{"product_id":"an-introduction-to-probability-and-statistics-isbn-9781118799642","title":"An Introduction to Probability and Statistics","description":"\u003cp\u003e\u003cb\u003eA well-balanced introduction to probability theory and mathematical statistics\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eFeaturing updated material, \u003ci\u003eAn Introduction to Probability and Statistics, Third Edition \u003c\/i\u003eremains a solid overview to probability theory and mathematical statistics. Divided intothree parts, the \u003ci\u003eThird Edition \u003c\/i\u003ebegins by presenting the fundamentals and foundationsof probability. The second part addresses statistical inference, and the remainingchapters focus on special topics.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eAn Introduction to Probability and Statistics, Third Edition \u003c\/i\u003eincludes:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eA new section on regression analysis to include multiple regression, logistic regression, and Poisson regression\u003c\/li\u003e \u003cli\u003eA reorganized chapter on large sample theory to emphasize the growing role of asymptotic statistics\u003c\/li\u003e \u003cli\u003eAdditional topical coverage on bootstrapping, estimation procedures, and resampling\u003c\/li\u003e \u003cli\u003eDiscussions on invariance, ancillary statistics, conjugate prior distributions, and invariant confidence intervals\u003c\/li\u003e \u003cli\u003eOver 550 problems and answers to most problems, as well as 350 worked out examples and 200 remarks\u003c\/li\u003e \u003cli\u003eNumerous figures to further illustrate examples and proofs throughout\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eAn Introduction to Probability and Statistics, Third Edition \u003c\/i\u003eis an ideal reference and resource for scientists and engineers in the fields of statistics, mathematics, physics, industrial management, and engineering. The book is also an excellent text for upper-undergraduate and graduate-level students majoring in probability and statistics.\u003c\/p\u003e \u003cp\u003ePREFACE TO THE THIRD EDITION xiii\u003c\/p\u003e \u003cp\u003ePREFACE TO THE SECOND EDITION xv\u003c\/p\u003e \u003cp\u003ePREFACE TO THE FIRST EDITION xvii\u003c\/p\u003e \u003cp\u003eACKNOWLEDGMENTS xix\u003c\/p\u003e \u003cp\u003eENUMERATION OF THEOREMS AND REFERENCES xxi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Probability 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.2 Sample Space 2\u003c\/p\u003e \u003cp\u003e1.3 Probability Axioms 7\u003c\/p\u003e \u003cp\u003e1.4 Combinatorics: Probability on Finite Sample Spaces 20\u003c\/p\u003e \u003cp\u003e1.5 Conditional Probability and Bayes Theorem 26\u003c\/p\u003e \u003cp\u003e1.6 Independence of Events 31\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Random Variables and Their Probability Distributions 39\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 39\u003c\/p\u003e \u003cp\u003e2.2 Random Variables 39\u003c\/p\u003e \u003cp\u003e2.3 Probability Distribution of a Random Variable 42\u003c\/p\u003e \u003cp\u003e2.4 Discrete and Continuous Random Variables 47\u003c\/p\u003e \u003cp\u003e2.5 Functions of a Random Variable 55\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Moments and Generating Functions 67\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 67\u003c\/p\u003e \u003cp\u003e3.2 Moments of a Distribution Function 67\u003c\/p\u003e \u003cp\u003e3.3 Generating Functions 83\u003c\/p\u003e \u003cp\u003e3.4 Some Moment Inequalities 93\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Multiple Random Variables 99\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 99\u003c\/p\u003e \u003cp\u003e4.2 Multiple Random Variables 99\u003c\/p\u003e \u003cp\u003e4.3 Independent Random Variables 114\u003c\/p\u003e \u003cp\u003e4.4 Functions of Several Random Variables 123\u003c\/p\u003e \u003cp\u003e4.5 Covariance, Correlation and Moments 143\u003c\/p\u003e \u003cp\u003e4.6 Conditional Expectation 157\u003c\/p\u003e \u003cp\u003e4.7 Order Statistics and Their Distributions 164\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Some Special Distributions 173\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 173\u003c\/p\u003e \u003cp\u003e5.2 Some Discrete Distributions 173\u003c\/p\u003e \u003cp\u003e5.2.1 Degenerate Distribution 173\u003c\/p\u003e \u003cp\u003e5.2.2 Two-Point Distribution 174\u003c\/p\u003e \u003cp\u003e5.2.3 Uniform Distribution on n Points 175\u003c\/p\u003e \u003cp\u003e5.2.4 Binomial Distribution 176\u003c\/p\u003e \u003cp\u003e5.2.5 Negative Binomial Distribution (Pascal or Waiting Time Distribution) 178\u003c\/p\u003e \u003cp\u003e5.2.6 Hypergeometric Distribution 183\u003c\/p\u003e \u003cp\u003e5.2.7 Negative Hypergeometric Distribution 185\u003c\/p\u003e \u003cp\u003e5.2.8 Poisson Distribution 186\u003c\/p\u003e \u003cp\u003e5.2.9 Multinomial Distribution 189\u003c\/p\u003e \u003cp\u003e5.2.10 Multivariate Hypergeometric Distribution 192\u003c\/p\u003e \u003cp\u003e5.2.11 Multivariate Negative Binomial Distribution 192\u003c\/p\u003e \u003cp\u003e5.3 Some Continuous Distributions 196\u003c\/p\u003e \u003cp\u003e5.3.1 Uniform Distribution (Rectangular Distribution) 199\u003c\/p\u003e \u003cp\u003e5.3.2 Gamma Distribution 202\u003c\/p\u003e \u003cp\u003e5.3.3 Beta Distribution 210\u003c\/p\u003e \u003cp\u003e5.3.4 Cauchy Distribution 213\u003c\/p\u003e \u003cp\u003e5.3.5 Normal Distribution (the Gaussian Law) 216\u003c\/p\u003e \u003cp\u003e5.3.6 Some Other Continuous Distributions 222\u003c\/p\u003e \u003cp\u003e5.4 Bivariate and Multivariate Normal Distributions 228\u003c\/p\u003e \u003cp\u003e5.5 Exponential Family of Distributions 240\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Sample Statistics and Their Distributions 245\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 245\u003c\/p\u003e \u003cp\u003e6.2 Random Sampling 246\u003c\/p\u003e \u003cp\u003e6.3 Sample Characteristics and Their Distributions 249\u003c\/p\u003e \u003cp\u003e6.4 Chi-Square, t-, and F-Distributions: Exact Sampling Distributions 262\u003c\/p\u003e \u003cp\u003e6.5 Distribution of (X,S2) in Sampling from a Normal Population 271\u003c\/p\u003e \u003cp\u003e6.6 Sampling from a Bivariate Normal Distribution 276\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Basic Asymptotics: Large Sample Theory 285\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 285\u003c\/p\u003e \u003cp\u003e7.2 Modes of Convergence 285\u003c\/p\u003e \u003cp\u003e7.3 Weak Law of Large Numbers 302\u003c\/p\u003e \u003cp\u003e7.4 Strong Law of Large Numbers 308\u003c\/p\u003e \u003cp\u003e7.5 Limiting Moment Generating Functions 316\u003c\/p\u003e \u003cp\u003e7.6 Central Limit Theorem 321\u003c\/p\u003e \u003cp\u003e7.7 Large Sample Theory 331\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Parametric Point Estimation 337\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 337\u003c\/p\u003e \u003cp\u003e8.2 Problem of Point Estimation 338\u003c\/p\u003e \u003cp\u003e8.3 Sufficiency, Completeness and Ancillarity 342\u003c\/p\u003e \u003cp\u003e8.4 Unbiased Estimation 359\u003c\/p\u003e \u003cp\u003e8.5 Unbiased Estimation (Continued): A Lower Bound for the Variance of An Estimator 372\u003c\/p\u003e \u003cp\u003e8.6 Substitution Principle (Method of Moments) 386\u003c\/p\u003e \u003cp\u003e8.7 Maximum Likelihood Estimators 388\u003c\/p\u003e \u003cp\u003e8.8 Bayes and Minimax Estimation 401\u003c\/p\u003e \u003cp\u003e8.9 Principle of Equivariance 418\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Neyman–Pearson Theory of Testing of Hypotheses 429\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 429\u003c\/p\u003e \u003cp\u003e9.2 Some Fundamental Notions of Hypotheses Testing 429\u003c\/p\u003e \u003cp\u003e9.3 Neyman–Pearson Lemma 438\u003c\/p\u003e \u003cp\u003e9.4 Families with Monotone Likelihood Ratio 446\u003c\/p\u003e \u003cp\u003e9.5 Unbiased and Invariant Tests 453\u003c\/p\u003e \u003cp\u003e9.6 Locally Most Powerful Tests 459\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Some Further Results on Hypotheses Testing 463\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 463\u003c\/p\u003e \u003cp\u003e10.2 Generalized Likelihood Ratio Tests 463\u003c\/p\u003e \u003cp\u003e10.3 Chi-Square Tests 472\u003c\/p\u003e \u003cp\u003e10.4 t-Tests 484\u003c\/p\u003e \u003cp\u003e10.5 F-Tests 489\u003c\/p\u003e \u003cp\u003e10.6 Bayes and Minimax Procedures 491\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Confidence Estimation 499\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 499\u003c\/p\u003e \u003cp\u003e11.2 Some Fundamental Notions of Confidence Estimation 499\u003c\/p\u003e \u003cp\u003e11.3 Methods of Finding Confidence Intervals 504\u003c\/p\u003e \u003cp\u003e11.4 Shortest-Length Confidence Intervals 517\u003c\/p\u003e \u003cp\u003e11.5 Unbiased and Equivariant Confidence Intervals 523\u003c\/p\u003e \u003cp\u003e11.6 Resampling: Bootstrap Method 530\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 General Linear Hypothesis 535\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 535\u003c\/p\u003e \u003cp\u003e12.2 General Linear Hypothesis 535\u003c\/p\u003e \u003cp\u003e12.3 Regression Analysis 543\u003c\/p\u003e \u003cp\u003e12.3.1 Multiple Linear Regression 543\u003c\/p\u003e \u003cp\u003e12.3.2 Logistic and Poisson Regression 551\u003c\/p\u003e \u003cp\u003e12.4 One-Way Analysis of Variance 554\u003c\/p\u003e \u003cp\u003e12.5 Two-Way Analysis of Variance with One Observation Per Cell 560\u003c\/p\u003e \u003cp\u003e12.6 Two-Way Analysis of Variance with Interaction 566\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Nonparametric Statistical Inference 575\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 575\u003c\/p\u003e \u003cp\u003e13.2 U-Statistics 576\u003c\/p\u003e \u003cp\u003e13.3 Some Single-Sample Problems 584\u003c\/p\u003e \u003cp\u003e13.3.1 Goodness-of-Fit Problem 584\u003c\/p\u003e \u003cp\u003e13.3.2 Problem of Location 590\u003c\/p\u003e \u003cp\u003e13.4 Some Two-Sample Problems 599\u003c\/p\u003e \u003cp\u003e13.4.1 Median Test 601\u003c\/p\u003e \u003cp\u003e13.4.2 Kolmogorov–Smirnov Test 602\u003c\/p\u003e \u003cp\u003e13.4.3 The Mann–Whitney–Wilcoxon Test 604\u003c\/p\u003e \u003cp\u003e13.5 Tests of Independence 608\u003c\/p\u003e \u003cp\u003e13.5.1 Chi-square Test of Independence—Contingency Tables 608\u003c\/p\u003e \u003cp\u003e13.5.2 Kendall’s Tau 611\u003c\/p\u003e \u003cp\u003e13.5.3 Spearman’s Rank Correlation Coefficient 614\u003c\/p\u003e \u003cp\u003e13.6 Some Applications of Order Statistics 619\u003c\/p\u003e \u003cp\u003e13.7 Robustness 625\u003c\/p\u003e \u003cp\u003e13.7.1 Effect of Deviations from Model Assumptions on Some Parametric Procedures 625\u003c\/p\u003e \u003cp\u003e13.7.2 Some Robust Procedures 631\u003c\/p\u003e \u003cp\u003eFREQUENTLY USED SYMBOLS AND ABBREVIATIONS 637\u003c\/p\u003e \u003cp\u003eREFERENCES 641\u003c\/p\u003e \u003cp\u003eSTATISTICAL TABLES 647\u003c\/p\u003e \u003cp\u003eANSWERS TO SELECTED PROBLEMS 667\u003c\/p\u003e \u003cp\u003eAUTHOR INDEX 677\u003c\/p\u003e \u003cp\u003eSUBJECT INDEX 679\u003c\/p\u003e \u003cp\u003e\"The book is an ideal reference and resource for scientists and engineers in the elds of statistics, mathematics, physics, industrial management, and engineering. The book is also an excellent text for upper-undergraduate and graduate-level students majoring in probability and statistics.\" (\u003ci\u003eZentralblatt MATH\u003c\/i\u003e, 2016)\u003c\/p\u003e \u003cp\u003e\u003cb\u003eVijay K. Rohatgi, PhD,\u003c\/b\u003e is Professor Emeritus in the Department of Mathematics and Statistics at Bowling Green State University.  An Investment Research Consultant for PRI Investments, he is also the author of several books and over 100 research papers. \u003c\/p\u003e \u003cp\u003e\u003cb\u003eA. K. Md. Ehsanes Saleh, PhD,\u003c\/b\u003e is Distinguished Research Professor in the School of Mathematics and Statistics at Carleton University. Dr. Saleh is the author of more than 200 journal articles, and his research interests include nonparametric statistics, order statistics, and robust estimation. \u003c\/p\u003e \u003cp\u003e\u003cb\u003eA well-balanced introduction to probability theory and mathematical statistics\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eFeaturing a comprehensive update,\u003ci\u003e An Introduction to Probability and Statistics, Third Edition\u003c\/i\u003e remains a solid overview to probability theory and mathematical statistics. Divided into three parts, the \u003ci\u003eThird Edition \u003c\/i\u003ebegins by presenting the fundamentals and foundations of probability. The second part addresses statistical inference, and the remaining chapters focus on special topics.\u003c\/p\u003e \u003cp\u003eFeaturing a substantial revision to include recent developments, \u003ci\u003eAn Introduction to Probability and Statistics, Third Edition\u003c\/i\u003e also includes:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eA new section on regression analysis to include multiple regression, logistic regression, and Poisson regression\u003c\/li\u003e \u003cli\u003eA reorganized chapter on large sample theory to emphasize the growing role of asymptotic statistics\u003c\/li\u003e \u003cli\u003eAdditional topical coverage on bootstrapping, estimation procedures, and resampling\u003c\/li\u003e \u003cli\u003eDiscussions on invariance, ancillary statistics, conjugate prior distributions, and invariant confidence intervals\u003c\/li\u003e \u003cli\u003eOver 550 problems and answers to  most  problems, as well as 350 worked-out examples and 200 remarks\u003c\/li\u003e \u003cli\u003eNumerous figures to further illustrate examples and proofs throughout\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eAn Introduction to Probability and Statistics, Third Edition\u003c\/i\u003e is an ideal reference and resource for scientists and engineers in the fields of statistics, mathematics, physics, industrial management, and engineering. The book is also an excellent text for upper-undergraduate and graduate- level students majoring in probability and statistics.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eVijay K. Rohatgi, PhD,\u003c\/b\u003e is Professor Emeritus in the Department of Mathematics and Statistics at Bowling Green State University.  An Investment Research Consultant for PRI Investments, he is also the author of several books and over 100 research papers. \u003c\/p\u003e \u003cp\u003e\u003cb\u003eA. K. Md. Ehsanes Saleh, PhD,\u003c\/b\u003e is Distinguished Research Professor in the School of Mathematics and Statistics at Carleton University. Dr. Saleh is the author of more than 200 journal articles, and his research interests include nonparametric statistics, order statistics, and robust estimation. \u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988729151717,"sku":"NP9781118799642","price":144.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118799642.jpg?v=1761781359","url":"https:\/\/k12savings.com\/products\/an-introduction-to-probability-and-statistics-isbn-9781118799642","provider":"K12savings","version":"1.0","type":"link"}