{"product_id":"handbook-of-probability-hardback-9780470647271","title":"Handbook of Probability (Hardback) 9780470647271","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eHandbook of Probability\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eIonut Florescu (Author), Ciprian A. Tudor (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780470647271, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 20 December 2013\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e472 pages, Tables: 175 B\u0026amp;W, 0 Color; Graphs: 125 B\u0026amp;W, 0 Color\u003cbr\u003e23.6 x 15.8 x 3 cm, 0.748 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e“On the whole, the book has two features that set it apart from similar books: the full solutions and the examples from finance. It is up to you to decide if that makes it worth your time checking it out.”  (\u003ci\u003eMathematical Association of America\u003c\/i\u003e, 1 November 2014)\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003cb\u003eTHE COMPLETE COLLECTION NECESSARY FOR A CONCRETE UNDERSTANDING OF PROBABILITY\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eWritten in a clear, accessible, and comprehensive manner, the \u003ci\u003eHandbook of Probability\u003c\/i\u003e presents the fundamentals of probability with an emphasis on the balance of theory, application, and methodology. Utilizing basic examples throughout, the handbook expertly transitions between concepts and practice to allow readers an inclusive introduction to the field of probability.\u003c\/p\u003e \u003cp\u003e\u003cbr\u003eThe book provides a useful format with self-contained chapters, allowing the reader easy and quick reference. Each chapter includes an introduction, historical background, theory and applications, algorithms, and exercises. The \u003ci\u003eHandbook of Probability\u003c\/i\u003e offers coverage of:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eProbability Space \u003c\/li\u003e \u003cli\u003eProbability Measure\u003c\/li\u003e \u003cli\u003eRandom Variables\u003c\/li\u003e \u003cli\u003eRandom Vectors in Rn\u003c\/li\u003e \u003cli\u003eCharacteristic Function\u003c\/li\u003e \u003cli\u003eMoment Generating Function\u003c\/li\u003e \u003cli\u003eGaussian Random Vectors\u003c\/li\u003e \u003cli\u003eConvergence Types\u003c\/li\u003e \u003cli\u003eLimit Theorems\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThe \u003ci\u003eHandbook of Probability\u003c\/i\u003e is an ideal resource for researchers and practitioners in numerous fields, such as mathematics, statistics, operations research, engineering, medicine, and finance, as well as a useful text for graduate students.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eList of Figures xv\u003cbr\u003e \u003cbr\u003e Preface xvii\u003cbr\u003e \u003cbr\u003e Introduction xix\u003cbr\u003e \u003cbr\u003e \u003cb\u003e1 Probability Space 1\u003c\/b\u003e\u003cbr\u003e \u003cbr\u003e 1.1 Introduction\/Purpose of the Chapter 1\u003cbr\u003e \u003cbr\u003e 1.2 Vignette\/Historical Notes 2\u003cbr\u003e \u003cbr\u003e 1.3 Notations and Definitions 2\u003cbr\u003e \u003cbr\u003e 1.4 Theory and Applications 4\u003cbr\u003e \u003cbr\u003e 1.4.1 Algebras 4\u003cbr\u003e \u003cbr\u003e 1.4.2 Sigma Algebras 5\u003cbr\u003e \u003cbr\u003e 1.4.3 Measurable Spaces 7\u003cbr\u003e \u003cbr\u003e 1.4.4 Examples 7\u003cbr\u003e \u003cbr\u003e 1.4.5 The Borel _-Algebra 9\u003cbr\u003e \u003cbr\u003e 1.5 Summary 12\u003cbr\u003e \u003cbr\u003e Exercises 12\u003cbr\u003e \u003cbr\u003e \u003cb\u003e2 Probability Measure 15\u003c\/b\u003e\u003cbr\u003e \u003cbr\u003e 2.1 Introduction\/Purpose of the Chapter 15\u003cbr\u003e \u003cbr\u003e 2.2 Vignette\/Historical Notes 16\u003cbr\u003e \u003cbr\u003e 2.3 Theory and Applications 17\u003cbr\u003e \u003cbr\u003e 2.3.1 Definition and Basic Properties 17\u003cbr\u003e \u003cbr\u003e 2.3.2 Uniqueness of Probability Measures 22\u003cbr\u003e \u003cbr\u003e 2.3.3 Monotone Class 24\u003cbr\u003e \u003cbr\u003e 2.3.4 Examples 26\u003cbr\u003e \u003cbr\u003e 2.3.5 Monotone Convergence Properties of Probability 28\u003cbr\u003e \u003cbr\u003e 2.3.6 Conditional Probability 31\u003cbr\u003e \u003cbr\u003e 2.3.7 Independence of Events and _-Fields 39\u003cbr\u003e \u003cbr\u003e 2.3.8 Borel–Cantelli Lemmas 46\u003cbr\u003e \u003cbr\u003e 2.3.9 Fatou’s Lemmas 48\u003cbr\u003e \u003cbr\u003e 2.3.10 Kolmogorov’s Zero–One Law 49\u003cbr\u003e \u003cbr\u003e 2.4 Lebesgue Measure on the Unit Interval (01] 50\u003cbr\u003e \u003cbr\u003e Exercises 52\u003cbr\u003e \u003cbr\u003e \u003cb\u003e3 Random Variables: Generalities 63\u003c\/b\u003e\u003cbr\u003e \u003cbr\u003e 3.1 Introduction\/Purpose of the Chapter 63\u003cbr\u003e \u003cbr\u003e 3.2 Vignette\/Historical Notes 63\u003cbr\u003e \u003cbr\u003e 3.3 Theory and Applications 64\u003cbr\u003e \u003cbr\u003e 3.3.1 Definition 64\u003cbr\u003e \u003cbr\u003e 3.3.2 The Distribution of a Random Variable 65\u003cbr\u003e \u003cbr\u003e 3.3.3 The Cumulative Distribution Function of a Random Variable 67\u003cbr\u003e \u003cbr\u003e 3.3.4 Independence of Random Variables 70\u003cbr\u003e \u003cbr\u003e Exercises 71\u003cbr\u003e \u003cbr\u003e \u003cb\u003e4 Random Variables: The Discrete Case 79\u003c\/b\u003e\u003cbr\u003e \u003cbr\u003e 4.1 Introduction\/Purpose of the Chapter 79\u003cbr\u003e \u003cbr\u003e 4.2 Vignette\/Historical Notes 80\u003cbr\u003e \u003cbr\u003e 4.3 Theory and Applications 80\u003cbr\u003e \u003cbr\u003e 4.3.1 Definition and Basic Facts 80\u003cbr\u003e \u003cbr\u003e 4.3.2 Moments 84\u003cbr\u003e \u003cbr\u003e 4.4 Examples of Discrete Random Variables 89\u003cbr\u003e \u003cbr\u003e 4.4.1 The (Discrete) Uniform Distribution 89\u003cbr\u003e \u003cbr\u003e 4.4.2 Bernoulli Distribution 91\u003cbr\u003e \u003cbr\u003e 4.4.3 Binomial (n p) Distribution 92\u003cbr\u003e \u003cbr\u003e 4.4.4 Geometric (p) Distribution 95\u003cbr\u003e \u003cbr\u003e 4.4.5 Negative Binomial (r p) Distribution 101\u003cbr\u003e \u003cbr\u003e 4.4.6 Hypergeometric Distribution (N m n) 102\u003cbr\u003e \u003cbr\u003e 4.4.7 Poisson Distribution 104\u003cbr\u003e \u003cbr\u003e Exercises 108\u003cbr\u003e \u003cbr\u003e \u003cb\u003e5 Random Variables: The Continuous Case 119\u003c\/b\u003e\u003cbr\u003e \u003cbr\u003e 5.1 Introduction\/Purpose of the Chapter 119\u003cbr\u003e \u003cbr\u003e 5.2 Vignette\/Historical Notes 119\u003cbr\u003e \u003cbr\u003e 5.3 Theory and Applications 120\u003cbr\u003e \u003cbr\u003e 5.3.1 Probability Density Function (p.d.f.) 120\u003cbr\u003e \u003cbr\u003e 5.3.2 Cumulative Distribution Function (c.d.f.) 124\u003cbr\u003e \u003cbr\u003e 5.3.3 Moments 127\u003cbr\u003e \u003cbr\u003e 5.3.4 Distribution of a Function of the Random Variable 128\u003cbr\u003e \u003cbr\u003e 5.4 Examples 130\u003cbr\u003e \u003cbr\u003e 5.4.1 Uniform Distribution on an Interval [ab] 130\u003cbr\u003e \u003cbr\u003e 5.4.2 Exponential Distribution 133\u003cbr\u003e \u003cbr\u003e 5.4.3 Normal Distribution (_ _2) 136\u003cbr\u003e \u003cbr\u003e 5.4.4 Gamma Distribution 139\u003cbr\u003e \u003cbr\u003e 5.4.5 Beta Distribution 144\u003cbr\u003e \u003cbr\u003e 5.4.6 Student’s t Distribution 147\u003cbr\u003e \u003cbr\u003e 5.4.7 Pareto Distribution 149\u003cbr\u003e \u003cbr\u003e 5.4.8 The Log-Normal Distribution 151\u003cbr\u003e \u003cbr\u003e 5.4.9 Laplace Distribution 153\u003cbr\u003e \u003cbr\u003e 5.4.10 Double Exponential Distribution 155\u003cbr\u003e \u003cbr\u003e Exercises 156\u003cbr\u003e \u003cbr\u003e \u003cb\u003e6 Generating Random Variables 177\u003c\/b\u003e\u003cbr\u003e \u003cbr\u003e 6.1 Introduction\/Purpose of the Chapter 177\u003cbr\u003e \u003cbr\u003e 6.2 Vignette\/Historical Notes 178\u003cbr\u003e \u003cbr\u003e 6.3 Theory and Applications 178\u003cbr\u003e \u003cbr\u003e 6.3.1 Generating One-Dimensional Random Variables by Inverting the Cumulative Distribution Function (c.d.f.) 178\u003cbr\u003e \u003cbr\u003e 6.3.2 Generating One-Dimensional Normal Random Variables 183\u003cbr\u003e \u003cbr\u003e 6.3.3 Generating Random Variables. Rejection Sampling Method 186\u003cbr\u003e \u003cbr\u003e 6.3.4 Generating from a Mixture of Distributions 193\u003cbr\u003e \u003cbr\u003e 6.3.5 Generating Random Variables. Importance Sampling 195\u003cbr\u003e \u003cbr\u003e 6.3.6 Applying Importance Sampling 198\u003cbr\u003e \u003cbr\u003e 6.3.7 Practical Consideration: Normalizing Distributions 201\u003cbr\u003e \u003cbr\u003e 6.3.8 Sampling Importance Resampling 203\u003cbr\u003e \u003cbr\u003e 6.3.9 Adaptive Importance Sampling 204\u003cbr\u003e \u003cbr\u003e 6.4 Generating Multivariate Distributions with Prescribed Covariance Structure 205\u003cbr\u003e \u003cbr\u003e Exercises 208\u003cbr\u003e \u003cbr\u003e \u003cb\u003e7 Random Vectors in Rn 210\u003c\/b\u003e\u003cbr\u003e \u003cbr\u003e 7.1 Introduction\/Purpose of the Chapter 210\u003cbr\u003e \u003cbr\u003e 7.2 Vignette\/Historical Notes 210\u003cbr\u003e \u003cbr\u003e 7.3 Theory and Applications 211\u003cbr\u003e \u003cbr\u003e 7.3.1 The Basics 211\u003cbr\u003e \u003cbr\u003e 7.3.2 Marginal Distributions 212\u003cbr\u003e \u003cbr\u003e 7.3.3 Discrete Random Vectors 214\u003cbr\u003e \u003cbr\u003e 7.3.4 Multinomial Distribution 219\u003cbr\u003e \u003cbr\u003e 7.3.5 Testing Whether Counts are Coming from a Specific Multinomial Distribution 220\u003cbr\u003e \u003cbr\u003e 7.3.6 Independence 221\u003cbr\u003e \u003cbr\u003e 7.3.7 Continuous Random Vectors 223\u003cbr\u003e \u003cbr\u003e 7.3.8 Change of Variables. Obtaining Densities of Functions of Random Vectors 229\u003cbr\u003e \u003cbr\u003e 7.3.9 Distribution of Sums of Random Variables. Convolutions 231\u003cbr\u003e \u003cbr\u003e Exercises 236\u003cbr\u003e \u003cbr\u003e \u003cb\u003e8 Characteristic Function 255\u003c\/b\u003e\u003cbr\u003e \u003cbr\u003e 8.1 Introduction\/Purpose of the Chapter 255\u003cbr\u003e \u003cbr\u003e 8.2 Vignette\/Historical Notes 255\u003cbr\u003e \u003cbr\u003e 8.3 Theory and Applications 256\u003cbr\u003e \u003cbr\u003e 8.3.1 Definition and Basic Properties 256\u003cbr\u003e \u003cbr\u003e 8.3.2 The Relationship Between the Characteristic Function and the Distribution 260\u003cbr\u003e \u003cbr\u003e 8.4 Calculation of the Characteristic Function for Commonly Encountered Distributions 265\u003cbr\u003e \u003cbr\u003e 8.4.1 Bernoulli and Binomial 265\u003cbr\u003e \u003cbr\u003e 8.4.2 Uniform Distribution 266\u003cbr\u003e \u003cbr\u003e 8.4.3 Normal Distribution 267\u003cbr\u003e \u003cbr\u003e 8.4.4 Poisson Distribution 267\u003cbr\u003e \u003cbr\u003e 8.4.5 Gamma Distribution 268\u003cbr\u003e \u003cbr\u003e 8.4.6 Cauchy Distribution 269\u003cbr\u003e \u003cbr\u003e 8.4.7 Laplace Distribution 270\u003cbr\u003e \u003cbr\u003e 8.4.8 Stable Distributions. L´evy Distribution 271\u003cbr\u003e \u003cbr\u003e 8.4.9 Truncated L´evy Flight Distribution 274\u003cbr\u003e \u003cbr\u003e Exercises 275\u003cbr\u003e \u003cbr\u003e \u003cb\u003e9 Moment-Generating Function 280\u003c\/b\u003e\u003cbr\u003e \u003cbr\u003e 9.1 Introduction\/Purpose of the Chapter 280\u003cbr\u003e \u003cbr\u003e 9.2 Vignette\/Historical Notes 280\u003cbr\u003e \u003cbr\u003e 9.3 Theory and Applications 281\u003cbr\u003e \u003cbr\u003e 9.3.1 Generating Functions and Applications 281\u003cbr\u003e \u003cbr\u003e 9.3.2 Moment-Generating Functions. Relation with the Characteristic Functions 288\u003cbr\u003e \u003cbr\u003e 9.3.3 Relationship with the Characteristic Function 292\u003cbr\u003e \u003cbr\u003e 9.3.4 Properties of the MGF 292\u003cbr\u003e \u003cbr\u003e Exercises 294\u003cbr\u003e \u003cbr\u003e \u003cb\u003e10 Gaussian Random Vectors 300\u003c\/b\u003e\u003cbr\u003e \u003cbr\u003e 10.1 Introduction\/Purpose of the Chapter 300\u003cbr\u003e \u003cbr\u003e 10.2 Vignette\/Historical Notes 301\u003cbr\u003e \u003cbr\u003e 10.3 Theory and Applications 301\u003cbr\u003e \u003cbr\u003e 10.3.1 The Basics 301\u003cbr\u003e \u003cbr\u003e 10.3.2 Equivalent Definitions of a Gaussian Vector 303\u003cbr\u003e \u003cbr\u003e 10.3.3 Uncorrelated Components and Independence 309\u003cbr\u003e \u003cbr\u003e 10.3.4 The Density of a Gaussian Vector 313\u003cbr\u003e \u003cbr\u003e 10.3.5 Cochran’s Theorem 316\u003cbr\u003e \u003cbr\u003e 10.3.6 Matrix Diagonalization and Gaussian Vectors 319\u003cbr\u003e \u003cbr\u003e Exercises 325\u003cbr\u003e \u003cbr\u003e \u003cb\u003e11 Convergence Types. Almost Sure Convergence. Lp-Convergence. Convergence in Probability 338\u003c\/b\u003e\u003cbr\u003e \u003cbr\u003e 11.1 Introduction\/Purpose of the Chapter 338\u003cbr\u003e \u003cbr\u003e 11.2 Vignette\/Historical Notes 339\u003cbr\u003e \u003cbr\u003e 11.3 Theory and Applications: Types of Convergence 339\u003cbr\u003e \u003cbr\u003e 11.3.1 Traditional Deterministic Convergence Types 339\u003cbr\u003e \u003cbr\u003e 11.3.2 Convergence of Moments of an r.v.—Convergence in Lp 341\u003cbr\u003e \u003cbr\u003e 11.3.3 Almost Sure (a.s.) Convergence 342\u003cbr\u003e \u003cbr\u003e 11.3.4 Convergence in Probability 344\u003cbr\u003e \u003cbr\u003e 11.4 Relationships Between Types of Convergence 346\u003cbr\u003e \u003cbr\u003e 11.4.1 a.s. and Lp 347\u003cbr\u003e \u003cbr\u003e 11.4.2 Probability and a.s.\/Lp 351\u003cbr\u003e \u003cbr\u003e 11.4.3 Uniform Integrability 357\u003cbr\u003e \u003cbr\u003e Exercises 359\u003cbr\u003e \u003cbr\u003e \u003cb\u003e12 Limit Theorems 372\u003c\/b\u003e\u003cbr\u003e \u003cbr\u003e 12.1 Introduction\/Purpose of the Chapter 372\u003cbr\u003e \u003cbr\u003e 12.2 Vignette\/Historical Notes 372\u003cbr\u003e \u003cbr\u003e 12.3 Theory and Applications 375\u003cbr\u003e \u003cbr\u003e 12.3.1 Weak Convergence 375\u003cbr\u003e \u003cbr\u003e 12.3.2 The Law of Large Numbers 384\u003cbr\u003e \u003cbr\u003e 12.4 Central Limit Theorem 401\u003cbr\u003e \u003cbr\u003e Exercises 409\u003cbr\u003e \u003cbr\u003e \u003cb\u003e13 Appendix A: Integration Theory. General Expectations 421\u003c\/b\u003e\u003cbr\u003e \u003cbr\u003e 13.1 Integral of Measurable Functions 422\u003cbr\u003e \u003cbr\u003e 13.1.1 Integral of Simple (Elementary) Functions 422\u003cbr\u003e \u003cbr\u003e 13.1.2 Integral of Positive Measurable Functions 424\u003cbr\u003e \u003cbr\u003e 13.1.3 Integral of Measurable Functions 428\u003cbr\u003e \u003cbr\u003e 13.2 General Expectations and Moments of a Random Variable 429\u003cbr\u003e \u003cbr\u003e 13.2.1 Moments and Central Moments. Lp Space 430\u003cbr\u003e \u003cbr\u003e 13.2.2 Variance and the Correlation Coefficient 431\u003cbr\u003e \u003cbr\u003e 13.2.3 Convergence Theorems 433\u003cbr\u003e \u003cbr\u003e \u003cb\u003e14 Appendix B: Inequalities Involving Random Variables and Their Expectations 434\u003c\/b\u003e\u003cbr\u003e \u003cbr\u003e 14.1 Functions of Random Variables. The Transport Formula 441\u003cbr\u003e \u003cbr\u003e Bibliography 445\u003cbr\u003e \u003cbr\u003e Index 447\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand New","offer_id":52276373815576,"sku":"9780470647271","price":95.39,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780470647271.jpg?v=1781368392","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/handbook-of-probability-hardback-9780470647271","provider":"Freshly Printed Books","version":"1.0","type":"link"}