The chapter begins with a description of probability theory followed by a discussion of random variables and its properties. A short but useful discussion on commonly used probability distribution functions were presented next that includes Gaussian, Rayleigh, Rician, Poisson distribution. Random processes and its various classifications are discussed highlighting the relation between autocorrelation and power spectral density. A discussion on transmission of random process through linear time invariant system is followed by design of an optimal filter that minimizes total output power of the filter. Besides numerical examples, a large number of case studies from practical communication field have been taken up to illustrate various concepts and use of random variables and processes.
