EL 6303: Probability Theory Fall 2009
Friday 11.00AM ~
Instructor: Prof. S. Unnikrishna Pillai
pillai@hora.poly.edu
(Tel) (718) 260-3732
(Fax) (718) 260-3906
LC 253
Homework .
>> Homeworks,
Exams Web page
Grading:
Homework: 5% Quiz #: 10% Midterm: 35% Final: 50%
Textbook
1. Papoulis and Pillai, “Probability,
Random Variables and Stochastic Processes”, 4th Edition, McGraw-Hill Book
Company, 2002.
2. V. K Rohatgi, “An Introduction to Probability Theory and Mathematical Statistics”,
John Wiley & Sons, 1976
3. V. K Rohatgi, “Statistical Inference”, John Wiley & Sons, 1984”
Friday 2 – 5 PM
Remark
Both books are highly recommended. Try to do all home works, which will
turn out to be very useful.
Use Lecture notes at Lecture Slides
Syllabus
1 (9/11) The axiomatic definition of experiment
and probability. Conditional Probability.
Bayes’ Theorem, Notion of
independence.
2 (9/18) Repeated trials. Bernoulli trials and their limiting forms. The concept
of a random variable.
3
(9/25) Probability
distribution and density functions. Probability mass function.
Examples of random
variables: Normal (Gaussian), Poisson, Gamma, Exponential, Laplace,
Cauchy, Rayleigh, etc.
Bayes’ Theorem revisited.
4
(10/2) Functions of one
random variable and their distributions.
5
(10/9) Expected value of a random variable:
Mean, Variance, Moments, and Characteristic function.
6 (10/16) Two random variables: Joint
distribution and joint density functions,
7 (10/23) One function of two random variables.
8 (10/30)
Midterm Examination. (
9-10
(11/6, 13) Two functions of
two random variables. Order statistics.
12
(11/20) Joint moments,
Uncorrelatedness, Orthogonality, Joint characteristic function.
More on Gaussian random variables.
13 (12/4) Conditional distribution and
conditional expected values.
14 (12/11) The central limit theorem.
The principle of maximum likelihood (ML).
Elements of parameter estimation
15 (12/18) Final Examination. (