{"product_id":"introduction-to-probability-9781118123331","title":"Introduction to Probability","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\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 te\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\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","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406833525079,"sku":"9781118123331","price":99.86,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118123331.jpg?v=1730497273","url":"https:\/\/bookcurl.com\/products\/introduction-to-probability-9781118123331","provider":"Book Curl","version":"1.0","type":"link"}