EL 6303: Probability Theory Spring 2008
Wednesday
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”
Wednesday 2 – 4 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 (1/23) The axiomatic definition of experiment
and probability. Conditional Probability.
Bayes’ Theorem, Notion of
independence.
2 (1/30) Repeated trials. Bernoulli trials and their limiting forms. The concept
of a random variable.
3
(2/6) 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
(2/13) Functions of one
random variable and their distributions.
5
(2/20) Expected value
of a random variable: Mean, Variance, Moments, and Characteristic function.
6
(2/27) Two random
variables: Joint distribution and joint density functions, Independence
7-8 (3/5, 3/12) One function of two
random variables.
9 (3/26) Midterm Examination. (Wednesday,
March 26, 2008, 6-9PM)
10-11
(3/28, 4/2) Two functions of
two random variables. Order statistics.
12
(4/9) Joint
moments, Uncorrelatedness, Orthogonality, Joint characteristic function.
More on Gaussian random variables.
13
(4/16) Conditional
distribution and conditional expected values.
14
(4/30) The principle
of maximum likelihood(ML). Elements of parameter estimation.
The central limit theorem.
15 5/2 Extra
Review Class (6-9PM)
16 (5/7) Final Examination.
(Wednesday , May 7, 2008, 6-9PM)