Theory of Probability 1

References:

• Probability and Measure, Billingsley, 1998, Third Edition.
• Probability Theory and Examples, Durret, 2010, Forth Edition

Course outline:

Probability space, Theory of large numbers, Random variables, Expectation, Conditional probability, Convergence theory, Central limit theorem

From Billingsley 's book, Sections 1, 2, 3, 4, 5, 6,10,11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 25, 26, 27.

Homework:

Billingsley:

Section 1: 3, 4, 5, 6

Section 2: 3-12, 17

Section 3: 1, 2, 6, 8, 11

Section 4: 1, 2, 3, 5, 11

Section 5:1-10, 12, 15, 17

Section6: 1, 5, 6, 8

Section 13: 1-6

Section 14: 2, 3, 5

Section 15: 5, 7

Section 16: 1, 2, 3

Section 20: 1- 6, 22,

Section 21: 7-21.

Section 22: 1, 2, 3, 8, 12, 13.

Section 25: 1, 5, 6, 7, 8, 9.

Section 27: 2, 4, 7.

Durret:

Chapter 1:  All exercises, but 1.6.

Chapter 2:  All exercises, but 1.6, 2.5, 3.2, 3.3, 3.7, 3.8, 3.9, 3.17, 3.19, 4.2, 4.3, 4.4, 5.2, 5.7, 5.8, 5.12 and exercises of Section 6.

Chapter 3: 1.2, 1.3, 1.4, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.9, 2.10, 2.11, 2.12, 2.13, 2.14, 2.15, 2.16, 3.1, 3.2, 3.3, 3.4, 3.8, 3.9, 3.10, 3.11, 4.2, 4.3, 4.4, 4.5.