Stat 409 L01 (Winter 2009)
"Theoretical Probability"
Course Outline
Instructor:
Anatoliy Swishchuk
E-mail: aswish@ucalgary.ca
Office: MS552
Tel.: (403) 220-3274
Office Hours: TR:12:30am-14:00am

Place: MS427
Lectures Schedule for  Stat 409
Lectures schedule (L01)
Monday/Wednesday/Friday: 16:00-16:50 (MS427)

Syllabus
Elementary measure theory, zero-one laws, weak and strong laws of large numbers, characteristics functions, central limit theorems, infinitely divisible distributions

Course Information Sheet
 Important Class Dates:
First day of class: 16:00, Monday, January 12, 2009
   Q# 1: Jan 26, Mon, 16:00-16:50 (MS427)
  Q# 2: Feb 23, Mon, 16:00-16:50 (MS427)
  Q# 3: Mar 16, Mon, 16:00-16:50 (MS427)
   Q# 4: Apr 13, Mon, 16:00-16:50 (MS427)
Midterm: March 4, 2009, Wednesday, 16:00-16:50 (MS427)
Final Exam: Tuesday, April 21, 12:00-2:00pm, MS427
     Last day of class: 16:00, April 17, Fri, 2009.
 
Recommended textbooks:
'Probability Theory' by Y. S. Chow and H. Teicher, Springer Texts in Statistics, 3d edition, 1997

Course Web Page:
The current official syllabus for this course is available in the wall pockets across from MS 476 and
on the webpage at www.math.ucalgary.ca Course Listing-Undergraduate (http://math.ucalgary.ca/courses/f08).
There is also a web page for this course which contains the course outline, tentative course schedule,  grading scheme, important class dates, etc.
Announcements made in class will be posted there (see end of this web-page). The address of this web page is: http://www.math.ucalgary.ca/~aswish/stat409W09.html/

Class work:
In-class lectures with typical examples (short lecture notes will be posted on the webpage in the form of pdf-files
);
your computer must have an Adobe Acrobat reader (for free downloading see www.adobe.com).

Quizzes, Midterm and Final Exam
There will be 4 Quizzes, 1 Midterm and 1 Final Exam

Grading scheme (Course Evaluation) for Stat409:
Quizzes (4)
20%=4x5%
Q1: Jan 26; Q2: Feb 23; Q3: Mar 16; Q4: Apr 13
Midterm
Final Exam
30%
50%
March 4, 2009, Wednesday, 16:00-16:50
Tuesday, April 21, 12:00-2:00pm, MS427

Tentative Lectures Schedule for Stat409
Month
Day
Monday
Day
Wednesday
Day
Friday
Jan
12
Lec1:  Overview and Introduction.
14
Lec2: Construction of Measures
16
Lec3: Integration
Jan
19
Lec4: Transformations
21
Lec5: Product Spaces
23
Lec6:  Distributions and Expectations
 Jan
26
Quiz#1 (Lec1-Lec6) 28
Lec7:  Zero-One Laws: Independence 30
Lec8: Zero-One Laws: Borel-Cantelli Theorem, Chebyshev's Inequality
Feb
2
Lec9: Zero-One Laws: Tail sigma-algebra, Kolmogorov Zero-One Law 4
Lec10: Zero-One Laws: Convergence of R.V.s, Kolmogorov and Levy Inequalities 6
Lec11: Zero-One Laws: Kolmogorov's Series Theorems
Feb
9
Lec12:  Weak and Strong Laws of Large Numbers (LLN);
11
Lec13: LLN: Weak LLN (Chebyshev's) and Strong LLN (with mean zero) 13
Lec14:  LLN: Kolmogorov's Strong LLN I
Feb
16
Reading Week (No Lectures) 18
Reading Week (No Lectures) 20
Reading Week (No Lectures)
Feb
23
Quiz#2 (Lec7-Lec14) 25
Lec15:  Characteristic Functions: Definition, Examples 27
Lec16:  Characteristic Functions: Definition, Examples II
Mar
2
Lec17: Characteristic Functions:  Applications of Uniqueness of DF 4
Midterm (Lec1-Lec 16) 6
Lec18: Moment Generating Functions and Laplace Transform



Mar
9
Lec19:  Weak Convergence, Helly's Theorems
11
Lec20: Characteristic Functions: Levy Limit Theorems 13
Lec21: Characteristic Functions: Bochner Theorem and Applications of MGF
Mar
16
Quiz#3 (Lec15-Lec 21) 18
Lec22:  Central Limit Theorems: Independent I.D. Components 20
Lec23: Central Limit Theorems: Lindeberg Condition
Mar
23
Lec24: Central Limit Theorems for Independent Components 25
Lec25: Central Limit Theorems: Lyapunov's Condition and Theorem 27
Lec26: Central Limit Theorems Aftermath
Mar-Apr
30
Lec27: Infinite Divisible Distributions: Definition, Convolution of Measures 1
Lec28:  Infinite Divisible Distributions: Examples and Compound Poisson R.V.s 3
Lec29: Infinite Divisible Distributions: Characterization and Weak Limit
Apr
6
Lec30: Infinite Divisible Distributions: The Levy-Khintchine Formula
8
Lec31:  Infinite Divisible Distributions: Stable Laws 10
Good Friday (No Lectures)
Apr
13
Quiz#4 (Lec22-Lec 30) 15
Lec32: Infinite Divisible Distributions:  Applications 17
Lec33: Course Review

Announcements: 

Your marks are available now. Send me e-mail to know your mark.
This page was updated on April 27, 2009.