menuPage Variable Odetype Function Desolve Laplace transform and inverses in the calculator Laplace Transforms 2inπt Fourier seriesFunction Fourier Lf t= F s = 0∞ f t ⋅ e− st dt Fourier series for a quadratic function Reference Page − r + Chapter Probability DistributionsMTH/PROBABILITY.. sub-menu part Factorials, combinations, and permutations Random numbers Student-t distribution MTH/PROB menu partNormal distribution F distribution Chi-square distribution Entering data Chapter Statistical Applications Sample vs. population Calculating single-variable statistics Obtaining frequency distributions Page 195238095238 + 2.00857242857*X Correlation Covariance Fitting data to a function y = fx Obtaining additional summary statistics Confidence intervals Page Hypothesis testing Page Reference Page Base menu Chapter Numbers in Different Bases Writing non-decimal numbers Formatting an SD card Chapter Using SD cardsInserting and removing an SD card Storing objects on the SD card Accessing objects on an SD card Purging an object from the SD card Recalling an object from the SD card Specifying a directory on an SD card Purging all objects on the SD card by reformatting `#EQLIB #EQNLI Chapter Equation Library Step 30 ##¢0#- L *!!!!!!V0!!!!!+ Reference Limited Warranty W-2 Europe Asia Pacific Country Telephone numbers Service America Country Telephone numbers Federal Communications Commission Notice Regulatory information Canadian Notice Korean Notice