Probability Theory An Introduction Using R

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.

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

Shailaja Deshmukh is a visiting faculty at the Department of Statistics, Savitribai Phule Pune University, formerly known as University of Pune, India. She retired as a Professor of Statistics from the Savitribai Phule Pune University. She has taught around twenty five different theoretical and applied courses. She worked as a visiting professor at the Department of Statistics, University of Michigan, Ann Arbor, Michigan, during 2009-10 academic year. She has served as an executive editor and as a chief editor of the Journal of Indian Statistical Association. She is an elected member of the International Statistical Institute. Her areas of interest are inference in stochastic processes, applied probability and analysis of microarray data. She has a number of research publications in various peer-reviewed journals, such as Biometrika, Journal of Multivariate Analysis, J. R. Statist. Society, Australian and New Zealand Journal of Statistics, Journal of Applied Statistics , Environmetrics, J. of Statistical Planning and Inference, Naval Research Logistics, Journal of Translational Medicine, Annals of Institute of Statistical Mathematics. She has published the following six books. (i) Microarray Data: Statistical Analysis Using R, published by Narosa in 2007, (ii) Statistics Using R, published by Narosa in 2008, (iii) Actuarial Statistics: An Introduction Using R, published by Universities Press in 2009, (iv) Multiple Decrement Models in Insurance: An Introduction Using R, published by Springer in 2012 and (v) Asymptotic Statistical Inference: An Introduction Using R, published by Springer in 2021. (vi) Stochastic Processes: An Introduction Using R", published by Springer in 2023.

Akanksha Kashikar is an Assistant Professor at Savitribai Phule Pune University (formerly known as the University of Pune) since 2012, specializing in Statistics. She obtained her masters and PhD in Statistics from the same university. Her research interests include Bra