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Unformatted text preview: d calculus, including Taylor series expansions, integration over regions in the plane, and the use
of polar coordinates.
The author gratefully acknowledges the students and faculty who have participated in this
course through the years. He is particularly grateful to Professor D. V. Sarwate, who ﬁrst introduced the course, and built up much material for it on the website.
July 2011 vii CONTENTS 1 Organization
Chapter 1 presents an overview of the many applications of probability theory, and then explains
the basic concepts of a probability model and the axioms commonly assumed of probability models.
Often probabilities are assigned to possible outcomes based on symmetry. For example, when a six
sided die is rolled, it is usually assumed that the probability a particular number i shows is 1/6,
for 1 ≤ i ≤ 6. For this reason, we also discuss in Chapter 1 how to determine the sizes of various
ﬁnite sets of possible outcomes.
Random variables are introduced in Chapter 2 and examined...
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- Spring '08
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