IE 111 Spring Semester 2009
Note Set #1
Introduction
This course will cover the fundamentals of probability theory. It is essentially a mathematics
course (indeed the Accreditation Board of Engineering and Technology, which accredits
engineering schools, classifies this course as a math course, not an engineering course. It is the
only course in Industrial Engineering classified as "math").
Probability is extremely useful in science and engineering. That is to say, it has many useful
applications. It is my hope that you will see why it is useful, and how it can be used. It is also
true that in this class, many of the examples are quite simple. For example, a probabilistic model
of flipping a fair coin (fair means 50% chance for heads, 50% for tails) is used over and over.
While quite simple, this model serves as a building block for increasingly more complex (and
useful) models. Many other courses in Industrial Engineering rely on basic knowledge of
probability and thus build on the fundamentals learned in this class.
Why is probability important? Many real world processes and phenomena exhibit
random
or
"uncertain" behavior. Nonetheless, these processes and phenomena do exhibit a certain amount
of
predictability
. The ability to use probability theory to predict the future outcomes of random
processes and phenomena is indeed quite useful. For example, probability models of the
behavior of the prices of stocks, bonds, and other equities are key to modern “quant” tools in the
world of finance. The other use of probability is to
quantify the amount of
randomness/uncertainty
exhibited by the process or phenomena.
For example, how much error
should be accounted for when using some measuring device?
Probability theory is also a prerequisite for learning statistics. Toward the end of this course we
will also learn some introductory statistics.
Statistics and probability are quite different subjects
.
Statistics is the science of analyzing and drawing inference from
DATA
, the key word being data.
Statistics is an inferential process whereby data is drawn from a population, then "statistics" is
applied to the data to make inferences and draw conclusions about the population as a whole.
Thus statistics is inherently
INDUCTIVE
.
In probability theory, there is no data to analyze. We start with an
assumed model
of how some
process or phenomenon behaves, and then apply probability theory to
DEDUCE
other properties
and behaviors. The point is that probability is deductive.
Examples of the use of statistics
•
100 people are randomly selected from the American population.
They are asked whom they
will vote for in the election, candidate A or B. 48 indicate "A" and 52 indicate "B". Estimate
the probability that "B" will win.
More importantly, determine the margin of error of your
estimate
.
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 Spring '08
 Rodriguez
 Statistics, Probability

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