Page 18 - Fundamentals of Probability and Statistics for Engineers

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Introduction

At present, almost all undergraduate curricula in engineering and applied
sciences contain at least one basic course in probability and statistical inference.
The recognition of this need for introducing the ideas of probability theory in
a wide variety of scientific fields today reflects in part some of the profound
changes in science and engineering education over the past 25 years.
One of the most significant is the greater emphasis that has been placed upon
complexity and precision. A scientist now recognizes the importance of study-
ing scientific phenomena having complex interrelations among their compon-
ents; these components are often not only mechanical or electrical parts but
also ‘soft-science’ in nature, such as those stemming from behavioral and social
sciences. The design of a comprehensive transportation system, for example,
requires a good understanding of technological aspects of the problem as well
as of the behavior patterns of the user, land-use regulations, environmental
requirements, pricing policies, and so on.
Moreover, precision is stressed – precision in describing interrelationships
among factors involved in a scientific phenomenon and precision in predicting
its behavior. This, coupled with increasing complexity in the problems we face,
leads to the recognition that a great deal of uncertainty and variability are
inevitably present in problem formulation, and one of the mathematical tools
that is effective in dealing with them is probability and statistics.
Probabilistic ideas are used in a wide variety of scientific investigations
involving randomness. Randomness is an empirical phenomenon characterized
by the property that the quantities in which we are interested do not have
a predictable outcome under a given set of circumstances, but instead there is
a statistical regularity associated with different possible outcomes. Loosely
speaking, statistical regularity means that, in observing outcomes of an exper-
iment a large number of times (say n), the ratio m/n, where m is the number of
observed occurrences of a specific outcome, tends to a unique limit as n
becomes large. For example, the outcome of flipping a coin is not predictable
but there is statistical regularity in that the ratio m/n approaches 1 for either
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Fundamentals of Probability and Statistics for Engineers T.T. Soong Ó 2004 John Wiley & Sons, Ltd
ISBNs: 0-470-86813-9 (HB) 0-470-86814-7 (PB)

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