Gaussian Distributions

Abstract

The Gaussian distribution is one of the five important distributions discussed in this book. Because of its importance, a separate chapter is devoted to this topic in this chapter. Chapter 8 provides further discussion on the Gaussian distribution and the Gaussian stochastic process as applied to communications channel modeling. This chapter starts with a brief discussion on the central limit theorem, which will show one of the fundamental reasons why the Gaussian distribution is important. This chapter discusses a Gaussian RV treated singly, two Gaussian RVs treated jointly, and multiple Gaussian RVs as vector RVs. This chapter derives the mean and the variance of the Gaussian RV and derives the characteristic function of the scalar Gaussian RV and that of the vector Gaussian RV. Finally, this chapter defines the Gaussian stochastic process.