Fundamentals of Probability Theory

The basic knowledge of probability, random variables, and stochastic process is essential to understand topics covered in the rest of the chapters. Chapter 1 is introduced to discuss probability, random variable, and stochastic process briefly in this direction. The chapter starts with a basic introduction to probability and some key concepts related to it. After discussing probability, the random variable is introduced. The cumulative distribution function (cdf) and probability density function (pdf) are defined, which are used to describe the random variables. Some key random variables frequently used in the book are discussed along with their pdf and cdf. Finally, the concept of a random variable is extended to discuss the stochastic process. Two stochastic process classes: strict sense stationary process and wide sense stationary process, are discussed. Gaussian process and white noise process are discussed at the end of the chapter.