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Mathematical statistics with applications / Dennis D. Wackerly, William Mendenhall, Richard L. Scheaffer

Main Author Wackerly, Dennis D. Coauthor Mendenhall, William Secondary Author Scheaffer, Richard L Country Estados Unidos. Edition 5th ed Publication Belmont : Duxbury Press, cop. 1996 Description XVI, 798 p. : il. ; 25 cm ISBN 0-534-20916-5 CDU 519.2
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Holdings
Item type Current location Call number Status Date due Barcode Item holds Course reserves
Monografia Biblioteca Geral da Universidade do Minho
BGUMD 138415 Available 217813

Licenciatura em Estatística Aplicada Probabilidade e Estatística II 1º semestre

Monografia Biblioteca Geral da Universidade do Minho
BGUMD 138416 Available 236313

Licenciatura em Matemática Estatística 2º semestre

Total holds: 0

Enhanced descriptions from Syndetics:

This best-selling book presents a solid foundation in statistical concepts and their application to the real world.

Table of contents provided by Syndetics

  • Preface (p. xiii)
  • Note to the Student (p. xvii)
  • 1 What Is Statistics? (p. 1)
  • 1.1 Introduction (p. 1)
  • 1.2 Characterizing a Set of Measurements: Graphical Methods (p. 3)
  • 1.3 Characterizing a Set of Measurements: Numerical Methods (p. 8)
  • 1.4 How Inferences Are Made (p. 12)
  • 1.5 Theory and Reality (p. 13)
  • 1.6 Summary (p. 14)
  • 2 Probability (p. 19)
  • 2.1 Introduction (p. 19)
  • 2.2 Probability and Inference (p. 20)
  • 2.3 A Review of Set Notation (p. 22)
  • 2.4 A Probabilistic Model for an Experiment: The Discrete Case (p. 25)
  • 2.5 Calculating the Probability of an Event: The Sample-Point Method (p. 34)
  • 2.6 Tools for Counting Sample Points (p. 39)
  • 2.7 Conditional Probability and the Independence of Events (p. 50)
  • 2.8 Two Laws of Probability (p. 55)
  • 2.9 Calculating the Probability of an Event: The Event-Composition Method (p. 59)
  • 2.10 The Law of Total Probability and Bayes' Rule (p. 67)
  • 2.11 Numerical Events and Random Variables (p. 72)
  • 2.12 Random Sampling (p. 74)
  • 2.13 Summary (p. 76)
  • 3 Discrete Random Variables and Their Probability Distributions (p. 83)
  • 3.1 Basic Definition (p. 83)
  • 3.2 The Probability Distribution for a Discrete Random Variable (p. 84)
  • 3.3 The Expected Value of a Random Variable or a Function of a Random Variable (p. 88)
  • 3.4 The Binomial Probability Distribution (p. 97)
  • 3.5 The Geometric Probability Distribution (p. 110)
  • 3.6 The Negative Binomial Probability Distribution (Optional) (p. 116)
  • 3.7 The Hypergeometric Probability Distribution (p. 119)
  • 3.8 The Poisson Probability Distribution (p. 124)
  • 3.9 Moments and Moment-Generating Functions (p. 131)
  • 3.10 Probability-Generating Functions (Optional) (p. 136)
  • 3.11 Tchebysheff's Theorem (p. 139)
  • 3.12 Summary (p. 142)
  • 4 Continuous Random Variables and Their Probability Distributions (p. 150)
  • 4.1 Introduction (p. 150)
  • 4.2 The Probability Distribution for a Continuous Random Variable (p. 151)
  • 4.3 Expected Values for Continuous Random Variables (p. 162)
  • 4.4 The Uniform Probability Distribution (p. 166)
  • 4.5 The Normal Probability Distribution (p. 170)
  • 4.6 The Gamma Probability Distribution (p. 175)
  • 4.7 The Beta Probability Distribution (p. 182)
  • 4.8 Some General Comments (p. 187)
  • 4.9 Other Expected Values (p. 188)
  • 4.10 Tchebysheff's Theorem (p. 194)
  • 4.11 Expectations of Discontinuous Functions and Mixed Probability Distributions (Optional) (p. 197)
  • 4.12 Summary (p. 201)
  • 5 Multivariate Probability Distributions (p. 209)
  • 5.1 Introduction (p. 209)
  • 5.2 Bivariate and Multivariate Probability Distributions (p. 210)
  • 5.3 Marginal and Conditional Probability Distributions (p. 222)
  • 5.4 Independent Random Variables (p. 233)
  • 5.5 The Expected Value of a Function of Random Variables (p. 241)
  • 5.6 Special Theorems (p. 244)
  • 5.7 The Covariance of Two Random Variables (p. 249)
  • 5.8 The Expected Value and Variance of Linear Functions of Random Variables (p. 255)
  • 5.9 The Multinomial Probability Distribution (p. 263)
  • 5.10 The Bivariate Normal Distribution (Optional) (p. 268)
  • 5.11 Conditional Expectations (p. 270)
  • 5.12 Summary (p. 275)
  • 6 Functions of Random Variables (p. 279)
  • 6.1 Introduction (p. 279)
  • 6.2 Finding the Probability Distribution of a Function of Random Variables (p. 280)
  • 6.3 The Method of Distribution Functions (p. 281)
  • 6.4 The Method of Transformations (p. 294)
  • 6.5 The Method of Moment-Generating Functions (p. 302)
  • 6.6 Multivariable Transformations Using Jacobians (Optional) (p. 310)
  • 6.7 Order Statistics (p. 317)
  • 6.8 Summary (p. 325)
  • 7 Sampling Distributions and the Central Limit Theorem (p. 330)
  • 7.1 Introduction (p. 330)
  • 7.2 Sampling Distributions Related to the Normal Distribution (p. 331)
  • 7.3 The Central Limit Theorem (p. 346)
  • 7.4 A Proof of the Central Limit Theorem (Optional) (p. 352)
  • 7.5 The Normal Approximation to the Binomial Distribution (p. 354)
  • 7.6 Summary (p. 360)
  • 8 Estimation (p. 364)
  • 8.1 Introduction (p. 364)
  • 8.2 The Bias and Mean Square Error of Point Estimators (p. 366)
  • 8.3 Some Common Unbiased Point Estimators (p. 370)
  • 8.4 Evaluating the Goodness of a Point Estimator (p. 373)
  • 8.5 Confidence Intervals (p. 380)
  • 8.6 Large-Sample Confidence Intervals (p. 385)
  • 8.7 Selecting the Sample Size (p. 395)
  • 8.8 Small-Sample Confidence Intervals for [mu] and [mu subscript 1] - [mu subscript 2] (p. 399)
  • 8.9 Confidence Intervals for [sigma superscript 2] (p. 407)
  • 8.10 Summary (p. 410)
  • 9 Properties of Point Estimators and Methods of Estimation (p. 416)
  • 9.1 Introduction (p. 416)
  • 9.2 Relative Efficiency (p. 417)
  • 9.3 Consistency (p. 420)
  • 9.4 Sufficiency (p. 429)
  • 9.5 The Rao-Blackwell Theorem and Minimum-Variance Unbiased Estimation (p. 435)
  • 9.6 The Method of Moments (p. 444)
  • 9.7 The Method of Maximum Likelihood (p. 448)
  • 9.8 Some Large-Sample Properties of MLEs (Optional) (p. 455)
  • 9.9 Summary (p. 457)
  • 10 Hypothesis Testing (p. 460)
  • 10.1 Introduction (p. 460)
  • 10.2 Elements of a Statistical Test (p. 461)
  • 10.3 Common Large-Sample Tests (p. 467)
  • 10.4 Calculating Type II Error Probabilities and Finding the Sample Size for the Z Test (p. 477)
  • 10.5 Relationships Between Hypothesis-Testing Procedures and Confidence Intervals (p. 480)
  • 10.6 Another Way to Report the Results of a Statistical Test: Attained Significance Levels or p-Values (p. 482)
  • 10.7 Some Comments on the Theory of Hypothesis Testing (p. 487)
  • 10.8 Small-Sample Hypothesis Testing for [mu] and [mu subscript 1] - [mu subscript 2] (p. 489)
  • 10.9 Testing Hypotheses Concerning Variances (p. 498)
  • 10.10 Power of Tests and the Neyman-Pearson Lemma (p. 507)
  • 10.11 Likelihood Ratio Tests (p. 517)
  • 10.12 Summary (p. 524)
  • 11 Linear Models and Estimation by Least Squares (p. 531)
  • 11.1 Introduction (p. 531)
  • 11.2 Linear Statistical Models (p. 534)
  • 11.3 The Method of Least Squares (p. 537)
  • 11.4 Properties of the Least Squares Estimators: Simple Linear Regression (p. 544)
  • 11.5 Inferences Concerning the Parameters [beta subscript i] (p. 552)
  • 11.6 Inferences Concerning Linear Functions of the Model Parameters: Simple Linear Regression (p. 557)
  • 11.7 Predicting a Particular Value of Y Using Simple Linear Regression (p. 562)
  • 11.8 Correlation (p. 567)
  • 11.9 Some Practical Examples (p. 571)
  • 11.10 Fitting the Linear Model by Using Matrices (p. 578)
  • 11.11 Linear Functions of the Model Parameters: Multiple Linear Regression (p. 584)
  • 11.12 Inferences Concerning Linear Functions of the Model Parameters: Multiple Linear Regression (p. 585)
  • 11.13 Predicting a Particular Value of Y Using Multiple Regression (p. 591)
  • 11.14 A Test for H[subscript 0]: [beta subscript g+1] = [beta subscript g+2] = ... = [beta subscript k] = 0 (p. 593)
  • 11.15 Summary and Concluding Remarks (p. 600)
  • 12 Considerations in Designing Experiments (p. 607)
  • 12.1 The Elements Affecting the Information in a Sample (p. 607)
  • 12.2 Designing Experiments to Increase Accuracy (p. 608)
  • 12.3 The Matched Pairs Experiment (p. 612)
  • 12.4 Some Elementary Experimental Designs (p. 618)
  • 12.5 Summary (p. 624)
  • 13 The Analysis of Variance (p. 628)
  • 13.1 Introduction (p. 628)
  • 13.2 The Analysis of Variance Procedure (p. 629)
  • 13.3 Comparison of More than Two Means: Analysis of Variance for a One-Way Layout (p. 635)
  • 13.4 An Analysis of Variance Table for a One-Way Layout (p. 639)
  • 13.5 A Statistical Model for the One-Way Layout (p. 645)
  • 13.6 Proof of Additivity of the Sums of Squares and E(MST) for a One-Way Layout (Optional) (p. 647)
  • 13.7 Estimation in the One-Way Layout (p. 649)
  • 13.8 A Statistical Model for the Randomized Block Design (p. 653)
  • 13.9 The Analysis of Variance for a Randomized Block Design (p. 655)
  • 13.10 Estimation in the Randomized Block Design (p. 662)
  • 13.11 Selecting the Sample Size (p. 663)
  • 13.12 Simultaneous Confidence Intervals for More than One Parameter (p. 665)
  • 13.13 Analysis of Variance Using Linear Models (p. 668)
  • 13.14 Summary (p. 672)
  • 14 Analysis of Categorical Data (p. 680)
  • 14.1 A Description of the Experiment (p. 680)
  • 14.2 The Chi-Square Test (p. 682)
  • 14.3 A Test of a Hypothesis Concerning Specified Cell Probabilities: A Goodness-of-Fit Test (p. 684)
  • 14.4 Contingency Tables (p. 688)
  • 14.5 r [times] c Tables with Fixed Row or Column Totals (p. 697)
  • 14.6 Other Applications (p. 701)
  • 14.7 Summary and Concluding Remarks (p. 703)
  • 15 Nonparametric Statistics (p. 708)
  • 15.1 Introduction (p. 708)
  • 15.2 A General Two-Sample Shift Model (p. 709)
  • 15.3 The Sign Test for a Matched Pairs Experiment (p. 711)
  • 15.4 The Wilcoxon Signed-Rank Test for a Matched Pairs Experiment (p. 716)
  • 15.5 The Use of Ranks for Comparing Two Population Distributions: Independent Random Samples (p. 722)
  • 15.6 The Mann-Whitney U Test: Independent Random Samples (p. 724)
  • 15.7 The Kruskal-Wallis Test for the One-Way Layout (p. 732)
  • 15.8 The Friedman Test for Randomized Block Designs (p. 738)
  • 15.9 The Runs Test: A Test for Randomness (p. 743)
  • 15.10 Rank Correlation Coefficient (p. 750)
  • 15.11 Some General Comments on Nonparametric Statistical Tests (p. 756)
  • Appendix 1 Matrices and Other Useful Mathematical Results (p. 763)
  • A1.1 Matrices and Matrix Algebra (p. 763)
  • A1.2 Addition of Matrices (p. 764)
  • A1.3 Multiplication of a Matrix by a Real Number (p. 765)
  • A1.4 Matrix Multiplication (p. 766)
  • A1.5 Identity Elements (p. 768)
  • A1.6 The Inverse of a Matrix (p. 769)
  • A1.7 The Transpose of a Matrix (p. 770)
  • A1.8 A Matrix Expression for a System of Simultaneous Linear Equations (p. 771)
  • A1.9 Inverting a Matrix (p. 772)
  • A1.10 Solving a System of Simultaneous Linear Equations (p. 777)
  • A1.11 Other Useful Mathematical Results (p. 778)
  • Appendix 2 Common Probability Distributions, Means, Variances, and Moment-Generating Functions (p. 781)
  • A2.1 Discrete Distributions (p. 781)
  • A2.2 Continuous Distributions (p. 782)
  • Appendix 3 Tables (p. 783)
  • Table 1 Binomial Probabilities (p. 783)
  • Table 2 Table of e[superscript -x] (p. 786)
  • Table 3 Poisson Probabilities (p. 787)
  • Table 4 Normal Curve Areas (p. 792)
  • Table 5 Percentage Points of the t Distributions (p. 793)
  • Table 6 Percentage Points of the x[superscript 2] Distributions (p. 794)
  • Table 7 Percentage Points of the F Distributions (p. 796)
  • Table 8 Distribution Function of U (p. 806)
  • Table 9 Critical Values of T in the Wilcoxon Matched-Pairs, Signed-Ranks Test (p. 812)
  • Table 10 Distribution of the Total Number of Runs R in Samples of Size (n[subscript 1], n[subscript 2]); P(R [less than or equal] a) (p. 814)
  • Table 11 Critical Values of Spearman's Rank Correlation Coefficient (p. 816)
  • Table 12 Random Numbers (p. 817)
  • Answers to Exercises (p. 821)
  • Index (p. 839)

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