Last Taught: Spring 2004-2005
Instructor: Billur Barshan
Office: EE-404
Office Hours: Tuesday 10:40-11:30 and 12:40-13:30
Phone: 290-2161 or x2161
E-mail: billur AT ee.bilkent.edu.tr

Teaching Assistants:
Tayfun Aytaç, Office: EA-232, Phone: 290-1286 E-mail: taytac@ee.bilkent.edu.tr
Çagri Yüzbasioglu, Office: EA-231, Phone: 290-1456 E-mail: cagri@ee.bilkent.edu.tr,

Course Objectives: ( pdf format)

Prerequisite:
MATH 102

Credit Units: 3

Textbook:
Introduction to Probability, Dimitri P. Bertsekas and John N. Tsitsiklis, Athena Scientific, 2002.

Weekly Topics:

Week 1: the meaning of probability, sets and set operations (intersection, union, complement), partition, Venn diagrams, algebra of sets, probabilistic models

Week 2: conditional probability, total probability theorem, inference and Bayes' rule

Week 3: independence, independent trials and binomial probabilities, counting, permutations, combinations, partitions

Week 4: discrete random variables: probability mass function, functions of a random variable, expectation, mean, and variance, moments

Week 5: properties of mean and variance, mean and variance of some common rvs, joint PMFs and multiple rvs, functions of multiple rvs

Week 6: conditioning, conditional expectation, independence of rvs

Week 7: Midterm Exam I, general rvs, continuous rvs and PDFs, uniform and exponential rvs, expectation, CDFs, geometric, exponential, normal rvs

Week 8: conditioning, independence, multiple continuous rvs, joint CDFs, inference and continuous Bayes' Rule, functions of continuous rvs

Week 9: functions of two or more rvs, probability integral transformation, transforms, transforms of Poisson, exponential, and normal rvs, moment generation

Week 10: sums of independent rvs (convolution), law of iterated expectations, law of total variance, sum of a random number of independent rvs, covariance and correlation

Week 11: Spring Break---no classes

Week 12: introduction to least-squares estimation (LSE)

Week 13: Midterm Exam II, LSE: properties of the estimation error, LLSE, the bivariate normal PDF, the multivariate normal PDF, introduction to limit theorems

Week 14: limit theorems: Markov and Chebyshev inequalities, WLLN, CLT, SLLN, convergence of random sequences

Week 15: introduction to random processes, basic concepts and examples, classification of rps, methods of describing a rp, stationarity

Examinations and Grading:
Midterm Exam I (28%) 15 March 2005, Tuesday evening
Midterm Exam II (28%) 26 April 2005, Tuesday evening
Final Exam (34%) 21 May 2005, Saturday 12:15, EB-101,102,103,104,204
Homework (10%)

There will be a single makeup exam few days after the final exam which will cover all the topics. You can only miss one of the exams and take the makeup if you have a valid, well documented excuse. Only those students who have missed an exam will be eligible to take the makeup exam. You cannot take the makeup exam to improve your grade.