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
(Lec1Lec6) 
28

Lec7:
ZeroOne Laws: Independence 
30

Lec8:
ZeroOne Laws: BorelCantelli Theorem, Chebyshev's Inequality

Feb

2

Lec9:
ZeroOne Laws: Tail
sigmaalgebra, Kolmogorov ZeroOne Law

4

Lec10:
ZeroOne Laws: Convergence
of R.V.s, Kolmogorov and Levy Inequalities 
6

Lec11:
ZeroOne 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 (Lec7Lec14) 
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
(Lec1Lec 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 (Lec15Lec 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

MarApr

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 LevyKhintchine Formula

8

Lec31:
Infinite Divisible Distributions: Stable Laws 
10

Good Friday (No Lectures) 
Apr

13

Quiz#4
(Lec22Lec 30) 
15

Lec32: Infinite Divisible
Distributions: Applications 
17

Lec33: Course Review
