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STAT501 Probability Theorey (I) (Fall 2019)
Instructor: Cheng Ouyang
Office Hours:
Time: Monday and Friday 45pm (or by appointment)
Location: SEO 502
Announcement:
Course Schedule (updated weekly):
Weeks 
Sections 
Brief Description 
08/26  08/30

1.1; 1.2; 1.3

Introduction; Basic Set Theory; Limits of Sets

09/02  09/06

Holiday(Monday); 1.4; 1.5

Limits of Sets and Monotone Sequences; Set Operations and Closure.

09/09  09/13

1.6 and 1.7; 1.8; 2.1

The sigmafield Generated by a Given Class; Comparing Borel Sets; Basic Definition and Properties of Probability Spaces

09/16  09/20

2.1; 2.2; 2.2

Basic Definition and Properties of Probability Spaces; More on Closure

09/23  09/27

2.3 and 2.4; 2.4; 2.4

Two Constructions; Constructions of Probability Spaces

09/30  10/04

2.4; 2.4, 2.5; 2.5

Constructions of Probability Spaces; Measure Constructions

10/07  10/11

3.1; 3.2; 3.2.

Inverse Maps; Measurable Maps, Random Elements, Induced Probability Measures. 
10/14  10/18

3.3; 4.1, 4.2; 4.2.

SigmaFields Generated by Maps; Basic Definitions of Independence, Independent Random Variables. 
10/21  10/25

4.4; 4.5; 4.5;

More on Independence: Groupings; Independence, ZeroOne Laws,
BorelCantelli Lemma. 
10/28  11/01

4.5; 5.1, 5.2; 5.2

Independence, ZeroOne laws, BorelCantelli Lemma;
Preparation for Integration; Expectation and Integration 
11/04  11/08

5.2; 5.3; 5.4.

Expectation and Integration; Limits and Integrals; Indefinite Integrals; 
11/11  11/15

5.4; 5.5; 5.6,

Indefinite Integrals; Transformation Theorem and Densities; Riemann vs Lebesgue Integral. 
11/18  11/22

5.7, 5.8; 5.9; 5.9.

Product Spaces, Probability Measures on Product Spaces; Fubini's Theorem. 
11/25  11/29

5.9,6.1; Holidy (Friday)

Fubini's Theorem, Almost Sure Convergence; Convergence in Probability;
Connections between a.s. and i.p. Convergence. 
12/02  12/06

6.2; 6.3; 6.5

Convergence in probability; Connections between a.s. and
i.p. convergence; Lp Convergence 
Homework (updated weekly):
 Homework #1 (due on 09/04): 1.9  6, 19.
 Homework #2 (due on 09/11): 1.9  10, 14, 16, 17, 18.
 Homework #3 (due on 09/18): 1.9  21, 22, 31(hard one!), 41.
 Homework #4 (due on 09/25): 1.9  33(i), 34, 44; 2.6  1(b).
 Homework #5 (due on 10/04): 2.6  3, 6, 7.
 No homework due on Friday (Oct 11).
 Homework #6 (due on 10/18): 2.6  9 (b) (d), 11, 19(a) (b) (c)
 Homework #7 (due on 10/25): 2.6  19(d) (e), 27(a) (b); 3.4  2
 Homework #8 (due on 11/01): 3.4  4, 5, 6, 17.
 Homework #9 (due on 11/08): 3.4  18, 22; 4.6  1, 3.
 Homework #10(due on 11/15): 4.6  8, 13, 17(a).
 No homework due on Friday (Nov 22)
 Homework #11(due on 12/02): 4.6  20, 24, 28;
 Homework #12(No need to turn in): 5.10  5 (a), 6(a) (b) (d), 15,
22(a) (b), 28.(Solution)
Relevant Course Materials:
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