Introduction to
Probability
Professor Douglas H. Jones
Overview
This is a graduate level introduction to probability theory with the goal of providing a thorough treatment of
basic and classical probability theory. Topics include an introduction to probability measures (σ-algebras, set
theory, measurability, total probability, inclusion-exclusion, and integration), random variables
(distributions, random vectors, expectation, independence, conditional distributions, tower law, compound
distributions, random walks), probability inequalities (Chebyshev, Markov), transformations of random
variables (moment generating function, probability generating function, characteristic function), modes of
convergence (Law of Large Numbers, Central Limit Theorem, strong, weak) and Monte Carlo methods
(optional topic). Students will explore many properties of probability distributions with the R programming
language.
Lectures
Lectures will draw from online resources and will be posted to BlackBoard.
Textbook
No specific textbook will be assigned, however, lectures and reading assignments will draw from the
Reference section. All references are freely downloadable from Rutgers Digital Library (RU-Online) searchable
at http://www.libraries.rutgers.edu/ (requires Rutgers NETID available at
https://netidmgmt.rutgers.edu/netid/index.htm).
Grading and Assignments
There will be several reading assignments (25%), one in-class midterm (25%) and a take-home final (50%).
References1
Chen, L. H. Y., Goldstein, L., & Shao, Q. (2011). Normal approximation by stein's method [electronic
resource]. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg.
DasGupta, A. (2011). Probability for statistics and machine learning [electronic resource]:
Fundamentals and advanced topics (1st ed.). New York, NY: Springer Science+Business Media,
LLC.
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All references are accessible online via Rutgers Digital Library (RU-Online).
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Dekking, F. M., Kraaikamp, C., Lopuhaä, H. P., & Meester, L. E. (2005). A modern introduction to
probability and statistics [electronic resource] : Understanding why and how. London: SpringerVerlag London Limited.
Gut, A. (2005). Probability: A graduate course [electronic resource]. New York, NY: Springer
Science+Business Media, Inc.
Klenke, A. (2008). Probability theory [electronic resource] : A comprehensive course. London:
Springer-Verlag London.
Lefebvre, M. (2008). Basic probability theory with applications [electronic resource]. New York, NY:
Springer-Verlag New York.
Meester, R. (2008). A natural introduction to probability theory [electronic resource] (Second Edition
ed.). Basel: Birkhäuser Verlag AG.
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