Exercises in Probability

ISBN-13: 9780387967356 / Angielski / Twarda / 1988 / 248 str.

T. Cacoullos

Opis

The author, the founder of the Greek Statistical Institute, has based this book on the two volumes of his Greek edition which has been used by over ten thousand students during the past fifteen years. It can serve as a companion text for an introductory or intermediate level probability course. Those will benefit most who have a good grasp of calculus, yet, many others, with less formal mathematical background can also benefit from the large variety of solved problems ranging from classical combinatorial problems to limit theorems and the law of iterated logarithms. It contains 329 problems with solutions as well as an addendum of over 160 exercises and certain complements of theory and problems.

Spis treści

I Elementary Probabilities.- I Basic Probabilities. Discrete Spaces.- Basic Definitions and Formulas Exercises.- Exercises.- 1. Sets. Events: 1–8.- 2. Combinatorics: 9–16.- 3. Properties of Binomial Coefficients: 17–25.- 4. Properties of Probability: 26–34.- 5. Classical Probabilities. Equally Likely Cases: 35–53.- 6. Independent Events. Conditional Probability: 54–79.- 2 Distributions. Random Variables.- Elements of Theory.- Exercises.- 1. Discrete Distributions: 80–89.- 2. Continuous Distributions: 90–100.- 3 Expectation. Variance. Moments.- Elements of Theory.- Exercises.- 1. Theoretical Exercises: 101–113.- 2. Mean and Variance: 114–125.- 4 General Problems: 126–170.- II Advanced Topics.- 5 Multivariate Distributions.- Elements of Theory.- Exercises: 171–190.- 6 Generating Functions. Characteristic Functions.- Elements of Theory.- Exercises: 191–215.- 7 Distribution of Functions of Random Variables.- Elements of Theory.- Exercises: 216–250.- 8 Limit Theorems. Laws of Large Numbers. Central Limit Theorems.- Elements of Theory.- Exercises: 251–269.- 9 Special Topics: Inequalities, Geometrical Probabilities, Difference Equations.- Elements of Theory.- A. Inequalities.- B. Geometrical Probabilities.- C. Difference Equations.- Exercises.- A. Inequalities: 270–282.- B. Geometrical Probabilities: 283–289.- C. Difference Equations: 290–300.- 10 General Exercises: 301–329.- Supplements.- Supplement I Miscellaneous Exercises: I-1–I-56.- Supplement II Complements and Problems.- 1. Multivariate Distributions: 1.1–1.27.- 2. Generating Functions: 2.1–2.22.- 3. Transformation of Random Variables: 3.1–3.15.- 4. Convergence of Random Variables: 4.1–4.19.- 5. Miscellaneous Complements and Problems: 5.1–5.29.- III Solutions.- Solutions: 1–329.