Concepts of Probability and Statistics

In this chapter, we examined some theoretical aspects of probability density functions and distributions encountered in the study of fading and shadowing in wireless channels. We started with the basic definition of probability, then discussed density functions and properties relating to the analysis of fading and shadowing. We also examined the transformations of random variables in conjunction with relationships of different types of random variables. This is important in the study of diversity and modeling of specific statistical behavior of the wireless channels. The density functions of some of the functions of two or more random variables were derived. We examined order statistics, placing emphasis on the density functions of interest in diversity analysis. Concepts of stochastic processes and their properties were outlined. Similarly, the characteristics of noise were delineated within the context of signal detection. In addition, this study included an exploration of ways of expressing some of the densities in more compact forms using the hypergeometric functions and MeijerG functions.

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