Includes bibliographical references and index.

Machine generated contents note: PREFACE 1. Probability -- 1.1 Introduction 1 -- 1.2 Algebra of Sets 2 -- 1.3 Properties of Functions 5 -- 1.4 Matrix Algebra 13 -- 1.5 Three Approaches 16 -- 1.6 Conditional Probability and Independence of Events 39 -- 1.7 Geometric Probability 48 -- 1.8 Miscellaneous Examples 54 -- Exercises 73 2. Univariate Distribution -- 2.1 Random Variable 80 -- 2.2 Expectation, Variance and Moments 89 -- 2.3 Moment Generating Function 104 -- 2.4 Characteristic Function and Cumulants 106 -- 2.5 Some Standard Discrete Distributions 100 -- 2.6 Some Standard Continuous distributions 128 -- 2.7 Transformation of Variables 143 -- 2.8 Miscellaneous Examples 153 -- Exercises 175 3. Bivariate Distributions -- 3.1 Joint, Marginal and Conditional Distributions 188 -- 3.2 Moments, Conditional Moments 200 -- 3.3 Correlation and Regression 209 -- 3.4 Transformation of Variables 215 -- 3.5 Bivariate Normal Distribution 228 -- 3.6 Bivariate Dirichlet Distribution 235 -- 3.7 Miscellaneous Examples 237 4. Multivariate Distributions -- 4.1 Different Aspects of a Multivariate Distribution 258 -- 4.2 2, t and F-Distributions 281 -- 4.3 Correlation and Regression 296 -- 4.4 Some Standard Multivariate Distributions 309 -- 4.5 Order Statistics 320 -- 4.6 Some Notions of Dependence 339 -- 4.7 Results on Symmetrization 348 -- 4.8 Miscellaneous Examples 353 -- Exercises 368 5. Limit Theorems -- 5.1 Chebyshev's Inequality 384 -- 5.2 Other Useful Inequalities 390 -- 5.3 Convergence in Distribution 403 -- 5.4 Convergence in Probability 411 -- 5.5 The Laws of Large Numbers 419 -- 5.6 Central Limit Theorems 429 -- 5.7 Miscellaneous Examples 438 -- Exercises 456.