Probability  Theory

 Fall 2010

Mondays 6:25-9:05 pm

DM 144
 Web Page: http://www.fiu.edu/~teboul/proba4ram-F10.html
Instructor:  Dr Tebou
 Email:  teboul@fiu.edu
 Office:  DM 413C
Tel:  305 348 2939
 Office Hours:  M 5:00-6:00 pm
 Other times:  by appointment only.


Prerequisite:   MAC 2313 or Calculus 3 with at least a C.
Contents:  probability spaces, random variables, limit theorems, conditional expectation, random walks, random processes, martingales

Text: Probability and Random Processes, by Geoffrey Grimmett and David Stirzaker, 3rd edition,  Oxford University Press.

Course requirements: There will be four take-home assignments worth 20% of your course grade. No late assignments will be collected. Collaboration on homework is encouraged, but free-riding is absolutely discouraged; you may discuss the problems on the homework assignment with other class mates, but I expect you to write down the solutions to the assigned problems with your own words. There will be a midterm exam (40% of crse grade), and a final exam (40% of crse grade); both exams will be taken in class. The date of the final exam will be discussed in class the first day.

 

Schedule

I reserve the right to change this schedule at any time

 

 

August 23

Probability spaces (chap 1)

 

August 30

Random variables (sections 2.1, 2.2, 2.3, 2.4)

Assignment 1
available online Sept. 06

September 13

Random vectors (sections 2.5, 3.1, 3.2, 3.3)

 

September 20

Discrete random variables (sections 3.4, 3.5, 3.6)

Assignment 1 due; Assignment 2 out

September 27

Conditional distribution or expectation (sections 3.7, 3.8,3.9)

 

October 04

Random walk and counting sample paths (section 3.10)

Assignment 2 due

October 11

Exam 1

 

October  18

Continuous random variables (sections 4.1 through 4.5 )

 

October 25

Continuous conditional expectation (4.6, 4.7, 4.8, 4.9)

Assignment 3 out

November 01

Generating functions (sections 5.1, 5.2, 5.3)

 

November 08

Characteristic functions (sections 5.6, 5.7, 5.8, 5.9)

 Assignment 3 due; Assignment 4 out

November 15

Limit Theorems (section 5.10)

 

November 22

 Convergence of random processes,  Martingales

Assignment 4 due

November  29

  Convergence of random processes,  Martingales  Cont'ed

 

 

Grading Scale:

0-39      F                      40-49   D-                     50-54    D       55-59   D+
60-64   C                      65-69   C+                      70-74    B-     75-79   B
80-84   B+                    85-89  A-                       90-100  A