Probability Theory

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.