Probability Theory : An Introduction Using R

Deshmukh, Shailaja R./ Kashikar, Akanksha S.

Chapman & Hall/CRC（2024/08発売）

• 製本 Hardcover:ハードカバー版／ページ数 596 p.
• 言語 ENG
• 商品コード 9781032617978
• DDC分類 519.202855133

Full Description

This book introduces Probability Theory with R software and explains abstract concepts in a simple and easy-to-understand way by combining theory and computation. It discusses conceptual and computational examples in detail, to provide a thorough understanding of basic techniques and develop an enjoyable read for students seeking suitable material for self-study. It illustrates fundamental concepts including fields, sigma-fields, random variables and their expectations, various modes of convergence of a sequence of random variables, laws of large numbers and the central limit theorem.

Computational exercises based on R software are included in each Chapter
Includes a brief introduction to the basic functions of R software for beginners in R and serves as a ready reference
Includes Numerical computations, simulation studies, and visualizations using R software as easy tools to explain abstract concepts
Provides multiple-choice questions for practice
Incorporates self-explanatory R codes in every chapter

This textbook is for advanced students, professionals, and academic researchers of Statistics, Biostatistics, Economics and Mathematics.

Contents

1. Sigma Field, Borel Field and Probability Measure 2. Random Variables and Random Vectors 3. Distribution Function 4. Expectation and Characteristic Function 5. Independence 6. Almost Sure Convergence and Borel Zero-One Law 7. Convergence in Probability, in Law and in r-th Mean 8. Convergence of a Sequence of Expectations 9. Laws of Large Numbers 10. Central Limit Theorem 11. Solutions to Conceptual Exercises 12. Bibliography 13. Index