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10

A Taste of Probability Theory*

10.1 Introduction
In addition to its everyday use in all aspects of our public, personal, and lei-
sure lives, probability plays an important role in electrical engineering prac-
tice in at least three important aspects. It is the mathematical tool to deal with
three broad areas:

1. The problems associated with the inherent uncertainty in the input of
certain systems. The random arrival time of certain inputs to a
system cannot be predetermined; for example, the log-on and the
log-off times of terminals and workstations connected to a com-
puter network, or the data packets’ arrival time to a computer
network node.
2. The problems associated with the distortion of a signal due to noise. The
effects of noise have to be dealt with satisfactorily at each stage of
a communication system from the generation, to the transmission,
to the detection phases. The source of this noise may be due to
either fluctuations inherent in the physics of the problem (e.g.,
quantum effects and thermal effects) or due to random distortions
due to externally generated uncontrollable parameters (e.g.,
weather, geography, etc.).
3. The problems associated with inherent human and computing machine
limitations while solving very complex systems. Individual treatment
of the dynamics of very large number of molecules in a material,
22
in which more than 10 molecules may exist in a quart-size con-
tainer, is not possible at this time, and we have to rely on statistical
averages when describing the behavior of such systems. This is the
field of statistical physics and thermodynamics.
Furthermore, probability theory provides the necessary mathematical tools
for error analysis in all experimental sciences. It permits estimation of the

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© 2000 by CRC Press LLC
© 2001 by CRC Press LLC