  This paper has several major purposes. The central purpose is to describe the
"Benford analysis" of a positive random variable and to summarize some results
from investigations into base dependence of Benford random variables. The
principal tools used to derive these results are Fourier series and Fourier
transforms, and a second major purpose of this paper is to present an
introductory exposition about these tools. My motivation for writing this paper
is twofold. First, I think the theory of Benford random variables and the
Benford analysis of a positive random variable are interesting and deserve to
be better known. Second, I think that Benford analysis provides a really
excellent illustration of the utility of Fourier series and transforms, and
reveals certain interconnections between series and transforms that are not
obvious from the usual way these subjects are introduced.
