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An introduction to probability and statistics / Vijay K. Rohatgi, A.K. Md. Ehsanes Saleh

Rohatgi, Vijay K.
Material type: materialTypeLabelBook; Format: print Series: Wiley Series in Probability and Statistics.Publisher: New York [etc.] : John Wiley and Sons, cop. 2001Edition: 2nd ed.Description: XIV, 716 p. : il. ; 24cm.ISBN: 0471348465.Subject(s): Probabilities | Mathematical statistics | Estadística matemática | Probabilidades
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TEORÍA DE LA PROBABILIDAD GRADO EN MATEMÁTICAS Asignatura actualizada 2017-2018

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INFERENCIA ESTADÍSTICA GRADO EN MATEMÁTICAS Asignatura actualizada 2017-2018

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Monografías 02. BIBLIOTECA CAMPUS PUERTO REAL
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Enhanced descriptions from Syndetics:

The second edition of a well-received book that was published 24 years ago and continues to sell to this day, An Introduction to Probability and Statistics is now revised to incorporate new information as well as substantial updates of existing material.

Tít. ed. 1976: Introduction to probability theory and mathematical statistics.

The second edition of a well-received book that was published 24 years ago and continues to sell to this day, An Introduction to Probability and Statistics is now revised to incorporate new information as well as substantial updates of existing material.

Índice: Probability. Random Variables and Their Probability Distributions.Moments and Generating Functions. Multiple Random Variables. Some Special Distributions. Limit Theorems. Sample Moments and Their Distributions. Parametric Point Estimation. Neyman-Pearson Theory of Testing of Hypotheses. Some Further Results of Hypothesis Testing. Confidence Estimation. General Linear Hypothesis. Nonparametric Statistical Inference. References. Frequently Used Symbols and Abbreviations. Statistical Tables. Answers to Selected Problems. Indexes.

Table of contents provided by Syndetics

  • Preface to the Second Edition (p. xi)
  • Preface to the First Edition (p. xiii)
  • 1. Probability (p. 1)
  • 1.1 Introduction (p. 1)
  • 1.2 Sample Space (p. 2)
  • 1.3 Probability Axioms (p. 7)
  • 1.4 Combinatorics: Probability on Finite Sample Spaces (p. 21)
  • 1.5 Conditional Probability and Bayes Theorem (p. 28)
  • 1.6 Independence of Events (p. 33)
  • 2. Random Variables and Their Probability Distributions (p. 40)
  • 2.1 Introduction (p. 40)
  • 2.2 Random Variables (p. 40)
  • 2.3 Probability Distribution of a Random Variable (p. 43)
  • 2.4 Discrete and Continuous Random Variables (p. 48)
  • 2.5 Functions of a Random Variable (p. 57)
  • 3. Moments and Generating Functions (p. 69)
  • 3.1 Introduction (p. 69)
  • 3.2 Moments of a Distribution Function (p. 69)
  • 3.3 Generating Functions (p. 85)
  • 3.4 Some Moment Inequalities (p. 95)
  • 4. Multiple Random Variables (p. 102)
  • 4.1 Introduction (p. 102)
  • 4.2 Multiple Random Variables (p. 102)
  • 4.3 Independent Random Variables (p. 119)
  • 4.4 Functions of Several Random Variables (p. 127)
  • 4.5 Covariance, Correlation, and Moments (p. 149)
  • 4.6 Conditional Expectation (p. 164)
  • 4.7 Order Statistics and Their Distributions (p. 171)
  • 5. Some Special Distributions (p. 180)
  • 5.1 Introduction (p. 180)
  • 5.2 Some Discrete Distributions (p. 180)
  • 5.3 Some Continuous Distributions (p. 204)
  • 5.4 Bivariate and Multivariate Normal Distributions (p. 238)
  • 5.5 Exponential Family of Distributions (p. 251)
  • 6. Limit Theorems (p. 256)
  • 6.1 Introduction (p. 256)
  • 6.2 Modes of Convergence (p. 256)
  • 6.3 Weak Law of Large Numbers (p. 274)
  • 6.4 Strong Law of Large Numbers (p. 281)
  • 6.5 Limiting Moment Generating Functions (p. 289)
  • 6.6 Central Limit Theorem (p. 293)
  • 7. Sample Moments and Their Distributions (p. 306)
  • 7.1 Introduction (p. 306)
  • 7.2 Random Sampling (p. 307)
  • 7.3 Sample Characteristics and Their Distributions (p. 310)
  • 7.4 Chi-Square, t-, and F-Distributions: Exact Sampling Distributions (p. 324)
  • 7.5 Large-Sample Theory (p. 334)
  • 7.6 Distribution of (X, S[superscript 2]) in Sampling from a Normal Population (p. 339)
  • 7.7 Sampling from a Bivariate Normal Distribution (p. 344)
  • 8. Parametric Point Estimation (p. 353)
  • 8.1 Introduction (p. 353)
  • 8.2 Problem of Point Estimation (p. 354)
  • 8.3 Sufficiency, Completeness, and Ancillarity (p. 358)
  • 8.4 Unbiased Estimation (p. 377)
  • 8.5 Unbiased Estimation (Continued): Lower Bound for the Variance of an Estimator (p. 391)
  • 8.6 Substitution Principle (Method of Moments) (p. 406)
  • 8.7 Maximum Likelihood Estimators (p. 409)
  • 8.8 Bayes and Minimax Estimation (p. 424)
  • 8.9 Principle of Equivariance (p. 442)
  • 9. Neyman-Pearson Theory of Testing of Hypotheses (p. 454)
  • 9.1 Introduction (p. 454)
  • 9.2 Some Fundamental Notions of Hypotheses Testing (p. 454)
  • 9.3 Neyman-Pearson Lemma (p. 464)
  • 9.4 Families with Monotone Likelihood Ratio (p. 472)
  • 9.5 Unbiased and Invariant Tests (p. 479)
  • 9.6 Locally Most Powerful Tests (p. 486)
  • 10. Some Further Results of Hypothesis Testing (p. 490)
  • 10.1 Introduction (p. 490)
  • 10.2 Generalized Likelihood Ratio Tests (p. 490)
  • 10.3 Chi-Square Tests (p. 500)
  • 10.4 t-Tests (p. 512)
  • 10.5 F-Tests (p. 518)
  • 10.6 Bayes and Minimax Procedures (p. 520)
  • 11. Confidence Estimation (p. 527)
  • 11.1 Introduction (p. 527)
  • 11.2 Some Fundamental Notions of Confidence Estimation (p. 527)
  • 11.3 Methods of Finding Confidence Intervals (p. 532)
  • 11.4 Shortest-Length Confidence Intervals (p. 546)
  • 11.5 Unbiased and Equivariant Confidence Intervals (p. 553)
  • 12. General Linear Hypothesis (p. 561)
  • 12.1 Introduction (p. 561)
  • 12.2 General Linear Hypothesis (p. 561)
  • 12.3 Regression Model (p. 569)
  • 12.4 One-Way Analysis of Variance (p. 577)
  • 12.5 Two-Way Analysis of Variance with One Observation per Cell (p. 583)
  • 12.6 Two-Way Analysis of Variance with Interaction (p. 590)
  • 13. Nonparametric Statistical Inference (p. 598)
  • 13.1 Introduction (p. 598)
  • 13.2 U-Statistics (p. 598)
  • 13.3 Some Single-Sample Problems (p. 608)
  • 13.4 Some Two-Sample Problems (p. 624)
  • 13.5 Tests of Independence (p. 633)
  • 13.6 Some Applications of Order Statistics (p. 644)
  • 13.7 Robustness (p. 650)
  • References (p. 663)
  • Frequently Used Symbols and Abbreviations (p. 669)
  • Statistical Tables (p. 673)
  • Answers to Selected Problems (p. 693)
  • Author Index (p. 705)
  • Subject Index (p. 707)

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