Department of Electrical and Computer Engineering
EC 381: PROBABILITY
THEORY IN
ELECTRICAL AND
COMPUTER ENGINEERING
SPRING 2014
(4 credits)
http://people.bu.edu/cgc/ec381
Professor Christos G. Cassandras
Room 425,
8 St. Mary's St. (
TEL: 353-7154, E-MAIL: cgc@bu.edu, WWW:
http://people.bu.edu/cgc
•
Organization: Lectures: M,W 12:00-2:00, PHO 210
• Prerequisites: Multivariate calculus (CAS MA 22)
•
Requirements:
|
1. Weekly Homework Assignments |
20% |
|
2. Midterm Exam |
40% |
|
3. Second Midterm (or Final Exam) |
40% |
•
Objectives:
1. Develop a solid foundation in
the concepts of probability theory.
2. Learn fundamental probabilistic modeling
and analysis techniques so you can use them in Electrical and Computer
Engineering applications.
3. Learn basic techniques for
managing and processing data and apply them to basic estimation and hypothesis
testing problems.
•
Office Hours: W: 2:00-3:00 pm.
•
Graduate Teaching Fellow: Michael George Sidhom Farag
(mgsfarag@bu.edu), PHO 401A.
•
Required Books: 1. Probability
and Stochastic Processes: A Friendly Introduction for Electrical and Computer
Engineers, R. Yates and D. Goodman, Wiley, Second Edition..
• In addition: Your
own lecture notes! (Most will be provided)
• COURSE OUTLINE •
1. FOUNDATIONS OF PROBABILITY
THEORY
1.1. What is “probability”?
1.2. Basic concepts (sample spaces,
events, probability measures)
1.3. Review of set theory
1.4. Definition of probability and
probability spaces
1.5. Probability axioms
1.6. Event independence
1.7. Conditional probability,
Bayes’ Theorem
1.8. Counting methods:
permutations, combinations, independent trials
2. DISCRETE RANDOM VARIABLES
2.1. Definition of random variable
2.2. Types of random variables
2.2. Probability mass functions (pmf)
2.3. Cumulative distribution
functions (cdf)
2.4. Statistics of random
variables: expectation (mean), variance
2.5. Families of useful discrete
random variables
2.6. Functions of discrete random
variables
2.7. Conditional probability mass
functions (pmf), Conditional expectation
2.8. Random vectors
3. CONTINUOUS RANDOM VARIABLES
3.1. Cumulative distribution
functions (cdf)
3.2. Probability density functions
(pdf)
3.3. Expectation
3.4. Families of useful continuous
random variables
3.5. Functions of random variables
3.6. Conditional probability
density functions (pdf), Conditional expectation
3.7. Mixed (discrete and
continuous) random variables
4. PAIRS OF RANDOM VARIABLES
4.1. Joint cumulative distribution
functions (cdf) and mass functions (pmf)
4.2. Marginal probability mass
functions
4.3. Joint probability density
functions
4.4. Marginal probability density
functions
4.5. Functions of two random
variables
4.6. Expectation, Covariance,
Correlation
4.7. Conditioning, conditional
expectations
4.8. Bivariate Gaussian random
variables
4.9. Random vectors of
continuous/discrete random variables
5. SUMS OF RANDOM VARIABLES AND
LIMIT THEOREMS
5.1. Sample averages
5.2. Moment generating functions
5.3. Markov and Chebychev
inequalities
5.4. Weak and strong laws of large
numbers
5.5. Central Limit Theorem
6. PARAMETER ESTIMATION
6.1. Point estimation
6.2. Interval estimation
7. MARKOV CHAINS
7.1. Chapman-Kolmogorov equations
7.2. Transient analysis
7.3. State classification
7.4. Steady-state analysis
8. HYPOTHESIS TESTING
8.1. Significance testing
8.2. Binary hypothesis testing
8.3. Multiple hypothesis testing