Page 24 - Fundamentals of Probability and Statistics for Engineers

2

Basic Probability Concepts

The mathematical theory of probability gives us the basic tools for constructing
and analyzing mathematical models for random phenomena. In studying a
random phenomenon, we are dealing with an experiment of which the outcome
is not predictable in advance. Experiments of this type that immediately come
to mind are those arising in games of chance. In fact, the earliest development
of probability theory in the fifteenth and sixteenth centuries was motivated by
problems of this type (for example, see Todhunter, 1949).
In science and engineering, random phenomena describe a wide variety of
situations. By and large, they can be grouped into two broad classes. The first
class deals with physical or natural phenomena involving uncertainties. Uncer-
tainty enters into problem formulation through complexity, through our lack
of understanding of all the causes and effects, and through lack of information.
Consider, for example, weather prediction. Information obtained from satellite
tracking and other meteorological information simply is not sufficient to permit
a reliable prediction of what weather condition will prevail in days ahead. It is
therefore easily understandable that weather reports on radio and television are
made in probabilistic terms.
The second class of problems widely studied by means of probabilistic
models concerns those exhibiting variability. Consider, for example, a problem
in traffic flow where an engineer wishes to know the number of vehicles cross-
ing a certain point on a road within a specified interval of time. This number
varies unpredictably from one interval to another, and this variability reflects
variable driver behavior and is inherent in the problem. This property forces us
to adopt a probabilistic point of view, and probability theory provides a
powerful tool for analyzing problems of this type.
It is safe to say that uncertainty and variability are present in our modeling of
all real phenomena, and it is only natural to see that probabilistic modeling and
analysis occupy a central place in the study of a wide variety of topics in science
and engineering. There is no doubt that we will see an increasing reliance on the
use of probabilistic formulations in most scientific disciplines in the future.

Fundamentals of Probability and Statistics for Engineers T.T. Soong  2004 John Wiley & Sons, Ltd
ISBNs: 0-470-86813-9 (HB) 0-470-86814-7 (PB)

TLFeBOOK