The Theory of Probability is a major tool that can be used to explain and understand the various phenomena in different natural, physical and social sciences. This book provides a systematic exposition of the theory in a setting which contains a balanced mixture of the classical approach and the modern day axiomatic approach. After reviewing the basis of the theory, the book considers univariate distributions, bivariate normal distribution, multinomial distribution, convergence of random variables and elements of stochastic process. Difficult ideas have been explained lucidly and augmented with explanatory notes, examples and exercises. The basic requirement for reading the book is the knowledge of mathematics at graduate level.This book tries to explain the difficult ideas in axiomatic approach to the theory in a clear and comprehensive manner. It addresses several unusual distributions including the power series distribution. Readers will find many worked-out examples and exercises with hints, which will make the book easily readable and engaging.The author is a former professor of the Indian Statistical Institute, India.
Classical Theory and Its Limitations; Axiomatic Approach; Random Variables and Distributions; Expectation of a Discrete Random Variable; Properties of Probability Distributions in R1; Generating Functions; Some Discrete Distributions in R1; Some Continuous Distributions in R1; Probability Distributions in Rn; Probability Distribution of Functions of Random Variables; Convergence of a Sequence of Random Variables.