{"product_id":"probability-concepts-and-theory-for-engineers-hardback-9780470748558","title":"Probability Concepts and Theory for Engineers (Hardback) 9780470748558","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eProbability Concepts and Theory for Engineers\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\"\u003eHarry Schwarzlander (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780470748558, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 14 January 2011\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e624 pages\u003cbr\u003e25.1 x 17.5 x 3.9 cm, 1.166 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\"After reading some introductory material on conventions and notions, it is possible to use separate chapters as introductions to various ideas. This is how readers should use this book.\" (Computing Reviews, 1 October 2011)\u003cbr\u003e\u003cbr\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cb\u003eA thorough introduction to the fundamentals of probability theory\u003c\/b\u003e\u003cbr\u003e \u003cbr\u003e   \u003cp\u003eThis book offers a detailed explanation of the basic models and mathematical principles used in applying probability theory to practical problems. It gives the reader a solid foundation for formulating and solving many kinds of probability problems for deriving additional results that may be needed in order to address more challenging questions, as well as for proceeding with the study of a wide variety of more advanced topics.\u003c\/p\u003e \u003cp\u003eGreat care is devoted to a clear and detailed development of the ‘conceptual model' which serves as the bridge between any real-world situation and its analysis by means of the mathematics of probability. Throughout the book, this conceptual model is not lost sight of. Random variables in one and several dimensions are treated in detail, including singular random variables, transformations, characteristic functions, and sequences. Also included are special topics not covered in many probability texts, such as fuzziness, entropy, spherically symmetric random variables, and copulas.\u003c\/p\u003e \u003cp\u003eSome special features of the book are:\u003c\/p\u003e \u003cul\u003e \u003cli\u003ea unique step-by-step presentation organized into 86 topical Sections, which are grouped into six Parts\u003c\/li\u003e \u003cli\u003eover 200 diagrams augment and illustrate the text, which help speed the reader's comprehension of the material\u003c\/li\u003e \u003cli\u003eshort answer review questions following each Section, with an answer table provided, strengthen the reader's detailed grasp of the material contained in the Section\u003c\/li\u003e \u003cli\u003eproblems associated with each Section provide practice in applying the principles discussed, and in some cases extend the scope of that material\u003c\/li\u003e \u003cli\u003ean online separate solutions manual is available for course tutors.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThe various features of this textbook make it possible for engineering students to become well versed in the ‘machinery' of probability theory. They also make the book a useful resource for self-study by practicing engineers and researchers who need a more thorough grasp of particular topics.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eIntroduction xiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I The Basic Model\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePart I Introduction 2\u003c\/p\u003e \u003cp\u003eSection 1 Dealing with ‘Real-World’ Problems 3\u003c\/p\u003e \u003cp\u003eSection 2 The Probabilistic Experiment 6\u003c\/p\u003e \u003cp\u003eSection 3 Outcome 11\u003c\/p\u003e \u003cp\u003eSection 4 Events 14\u003c\/p\u003e \u003cp\u003eSection 5 The Connection to the Mathematical World 17\u003c\/p\u003e \u003cp\u003eSection 6 Elements and Sets 20\u003c\/p\u003e \u003cp\u003eSection 7 Classes of Sets 23\u003c\/p\u003e \u003cp\u003eSection 8 Elementary Set Operations 26\u003c\/p\u003e \u003cp\u003eSection 9 Additional Set Operations 30\u003c\/p\u003e \u003cp\u003eSection 10 Functions 33\u003c\/p\u003e \u003cp\u003eSection 11 The Size of a Set 36\u003c\/p\u003e \u003cp\u003eSection 12 Multiple and Infinite Set Operations 40\u003c\/p\u003e \u003cp\u003eSection 13 More About Additive Classes 44\u003c\/p\u003e \u003cp\u003eSection 14 Additive Set Functions 49\u003c\/p\u003e \u003cp\u003eSection 15 More about Probabilistic Experiments 53\u003c\/p\u003e \u003cp\u003eSection 16 The Probability Function 58\u003c\/p\u003e \u003cp\u003eSection 17 Probability Space 62\u003c\/p\u003e \u003cp\u003eSection 18 Simple Probability Arithmetic 65\u003c\/p\u003e \u003cp\u003ePart I Summary 71\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II The Approach to Elementary Probability Problems\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePart II Introduction 74\u003c\/p\u003e \u003cp\u003eSection 19 About Probability Problems 75\u003c\/p\u003e \u003cp\u003eSection 20 Equally Likely Possible Outcomes 81\u003c\/p\u003e \u003cp\u003eSection 21 Conditional Probability 86\u003c\/p\u003e \u003cp\u003eSection 22 Conditional Probability Distributions 91\u003c\/p\u003e \u003cp\u003eSection 23 Independent Events 99\u003c\/p\u003e \u003cp\u003eSection 24 Classes of Independent Events 104\u003c\/p\u003e \u003cp\u003eSection 25 Possible Outcomes Represented as Ordered k-Tuples 109\u003c\/p\u003e \u003cp\u003eSection 26 Product Experiments and Product Spaces 114\u003c\/p\u003e \u003cp\u003eSection 27 Product Probability Spaces 120\u003c\/p\u003e \u003cp\u003eSection 28 Dependence Between the Components in an Ordered k-Tuple 125\u003c\/p\u003e \u003cp\u003eSection 29 Multiple Observations Without Regard to Order 128\u003c\/p\u003e \u003cp\u003eSection 30 Unordered Sampling with Replacement 132\u003c\/p\u003e \u003cp\u003eSection 31 More Complicated Discrete Probability Problems 135\u003c\/p\u003e \u003cp\u003eSection 32 Uncertainty and Randomness 140\u003c\/p\u003e \u003cp\u003eSection 33 Fuzziness 146\u003c\/p\u003e \u003cp\u003ePart II Summary 152\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Introduction to Random Variables\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePart III Introduction 154\u003c\/p\u003e \u003cp\u003eSection 34 Numerical-Valued Outcomes 155\u003c\/p\u003e \u003cp\u003eSection 35 The Binomial Distribution 161\u003c\/p\u003e \u003cp\u003eSection 36 The Real Numbers 165\u003c\/p\u003e \u003cp\u003eSection 37 General Definition of a Random Variable 169\u003c\/p\u003e \u003cp\u003eSection 38 The Cumulative Distribution Function 173\u003c\/p\u003e \u003cp\u003eSection 39 The Probability Density Function 180\u003c\/p\u003e \u003cp\u003eSection 40 The Gaussian Distribution 186\u003c\/p\u003e \u003cp\u003eSection 41 Two Discrete Random Variables 191\u003c\/p\u003e \u003cp\u003eSection 42 Two Arbitrary Random Variables 197\u003c\/p\u003e \u003cp\u003eSection 43 Two-Dimensional Distribution Functions 202\u003c\/p\u003e \u003cp\u003eSection 44 Two-Dimensional Density Functions 208\u003c\/p\u003e \u003cp\u003eSection 45 Two Statistically Independent Random Variables 216\u003c\/p\u003e \u003cp\u003eSection 46 Two Statistically Independent Random Variables—Absolutely Continuous Case 221\u003c\/p\u003e \u003cp\u003ePart III Summary 226\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV Transformations and Multiple Random Variables\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePart IV Introduction 228\u003c\/p\u003e \u003cp\u003eSection 47 Transformation of a Random Variable 229\u003c\/p\u003e \u003cp\u003ea) Transformation of a discrete random variable 229\u003c\/p\u003e \u003cp\u003eb) Transformation of an arbitrary random variable 231\u003c\/p\u003e \u003cp\u003ec) Transformation of an absolutely continuous random variable 235\u003c\/p\u003e \u003cp\u003eSection 48 Transformation of a Two-Dimensional Random Variable 238\u003c\/p\u003e \u003cp\u003eSection 49 The Sum of Two Discrete Random Variables 243\u003c\/p\u003e \u003cp\u003eSection 50 The Sum of Two Arbitrary Random Variables 247\u003c\/p\u003e \u003cp\u003eSection 51 n-Dimensional Random Variables 253\u003c\/p\u003e \u003cp\u003eSection 52 Absolutely Continuous n-Dimensional R.V.’s 259\u003c\/p\u003e \u003cp\u003eSection 53 Coordinate Transformations 263\u003c\/p\u003e \u003cp\u003eSection 54 Rotations and the Bivariate Gaussian Distribution 268\u003c\/p\u003e \u003cp\u003eSection 55 Several Statistically Independent Random Variables 274\u003c\/p\u003e \u003cp\u003eSection 56 Singular Distributions in One Dimension 279\u003c\/p\u003e \u003cp\u003eSection 57 Conditional Induced Distribution, Given an Event 284\u003c\/p\u003e \u003cp\u003eSection 58 Resolving a Distribution into Components of Pure Type 290\u003c\/p\u003e \u003cp\u003eSection 59 Conditional Distribution Given the Value of a Random Variable 293\u003c\/p\u003e \u003cp\u003eSection 60 Random Occurrences in Time 298\u003c\/p\u003e \u003cp\u003ePart IV Summary 304\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart V Parameters for Describing Random Variables and Induced Distributions\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePart V Introduction 306\u003c\/p\u003e \u003cp\u003eSection 61 Some Properties of a Random Variable 307\u003c\/p\u003e \u003cp\u003eSection 62 Higher Moments 314\u003c\/p\u003e \u003cp\u003eSection 63 Expectation of a Function of a Random Variable 320\u003c\/p\u003e \u003cp\u003ea) Scale change and shift of origin 320\u003c\/p\u003e \u003cp\u003eb) General formulation 320\u003c\/p\u003e \u003cp\u003ec) Sum of random variables 322\u003c\/p\u003e \u003cp\u003ed) Powers of a random variable 323\u003c\/p\u003e \u003cp\u003ee) Product of random variables 325\u003c\/p\u003e \u003cp\u003eSection 64 The Variance of a Function of a Random Variable 328\u003c\/p\u003e \u003cp\u003eSection 65 Bounds on the Induced Distribution 332\u003c\/p\u003e \u003cp\u003eSection 66 Test Sampling 336\u003c\/p\u003e \u003cp\u003ea) A Simple random sample 336\u003c\/p\u003e \u003cp\u003eb) Unbiased estimators 338\u003c\/p\u003e \u003cp\u003ec) Variance of the sample average 339\u003c\/p\u003e \u003cp\u003ed) Estimating the population variance 341\u003c\/p\u003e \u003cp\u003ee) Sampling with replacement 342\u003c\/p\u003e \u003cp\u003eSection 67 Conditional Expectation with Respect to an Event 345\u003c\/p\u003e \u003cp\u003eSection 68 Covariance and Correlation Coefficient 350\u003c\/p\u003e \u003cp\u003eSection 69 The Correlation Coefficient as Parameter in a Joint Distribution 356\u003c\/p\u003e \u003cp\u003eSection 70 More General Kinds of Dependence Between Random Variables 362\u003c\/p\u003e \u003cp\u003eSection 71 The Covariance Matrix 367\u003c\/p\u003e \u003cp\u003eSection 72 Random Variables as the Elements of a Vector Space 374\u003c\/p\u003e \u003cp\u003eSection 73 Estimation 379\u003c\/p\u003e \u003cp\u003ea) The concept of estimating a random variable 379\u003c\/p\u003e \u003cp\u003eb) Optimum constant estimates 379\u003c\/p\u003e \u003cp\u003ec) Mean-square estimation using random variables 381\u003c\/p\u003e \u003cp\u003ed) Linear mean-square estimation 382\u003c\/p\u003e \u003cp\u003eSection 74 The Stieltjes Integral 386\u003c\/p\u003e \u003cp\u003ePart V Summary 393\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart VI Further Topics in Random Variables\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePart VI Introduction 396\u003c\/p\u003e \u003cp\u003eSection 75 Complex Random Variables 397\u003c\/p\u003e \u003cp\u003eSection 76 The Characteristic Function 402\u003c\/p\u003e \u003cp\u003eSection 77 Characteristic Function of a Transformed Random Variable 408\u003c\/p\u003e \u003cp\u003eSection 78 Characteristic Function of a Multidimensional Random Variable 412\u003c\/p\u003e \u003cp\u003eSection 79 The Generating Function 417\u003c\/p\u003e \u003cp\u003eSection 80 Several Jointly Gaussian Random Variables 422\u003c\/p\u003e \u003cp\u003eSection 81 Spherically Symmetric Vector Random Variables 428\u003c\/p\u003e \u003cp\u003eSection 82 Entropy Associated with Random Variables 435\u003c\/p\u003e \u003cp\u003ea) Discrete random variables 435\u003c\/p\u003e \u003cp\u003eb) Absolutely continuous random variables 438\u003c\/p\u003e \u003cp\u003eSection 83 Copulas 443\u003c\/p\u003e \u003cp\u003eSection 84 Sequences of Random Variables 454\u003c\/p\u003e \u003cp\u003ea) Preliminaries 454\u003c\/p\u003e \u003cp\u003eb) Simple gambling schemes 455\u003c\/p\u003e \u003cp\u003ec) Operations on sequences 458\u003c\/p\u003e \u003cp\u003eSection 85 Convergent Sequences and Laws of Large Numbers 461\u003c\/p\u003e \u003cp\u003ea) Convergence of sequences 461\u003c\/p\u003e \u003cp\u003eb) Laws of large numbers 464\u003c\/p\u003e \u003cp\u003ec) Connection with statistical regularity 468\u003c\/p\u003e \u003cp\u003eSection 86 Convergence of Probability Distributions and the Central Limit Theorem 470\u003c\/p\u003e \u003cp\u003ePart VI Summary 477\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendices 479\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAnswers to Queries 479\u003c\/p\u003e \u003cp\u003eTable of the Gaussian Integral 482\u003c\/p\u003e \u003cp\u003ePart I Problems 483\u003c\/p\u003e \u003cp\u003ePart II Problems 500\u003c\/p\u003e \u003cp\u003ePart III Problems 521\u003c\/p\u003e \u003cp\u003ePart IV Problems 537\u003c\/p\u003e \u003cp\u003ePart V Problems 556\u003c\/p\u003e \u003cp\u003ePart VI Problems 574\u003c\/p\u003e \u003cp\u003eNotation and Abbreviations 587\u003c\/p\u003e \u003cp\u003eReferences 595\u003c\/p\u003e \u003cp\u003eSubject Index 597\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Electronics \u0026amp; communications engineering [\u003ca title=\"See our other books on Electronics \u0026amp; communications engineering\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Electronics%20\u0026amp;%20communications%20engineering%20%5BTJ%5D%22\"\u003eTJ\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":52173782679832,"sku":"9780470748558","price":65.79,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780470748558.jpg?v=1781171880","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/probability-concepts-and-theory-for-engineers-hardback-9780470748558","provider":"Freshly Printed Books","version":"1.0","type":"link"}