The Chinese University of Hong Kong

The Department of Electronic Engineering

Part-time MSc Program

Foundation Course - Probability Theory & Random Processes Basic

Introduction

The foundation course - Probability Theory & Random Processes Basic - will be conducted on August and September from 2:30 p.m.5:30 p.m. in the campus. The three-hour lecture will cover probability theory, random variables and random processes.

The course, and the other two foundation courses, are free for EE MSc students. They are optional and students are voluntary to attend. 

You will find some questions below. The questions are designed to test how much you know about the subjects. The answers can be found in the course materials. If you after reading the course materials still do not know the answers, we would advise you to attend the foundation course. 

If you have decided to attend the course, you are strongly advised to read the course material first, and then identify what you do not know before the lecture which is only three-hour for each foundation course. You are most welcome to ask questions during the lecture time.

Probability Theory

*  Questions

  1. In order to develop a useful theory of probability, it is important to separate 3 stages in the consideration of any real probability. What are these 3 stages?

  2. What is a trial?

  3. What is an event?

  4. How to find the probability of an event?

  5. Two events are said to be independent. What does it mean?

1.   Course material - Probability

Random Variables

*  Questions

  1. What is a random variable?

  2. How to measure the probability density function of a random variable?

  3. How to compute the nth moment of a random variable?

  4. What is a Gaussian random variable?

  5. What does Central Limit Theorem say?

  6. What is the condition under which two random variables are independent?

  7. What is the condition under which two random variables are uncorrelated?

  8. When does independent imply uncorrelated?

  9. When does uncorrelated imply independent?

1.   Course material - Random Variables

Random Processes

*  Questions

  1. What is a random process?

  2. What is the condition under which a random process is statistical determined?

  3. What is a random vector?

  4. What is the autocorrelation matrix of a random vector?

  5. What is a Gaussian random process?

  6. What is a strict-sense stationary random process?

  7. What is a wide-sense stationary random process?

  8. When does strict-sense stationary imply wide-sense stationary?

  9. When does wide-sense stationary imply strict-sense stationary?

  10. What is an ergodic random process?

  11. What is the correlation function of an ergodic random process?

  12. What is the power spectrum of an ergodic random process?

  13. What is the relationship between the correlation function and the power spectrum of an ergodic random process?

1.   Course material - Random Processes