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Probability
Spring 2011


⇒ to time table and download of class material

News

  • Class Evaluation: The class evaluation will be online between 1 and 17 June. I would very much appreciate your feedback, so please spend a couple of minutes to fill out the online form. Thanks!
  • Final Exam: The final exam will take place on
    • Wednesday, 22 June, 10:10–13:00 (Note that this is one hour longer than usual!)
    Regulations:
    • open book: any book is allowed
    • not allowed are: any telecommunication devices like mobile phones, any laptop with wireless capabilities, any "friend", or any other help from outside...
    • covered material: everything covered in class except Gaussian stochastic processes
  • Mid-Term Exam: The mid-term exam will take place on
    • Wednesday, 20 April, 10:10–13:00 (Note that this is one hour longer than usual!)
    Regulations:
    • open-book: any book, notes, and exercises are allowed
    • not allowed are: any telecommunication devices like mobile phones, any laptop with wireless capabilities, any "friend", or any other help from outside...
    • covered material: everything covered in class until 13 April (derived distributions), i.e., Chapters 1 to 3 (first edition) or Chapters 1 to 4.1 (second edition)
  • Change of TAs: For administrative reasons we had to change the TAs of this class. Please see the TA-section below for more details.

Course Objectives

This course is an introduction to probability. Its goal is to give the students a profound knowledge about probability theory and some of its important applications. We will cover the following subjects:

  • Sample Space and Probability
    • probabilistic models and conditional probability
    • total probability and Bayes' Rule
    • independence
  • Discrete Random Variables (RV)
    • probability mass function (PMF)
    • transforming RVs
    • expectations
    • joint PMF
    • conditioning and independence
  • General Random Variables
    • probability density function (PDF) and cumulative distribution function (CDF)
    • joint PDF
    • Gaussian RVs
    • conditioning
    • transforming RVs
    • sum of random number of independent RVs
    • least squares estimation
  • Stochastic Processes
    • Bernoulli process
    • Poisson process
    • Markov chains
  • Limit Theorems
    • Markov and Chebyshev inequalities
    • weak and strong law of large numbers
    • convergence
    • ergodicity
    • central limit theorem

For more detail see the time table below.

We believe that this course is essential for any engineer and we very much hope that a student who finishes the course will feel comfortable with the theory and can apply it.

Prerequisites

The following lectures/topics are recommended:

  • basic math from high-school

Instructor

Prof. Stefan M. Moser
Engineering Building IV, Office 727
phone: 03-571 21 21 ext. 54548
e-mail:

Teaching Assistants

In case you would like to discuss some questions in Chinese, you may contact the TAs of this class:

Kuo Yuan-ChuChang Hui-Ting
e-mail:
office:Engineering Building IV, Office 716A (ED716A)Engineering Building IV, Office 716A (ED716A)
phone:03-571 21 21 ext. 5463003-571 21 21 ext. 54630
office hours:on appointmenton appointment

To make our and your life easier, let's agree on the following rule: You may contact or visit the TAs at any time also outside of office hours. However, if you haven't made an appointment in advance, they have the right to tell you that they haven't got time right at that moment.

Time and Place

The course is scheduled for 3 hours per week:

  • Tuesday, 9:00–9:50 (B), Engineering Building IV, Room B26 (EDB26)
  • Wednesday, 10:10–12:00 (CD), Engineering Building IV, Room B26 (EDB26)

The course starts on Tuesday, 22 February, and finishes on Wednesday, 22 June.

Office Hours

NCTU requests that every teacher offers two hours per week where students may come to ask questions:

  • Tuesday, 15:30–17:30, Engineering Building IV, Office 727

However, we would like to encourage you to show up in the teacher's or teaching assistant's office at any time in case you have questions about the class or related subjects. Moreover, we are always available during and after classes.

Textbook

Dimitri P. Bertsekas, John N. Tsitsiklis: "Introduction to Probability," Athena Scientific, Massachusetts, 2002 (first edition) or 2008 (second edition).

For certain topics there will be additional handouts during class.

Exercises

Every week, an exercise will be distributed in class and also made available online for download. This exercise will consist of several problems that need to be solved at home and handed in during the class of the following week. A model solution will be distributed in class and made available online afterwards.

We believe the exercises to be extremely important and crucial to the understanding of the course. They also serve as a preparation for the mid-term and final exams and we therefore highly recommend to solve them. To pass the course you need to hand in at least 10 exercises.

Exams

There will be one mid-term and one final exam. Both exams are going to last three hours and be open-book. Details about the covered material will be published in due time.

Grading

The grade will be an average of

  • the homework and class participation (15%),
  • the mid-term exam (35%), and
  • the final exam (50%).

The grade of the homework will not be based on the correctness of the answers, but rather on the effort the student shows in trying to solve them. Moreover, I will try to reward students who participate actively in the course.

This course is worth 3 credits.

Special Remarks

The lecture will be held in English.

Time Table

Note that some details of this program might change in the course of the semester.

Note that some linked documents in this table can only be downloaded from within NCTU and NTHU!

W Date Topic Handouts Exercise (due on) Solutions Comments
1 22 Feb. Introduction, set theory, probabilistic models Syllabus (Version 2) Exercise 1 (1 Mar.)    
  23 Feb. Conditional probability, total probability theorem    
 
2 1 Mar. Total probability theorem, Bayes' rule, independence   Exercise 2 (8 Mar.)    
  2 Mar. Independence, counting, discrete RV     Solutions 1  
3 8 Mar. Discrete RV: PMF   Exercise 3 (15 Mar.)    
  9 Mar. Functions of RVs, expectations, mean, variance, joint PMF     Solutions 2  
4 15 Mar. Conditional PMF   Exercise 4 (22 Mar.)    
  16 Mar. Conditional PMF, independent RVs; continuous RVs: PDF, CDF     Solutions 3  
5 22 Mar. Continuous RVs: PDF, CDF, Exponential RV   Exercise 5 (29 Mar.)    
  23 Mar. Continuous RVs: Gaussian RV, conditioning     Solutions 4  
6 29 Mar. Continuous RVs: conditioning, joint PDF   Exercise 6 (12 Apr.)    
  30 Mar. Continuous RVs: joint PDF, Bayes' rule, derived distributions     Solutions 5  
7 5 Apr. No lecture (Holiday)  
   
  6 Apr. No lecture (Holiday)    
 
8 12 Apr. Continuous RVs: derived distributions Handout 1 Exercise 7 (26 Apr.)    
  13 Apr. Continuous RVs: derived distributions, transform, moment generating function     Solutions 6  
9 19 Apr. Moment generating function, conditional variance  
Solutions 7 (short version)  
  20 Apr. Mid-Term Exam    
ATTENTION: This is a 3 hours exam: 10:10–13:00
10 26 Apr. Discussion exam, sum of random number of independent RVs   Exercise 8 (3 May)    
  27 Apr. Covariance and correlation, MMSEE, LMMSEE     Solutions 7  
11 3 May MMSEE, LMMSEE, covariance matrices   Exercise 9 (10 May)    
  4 May Covariance matrices, multivariate Gaussian distribution     Solutions 8  
12 10 May Multivariate Gaussian distribution, stochastic processes, stationarity   Exercise 10 (17 May)    
  11 May Stochastic processes, stationarity, Bernoulli process     Solutions 9  
13 17 May Poisson process   Exercise 11 (24 May)    
  18 May Poisson process     Solutions 10  
14 24 May Markov process: definitions, classifications   Exercise 12 (31 May)    
  25 May Markov process: classifications, steady state and stationarity     Solutions 11  
15 31 May Markov process: steady state and stationarity   Exercise 13 (7 Jun.)    
  1 Jun. Markov process: steady state and stationarity     Solutions 12 Please fill out online class evaluation before 17 June!
16 7 Jun. Markov process: long-term frequency interpretation, short-term transient behavior   Exercise 14 (15 Jun.)
Exercise 15 (15 Jun.)
   
  8 Jun. Markov process: short-term transient behavior, limit theorems: inequalities     Solutions 13  
17 14 Jun. Limit theorems: convergence, strong law of large numbers  
   
  15 Jun. Limit theorems: convergence, strong law of large numbers, central limit theorem     Solutions 14,
Solutions 15
 
18 21 Jun. No lecture (moved to Friday)  
   
  22 Jun. Final Exam    
ATTENTION: This is a 3 hours exam: 10:00–13:00!
  24 Jun. Discussion of final exam and Coffee Time       We meet at 13:30 outside in the coffee-shop beside the information building

-||-   _|_ _|_     /    __|__   Stefan M. Moser
[-]     --__|__   /__\    /__   Senior Researcher & Lecturer, ETH Zurich, Switzerland
_|_     -- --|-    _     /  /   Adj. Professor, National Chiao Tung University (NCTU), Taiwan
/ \     []  \|    |_|   / \/    Web: http://moser-isi.ethz.ch/


Last modified: Wed Jun 22 14:11:13 UTC+8 2011