TN402 − THEORY OF PROBABILITY

Credits: 4

Theory: 3 credits, Practice: 1 credit

I. Overview

This course provides :

- The fundametal concepts of mathematical probability which is the science of random.

- The applications to others sciences.

II. Prerequisites

- TN020 - Calculus A1.

- TN021 - Calculus A2.

III. Contents

Chapter 1 Events and the probability of events

1.1 Random experiment and sample spaces

1.2 Events, the algebra of events

1.3 Probability of an event, rules of probability

1.4 Conditional probability, the Law of total probability, Bayes’ formula

Chapter 2 Discrete random variables

2.1 Distribution function

2.2 Characteristics of discrete random variables

2.3 The Binomial distribution, the Poission distribution

Chapter 3 Continuouse random variables

3.1 Distribution function and density

3.2 Characteristics of continuouse random variables

3.3 The Normal, the Exponential, the Uniform distribution

and others distributions

Chapter 4 Random vectors

4.1 Distribution function and density

4.2 Independence of components

4.3 Conditional probability distribution

4.4 Covatinace and correlation coefficient

4.5 The bivariate Normal distribution

Chapter 5 Characteristic function

5.1 Definition and properties

5.2 Method of characteristic function

Chapter 6 Law of large numbers and limit theorems

6.1 Inequalities

6.2 Law of large numbers

6.3 The Poisson limit theorem

6.4 Central limit theorems

Lab assignment : none

IV. References

[1] Nguyen Duy Tien, Vu Viet Phu. Theory of probability. Education, Hanoi (2000).

[2] Kai Lai Chung. A Course in the theory of probability. Academic Press (1974).

[3] Feller W. An introduction to probability and its applications. Willey (1968).