{"product_id":"introduction-to-probability-isbn-9781118123331","title":"Introduction to Probability","description":"\u003cb\u003eINTRODUCTION TO PROBABILITY\u003c\/b\u003e \u003cp\u003e\u003cb\u003eDiscover practical models and real-world applications of multivariate models useful in engineering, business, and related disciplines\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eIn \u003ci\u003eIntroduction to Probability: Multivariate Models and Applications, \u003c\/i\u003ea team of distinguished researchers delivers a comprehensive exploration of the concepts, methods, and results in multivariate distributions and models. Intended for use in a second course in probability, the material is largely self-contained, with some knowledge of basic probability theory and univariate distributions as the only prerequisite. \u003c\/p\u003e\u003cp\u003eThis textbook is intended as the sequel to\u003ci\u003e Introduction to Probability: Models and Applications.\u003c\/i\u003e Each chapter begins with a brief historical account of some of the pioneers in probability who made significant contributions to the field. It goes on to describe and explain a critical concept or method in multivariate models and closes with two collections of exercises designed to test basic and advanced understanding of the theory. \u003c\/p\u003e\u003cp\u003eA wide range of topics are covered, including joint distributions for two or more random variables, independence of two or more variables, transformations of variables, covariance and correlation, a presentation of the most important multivariate distributions, generating functions and limit theorems. This important text: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eIncludes classroom-tested problems and solutions to probability exercises \u003c\/li\u003e \u003cli\u003eHighlights real-world exercises designed to make clear the concepts presented \u003c\/li\u003e \u003cli\u003eUses Mathematica software to illustrate the text’s computer exercises\u003c\/li\u003e \u003cli\u003eFeatures applications representing worldwide situations and processes \u003c\/li\u003e \u003cli\u003eOffers two types of self-assessment exercises at the end of each chapter, so that students may review the material in that chapter and monitor their progress\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003ePerfect for students majoring in statistics, engineering, business, psychology, operations research and mathematics taking a second course in probability, \u003ci\u003eIntroduction to Probability: Multivariate Models and Applications\u003c\/i\u003e is also an indispensable resource for anyone who is required to use multivariate distributions to model the uncertainty associated with random phenomena. \u003c\/p\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eAcknowledgments xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Two-Dimensional Discrete Random Variables and Distributions 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 2\u003c\/p\u003e \u003cp\u003e1.2 Joint Probability Function 2\u003c\/p\u003e \u003cp\u003e1.3 Marginal Distributions 15\u003c\/p\u003e \u003cp\u003e1.4 Expectation of a Function 24\u003c\/p\u003e \u003cp\u003e1.5 Conditional Distributions and Expectations 32\u003c\/p\u003e \u003cp\u003e1.6 Basic Concepts and Formulas 41\u003c\/p\u003e \u003cp\u003e1.7 Computational Exercises 42\u003c\/p\u003e \u003cp\u003e1.8 Self-assessment Exercises 46\u003c\/p\u003e \u003cp\u003e1.8.1 True–False Questions 46\u003c\/p\u003e \u003cp\u003e1.8.2 Multiple Choice Questions 47\u003c\/p\u003e \u003cp\u003e1.9 Review Problems 50\u003c\/p\u003e \u003cp\u003e1.10 Applications 54\u003c\/p\u003e \u003cp\u003e1.10.1 Mixture Distributions and Reinsurance 54\u003c\/p\u003e \u003cp\u003eKey Terms 57\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Two-Dimensional Continuous Random Variables and Distributions 59\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 60\u003c\/p\u003e \u003cp\u003e2.2 Joint Density Function 60\u003c\/p\u003e \u003cp\u003e2.3 Marginal Distributions 73\u003c\/p\u003e \u003cp\u003e2.4 Expectation of a Function 79\u003c\/p\u003e \u003cp\u003e2.5 Conditional Distributions and Expectations 82\u003c\/p\u003e \u003cp\u003e2.6 Geometric Probability 91\u003c\/p\u003e \u003cp\u003e2.7 Basic Concepts and Formulas 98\u003c\/p\u003e \u003cp\u003e2.8 Computational Exercises 100\u003c\/p\u003e \u003cp\u003e2.9 Self-assessment Exercises 107\u003c\/p\u003e \u003cp\u003e2.9.1 True–False Questions 107\u003c\/p\u003e \u003cp\u003e2.9.2 Multiple Choice Questions 109\u003c\/p\u003e \u003cp\u003e2.10 Review Problems 111\u003c\/p\u003e \u003cp\u003e2.11 Applications 114\u003c\/p\u003e \u003cp\u003e2.11.1 Modeling Proportions 114\u003c\/p\u003e \u003cp\u003eKey Terms 119\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Independence and Multivariate Distributions 121\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 122\u003c\/p\u003e \u003cp\u003e3.2 Independence 122\u003c\/p\u003e \u003cp\u003e3.3 Properties of Independent Random Variables 137\u003c\/p\u003e \u003cp\u003e3.4 Multivariate Joint Distributions 142\u003c\/p\u003e \u003cp\u003e3.5 Independence of More Than Two Variables 156\u003c\/p\u003e \u003cp\u003e3.6 Distribution of an Ordered Sample 165\u003c\/p\u003e \u003cp\u003e3.7 Basic Concepts and Formulas 176\u003c\/p\u003e \u003cp\u003e3.8 Computational Exercises 178\u003c\/p\u003e \u003cp\u003e3.9 Self-assessment Exercises 185\u003c\/p\u003e \u003cp\u003e3.9.1 True–False Questions 185\u003c\/p\u003e \u003cp\u003e3.9.2 Multiple Choice Questions 186\u003c\/p\u003e \u003cp\u003e3.10 Review Problems 189\u003c\/p\u003e \u003cp\u003e3.11 Applications 194\u003c\/p\u003e \u003cp\u003e3.11.1 Acceptance Sampling 194\u003c\/p\u003e \u003cp\u003eKey Terms 200\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Transformations of Variables 201\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 202\u003c\/p\u003e \u003cp\u003e4.2 Joint Distribution for Functions of Variables 202\u003c\/p\u003e \u003cp\u003e4.3 Distributions of sum, difference, product and quotient 210\u003c\/p\u003e \u003cp\u003e4.4 \u003ci\u003e𝜒\u003c\/i\u003e\u003csup\u003e2\u003c\/sup\u003e, \u003ci\u003et \u003c\/i\u003eand \u003ci\u003eF \u003c\/i\u003eDistributions 223\u003c\/p\u003e \u003cp\u003e4.5 Basic Concepts and Formulas 236\u003c\/p\u003e \u003cp\u003e4.6 Computational Exercises 237\u003c\/p\u003e \u003cp\u003e4.7 Self-assessment Exercises 242\u003c\/p\u003e \u003cp\u003e4.7.1 True–False Questions 242\u003c\/p\u003e \u003cp\u003e4.7.2 Multiple Choice Questions 243\u003c\/p\u003e \u003cp\u003e4.8 Review Problems 246\u003c\/p\u003e \u003cp\u003e4.9 Applications 250\u003c\/p\u003e \u003cp\u003e4.9.1 Random Number Generators Coverage – Planning Under Random Event Occurrences 250\u003c\/p\u003e \u003cp\u003eKey Terms 255\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Covariance and Correlation 257\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 258\u003c\/p\u003e \u003cp\u003e5.2 Covariance 258\u003c\/p\u003e \u003cp\u003e5.3 Correlation Coefficient 272\u003c\/p\u003e \u003cp\u003e5.4 Conditional Expectation and Variance 281\u003c\/p\u003e \u003cp\u003e5.5 Regression Curves 293\u003c\/p\u003e \u003cp\u003e5.6 Basic Concepts and Formulas 307\u003c\/p\u003e \u003cp\u003e5.7 Computational Exercises 308\u003c\/p\u003e \u003cp\u003e5.8 Self-assessment Exercises 314\u003c\/p\u003e \u003cp\u003e5.8.1 True–False Questions 314\u003c\/p\u003e \u003cp\u003e5.8.2 Multiple Choice Questions 316\u003c\/p\u003e \u003cp\u003e5.9 Review Problems 320\u003c\/p\u003e \u003cp\u003e5.10 Applications 326\u003c\/p\u003e \u003cp\u003e5.10.1 Portfolio Optimization Theory 326\u003c\/p\u003e \u003cp\u003eKey Terms 330\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Important Multivariate Distributions 331\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 332\u003c\/p\u003e \u003cp\u003e6.2 Multinomial Distribution 332\u003c\/p\u003e \u003cp\u003e6.3 Multivariate Hypergeometric Distribution 344\u003c\/p\u003e \u003cp\u003e6.4 Bivariate Normal Distribution 358\u003c\/p\u003e \u003cp\u003e6.5 Basic Concepts and Formulas 371\u003c\/p\u003e \u003cp\u003e6.6 Computational Exercises 373\u003c\/p\u003e \u003cp\u003e6.7 Self-Assessment Exercises 378\u003c\/p\u003e \u003cp\u003e6.7.1 True–False Questions 378\u003c\/p\u003e \u003cp\u003e6.7.2 Multiple Choice Questions 380\u003c\/p\u003e \u003cp\u003e6.8 Review Problems 383\u003c\/p\u003e \u003cp\u003e6.9 Applications 387\u003c\/p\u003e \u003cp\u003e6.9.1 The Effect of Dependence on the Distribution of the Sum 387\u003c\/p\u003e \u003cp\u003eKey Terms 390\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Generating Functions 391\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 392\u003c\/p\u003e \u003cp\u003e7.2 Moment Generating Function 392\u003c\/p\u003e \u003cp\u003e7.3 Moment Generating Functions of Some Important Distributions 401\u003c\/p\u003e \u003cp\u003e7.3.1 Binomial Distribution 401\u003c\/p\u003e \u003cp\u003e7.3.2 Negative Binomial Distribution 402\u003c\/p\u003e \u003cp\u003e7.3.3 Poisson Distribution 403\u003c\/p\u003e \u003cp\u003e7.3.4 Uniform Distribution 403\u003c\/p\u003e \u003cp\u003e7.3.5 Normal Distribution 403\u003c\/p\u003e \u003cp\u003e7.3.6 Gamma Distribution 404\u003c\/p\u003e \u003cp\u003e7.4 Moment Generating Functions for Sum of Variables 407\u003c\/p\u003e \u003cp\u003e7.5 Probability Generating Function 416\u003c\/p\u003e \u003cp\u003e7.6 Characteristic Function 428\u003c\/p\u003e \u003cp\u003e7.7 Generating Functions for Multivariate Case 433\u003c\/p\u003e \u003cp\u003e7.8 Basic Concepts and Formulas 441\u003c\/p\u003e \u003cp\u003e7.9 Computational Exercises 443\u003c\/p\u003e \u003cp\u003e7.10 Self-assessment Exercises 446\u003c\/p\u003e \u003cp\u003e7.10.1 True–False Questions 446\u003c\/p\u003e \u003cp\u003e7.10.2 Multiple Choice Questions 448\u003c\/p\u003e \u003cp\u003e7.11 Review Problems 452\u003c\/p\u003e \u003cp\u003e7.12 Applications 460\u003c\/p\u003e \u003cp\u003e7.12.1 Random Walks 460\u003c\/p\u003e \u003cp\u003eKey Terms 465\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Limit Theorems 467\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 468\u003c\/p\u003e \u003cp\u003e8.2 Laws of Large Numbers 468\u003c\/p\u003e \u003cp\u003e8.3 Central Limit Theorem 476\u003c\/p\u003e \u003cp\u003e8.4 Basic Concepts and Formulas 492\u003c\/p\u003e \u003cp\u003e8.5 Computational Exercises 493\u003c\/p\u003e \u003cp\u003e8.6 Self-assessment Exercises 497\u003c\/p\u003e \u003cp\u003e8.6.1 True–False Questions 497\u003c\/p\u003e \u003cp\u003e8.6.2 Multiple Choice Questions 498\u003c\/p\u003e \u003cp\u003e8.7 Review Problems 501\u003c\/p\u003e \u003cp\u003e8.8 Applications 504\u003c\/p\u003e \u003cp\u003e8.8.1 Use of the CLT for Capacity Planning 504\u003c\/p\u003e \u003cp\u003eKey Terms 507\u003c\/p\u003e \u003cp\u003eAppendix A Tail Probability Under Standard Normal Distribution 509\u003c\/p\u003e \u003cp\u003eAppendix B Critical Values Under Chi-Square Distribution 511\u003c\/p\u003e \u003cp\u003eAppendix C Student’s \u003ci\u003et\u003c\/i\u003e-Distribution 515\u003c\/p\u003e \u003cp\u003eAppendix D \u003ci\u003eF\u003c\/i\u003e-Distribution: 5% (Lightface Type) and 1% (Boldface Type) Points for the \u003ci\u003eF\u003c\/i\u003e-Distribution 517\u003c\/p\u003e \u003cp\u003eAppendix E Generating Functions 521\u003c\/p\u003e \u003cp\u003eBibliography 525\u003c\/p\u003e \u003cp\u003eIndex 527\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eN. Balakrishnan, PhD,\u003c\/b\u003e is Distinguished University Professor in the Department of Mathematics and Statistics at McMaster University in Ontario, Canada. He is the author of over twenty books, including \u003ci\u003eEncyclopedia of Statistical Sciences, Second Edition.\u003c\/i\u003e \u003c\/p\u003e\u003cp\u003e\u003cb\u003eMarkos V. Koutras, PhD,\u003c\/b\u003e is Professor in the Department of Statistics and Insurance Science at the University of Piraeus. He is the author\/coauthor\/editor of 19 books (13 in Greek, 6 in English). His research interests include multivariate analysis, combinatorial distributions, theory of runs\/scans\/patterns, statistical quality control, and reliability theory. \u003c\/p\u003e\u003cp\u003e\u003cb\u003eKonstadinos G. Politis, PhD,\u003c\/b\u003e is Associate Professor in the Department of Statistics and Insurance Science at the University of Piraeus. He is the author of several articles ­published in scientific journals.   \u003c\/p\u003e\u003cp\u003e\u003cb\u003eDiscover practical models and real-world applications of multivariate models useful in engineering, business, and related disciplines\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eIn \u003ci\u003eIntroduction to Probability: Multivariate Models and Applications, \u003c\/i\u003ea team of distinguished researchers delivers a comprehensive exploration of the concepts, methods, and results in multivariate distributions and models. Intended for use in a second course in probability, the material is largely self-contained, with some knowledge of basic probability theory and univariate distributions as the only prerequisite. \u003c\/p\u003e\u003cp\u003eThis textbook is intended as the sequel to\u003ci\u003e Introduction to Probability: Models and Applications.\u003c\/i\u003e Each chapter begins with a brief historical account of some of the pioneers in probability who made significant contributions to the field. It goes on to describe and explain a critical concept or method in multivariate models and closes with two collections of exercises designed to test basic and advanced understanding of the theory. \u003c\/p\u003e\u003cp\u003eA wide range of topics are covered, including joint distributions for two or more random variables, independence of two or more variables, transformations of variables, covariance and correlation, a presentation of the most important multivariate distributions, generating functions and limit theorems. This important text: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eIncludes classroom-tested problems and solutions to probability exercises\u003c\/li\u003e \u003cli\u003eHighlights real-world exercises designed to make clear the concepts presented\u003c\/li\u003e \u003cli\u003eUses Mathematica software to illustrate the text’s computer exercises\u003c\/li\u003e \u003cli\u003eFeatures applications representing worldwide situations and processes\u003c\/li\u003e \u003cli\u003eOffers two types of self-assessment exercises at the end of each chapter, so that students may review the material in that chapter and monitor their progress\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003ePerfect for students majoring in statistics, engineering, business, psychology, operations research and mathematics taking a second course in probability, \u003ci\u003eIntroduction to Probability: Multivariate Models and Applications\u003c\/i\u003e is also an indispensable resource for anyone who is required to use multivariate distributions to model the uncertainty associated with random phenomena.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989465252069,"sku":"NP9781118123331","price":146.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118123331.jpg?v=1761784211","url":"https:\/\/k12savings.com\/es\/products\/introduction-to-probability-isbn-9781118123331","provider":"K12savings","version":"1.0","type":"link"}