TABLE OF CONTENTS This appendix reviews some basic statistics which are commonly used in mobile communications and signal processing, and is associated with Chapter 2. The results are well known and are drawn from several sources such as the classical text by Papoulis (1965) and more recent texts such as Kay (1993).
The probability of the real random variable z being less than or equal to a value Z, is written
where P Z is the cumulative density function (cdf), also called the cumulative probability function (cpf), and p z( z) is the probability density function (pdf); k random variables are statistically independent if their joint pdf, p z( x), factors into the product of the individual random variable pdfs:
where z and x are the set of z i and x i , respectively.
If the pdf of z, p z( z), is known, then the pdf of a function g( z) is found (Papoulis, 1965) from
where the prime denotes differentiation with respect to the argument and z (n) are the real roots of g( z).
A change in variables, say from z = ( z 1 , z 2,...,z p) to w = ( w 1, w 2
