MA 590 - Introduction to Probability Theory

Summer 2007

Lectures: SMG, Room 240
Mon,Wed, 5-8.30 pm
Instructor:
Paolo Guasoni

Office:
143 Bay State Rd, 4th floor
Phone:
(617) 353-4992
e-mail:
WWW:
http://math.bu.edu/people/guasoni
Office hours:
Mon,Wed 1-2.30 pm, or by appointment
Teaching Fellow:
 Zhongkai Cui
MCS 250, (617) 353-1497, czkzju@yahoo.com
Office hours:
Textbooks:
Required:
Introduction to Probability
by Dimitri P. Bertsekas, John N. Tsitsiklis
Athena Scientific
ISBN: 188652940X
Book Web Page 		Recommended:
Weighing the Odds: A Course in Probability and Statistics
by David Williams
Cambridge University Press
ISBN: 052100618X
Objectives and Prerequisites:
 This course is a problem-based introduction to probability and its applications.
No previous knowledge of probability is assumed, but knowledge of calculus in one or more variables is required.
Course Outline:
  1. Axiomatic definition of probability. Uniform probability spaces. Counting methods: replacement, ordering. Conditional probability. Independence for events. The law of total probability. Bayes' rule.
  2. Discrete random variables. Independence for random variables. Joint, marginal, and conditional densities. Common random variables and their interpretation: Bernoulli, dicrete uniform, binomial, hypergeometric, geometric, Poisson, Pascal.
  3. Expectation of dicrete random variables. Variance and its properties. Expectation and variance of common random variables. Covariance and correlation. Variance of a sum. Null correlation and independence. Linear prediction.
  4. Conditional expectation and its properties. Conditional Variance. Sigma-algebras, Continuous Random variables. The Uniform and Exponential distributions. Distribution functions and densities.
  5. Marginal, joint and conditional densities. Gamma, Normal and Cauchy distribution. Derived Distributions: monotonic and general case. Conditional Expectation. Law of total expectation. Markov and Chebishev Inequalities.
  6. Convergence of Random Variables. The Weak and Strong Laws of Large Numbers. Characteristic Functions and their properties. CF of a sum. CF of common random variables. The Central Limit Theorem.
Exams:
Midterm: 7/20 3.00-5.00 pm
Final: 8/14 5.00-8.30 pm
Grading:
HomeworkMidtermFinal
30%30%40%
Rules: No late homework will be accepted.
Midterm and finals are open books and notebooks.
Calculators of any kind can be used freely, although they will not be necessary.
Cellular phones and other communications devices must be turned off.
Instances of cheating will be dealt with in accordance with University policy, and may result in failure of the course.