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MATH/STAT 394A-Probability I, FALL 2011
Introduction to Probability Theory and its Applications
SYLLABUS
Class meetings: MWF 9:30-10:20 Gowen Hall 201
Instructor: Fritz Scholz, Department of Statistics
Office: C310 Padelford Hall, next to Math/Stat Library 3rd floor
Phone: (206) 543-3866 (not the best way to reach me)
Email: [email protected] (better than phone)
Office hours: Tue 1-2 pm, Fri 2-3 pm, by appointment, or as you catch me after class.
Course Description:
We will cover the mathematical foundations of probability theory.
The basic terminology and concepts of probability theory include: random experiments, sample or outcome
spaces (discrete and continuous case), events and their algebra, probability measures, conditional probability
and Bayes’ formula, independent events, random variables, their distributions, probability mass functions
(discrete), probability density function (continuous), cumulative distribution function, independent random
variables, conditional distributions, expected/mean values, conditional expectations, variance, standard deviation, moments, random vectors.
Special distributions include the Bernoulli, binomial, geometric, negative binomial, Poisson, hypergeometric, uniform, normal or Gaussian, exponential, gamma, and Weibull distributions.
Required Readings:
A First Course in Probability (8th ed.) by S. Ross. This is a lively text that covers the basic ideas of
probability theory including those needed in statistics. Theoretical concepts are introduced via interesting
concrete examples.
In 394 I will begin my lectures with the basics of probability theory in Chapter 2. However, your first
assignment is to review Chapter 1, which treats elementary counting methods. They are used in applications
in Chapter 2.
I expect to cover Chapters 2-5 plus portions of 6 and 7. You are encouraged to read ahead. In lectures I will
not be able to cover every topic and example in Ross, and conversely, I may cover some topics/examples in
lectures that are not treated in Ross.
You will be responsible for all material in my lectures, assigned reading, and homework, including supplementary handouts if any. I will post the lecture notes and other material on the class web page.
Additional References:
”An Introduction to Probability Theory and Its Applications” (Vol. I) by W. Feller. This is a classic introductory text, written by a master. Only discrete probability spaces are treated, limiting its use as a textbook,
but Feller shows us how to ”think probabilistically”, with many interesting and important examples.
”Introduction to Probability Theory” by D. Hoel, S. Port, and C. Stone.
Copies of these books, plus Ross, are on reserve in the Math Research Library, Padelford Hall, 3rd Floor,
and/or in Odegaard Undergraduate Library.
”Introduction to Probability, second revised edition” by Grinstad and Snell, free at
http :// www . dartmouth . edu /~chance / teaching_aids / books_articles /
probability_book / book . html
Prerequisites:
MATH 126, MATH 129, or MATH 136. Recommended: MATH 324 or 327.
MATH/STAT 394-5 is an introductory sequence in probability, but not in mathematics. Calculus (including
multiple integrals), elementary combinatorics, and some linear and matrix algebra will be used. A math
self-diagnostic exam will be provided on the class web site - it indicates the math level and some of the
content that will be assumed for 394/395. You should be able to perform elementary arithmetic without
electronic devices, since I don’t allow them during tests.
Homework:
HW assignments, posted on the class web page, will be given on Wednesdays and due in class the following
Wednesday – HW 1 is due Oct. 5. Please write neatly and legibly and write your NAME clearly on all HW,
and staple all sheets together. Late HW will be acknowledged but not graded.
The problems and exercises in Ross are generally of good quality. Not all will be assigned formally, but
you are strongly encouraged to read and attempt as many as possible. (Note that complete solutions to the
”self-test problems and exercises” are presented beginning on page 461.) Most homework problems will
come from Ross, but occasionally I will assign supplementary ones.
Email Questions:
I will also be happy to respond to questions by email, time permitting. I may send my reply to the entire
class if it is of general interest.
Exams:
One Midterm Exam and a comprehensive Final Exam. Exams are closed book and notes. No electronic
devices are allowed. For the midterm you are allowed one crib sheet (8.5” x 11”, both sides), for the final
you can have two.
Grading Policy:
Homework 25%, Midterm 25%, Final 50%