Probability, Random Variables and Random Processes

Abstract

This chapter contains an introduction to probability, followed by the concept of a random variable. The probability density function (PDF) and cumulative density function (CDF) is also introduced. These notions are extended to several random variables and functions of random variables. The concept of a random process is treated, in depth, which is extended to different types of noise: additive white Gaussian noise, narrowband noise and thermal noise. The connection between the autocorrelation function and the power spectral density is explained with the help of the Wiener–Khinchin theorem. Some of the other topics are central limit theorem, transmission of noise through linear systems and Rayleigh distribution.