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A p p e n d i x
PROBABILITY AND
RANDOM VARIABLES
B–1 INTRODUCTION
The need for probability theory arises in every scientific discipline, since it is impossible to be
exactly sure of values that are obtained by measurement. For example, we might say that we
are 90% sure that a voltage is within ;0.1 V of a 5-V level. This is a statistical description of
the voltage parameter as opposed to a deterministic description, whereby we might define the
voltage as being exactly 5 V.
This appendix is intended to be a short course in probability and random variables.
Numerous excellent books cover this topic in more detail [Miller, 2012; Childers, 1997;
Papoulis, 1991; Peebles, 1993; Shanmugan and Breipohl, 1988]. This appendix will provide a
good introduction to the topic for the new student or a quick review for the student who is
already knowledgeable in this area.
If probability and random variables are new topics for you, you will soon realize that to
understand them, you will need to master many new definitions that seem to be introduced all
at once. It is important to memorize these definitions in order to have a vocabulary that can be
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