Modern Communications A Systematic Introduction

In this chapter we review probability and statistics. We define the ideas of probability, the probability density function, and the cumulative density function. We introduce Bayes’ theorem that relates prior, marginal, posterior, and conditional probability densities, which allows us to define the maximum a posterior and the maximum likelihood estimators. We discuss central moments of distributions. We review multivariate probability distributions including the correlated multivariate complex circularly symmetric Gaussian distributions. We also review a set of useful distributions, including Rayleigh, exponential, χ2, and Rician. Finally, we discuss random processes.