EE306000 ¾÷²v Probability

Prof. Cheng-Shang Chang

Institute of Communications Engineering

National Tsing Hua University

Hsinchu, Taiwan, R.O.C.

cschang@ee.nthu.edu.tw

Instructor: Prof. Cheng-Shang Chang  ±i¥¿©|±Ð±Â

Office: EECS 817

Phone: (03) 571-5131 ext. 42579

Email: cschang@ee.nthu.edu.tw


Lecture Hours: M7, M8, and R6.

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Office Hours: Monday: 13:10¡ã15:00

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Location: EECS Building 207


Teaching Assistants

¡P TA : ¥j¦Ë¥Í   g9564509@oz.nthu.edu.tw
    
¿c§Ó¾Ë   g9564527@oz.nthu.edu.tw
    
§d¨ä®p   g9564528@oz.nthu.edu.tw

¡P Office : EECS 606

¡P Phone : (03) 571-5131 ext. 34129

¡P Office Hours : Monday: 20:00¡ã22:00; Wednesday: 13:10¡ã14:00


Course Description

This course gives an elementary introduction to the theory of probability and its applications.

Prerequisites

¡P         High-school Mathematics

¡P         Calculus

¡P         Linear algebra

Textbook

¡P         S. Ghahramani, Fundamentals of Probability, with Stochastic Processes, 3rd ed. Upper Saddle River, NJ: Prentice Hall, 2005.

References

  • S. Ross, a First Course in Probability, 6th ed. Upper Saddle River, NJ: Prentice Hall, 2002.
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  • A. Papoulis, Probability and Statistics. Englewood Cliffs, NJ: Prentice-Hall, 1990.
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  • P. G. Hoel, and S. C. Port, and C. J. Stone, Introduction to Probability Theory. Boston: Houghton Mifflin, 1971.
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  • A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes, 4th ed. New York: McGraw-Hill, 2002.
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  • W. Feller, an Introduction to Probability Theory and Its Application,
    vol. I & vol. II.
    New York: Wiley, 1968.

Table of Contents

  • Ch1   : Axioms of Probability
    • 1.1 : Introduction 2007/09/10(¤@)(1)(2)
    • 1.2 : Sample Space and Events 2007/09/10(¤@)(2)
    • 1.3 : Axioms of Probability 2007/09/13(¥|)(1)
    • 1.4 : Basic Theorems 2007/09/17(¤@)(1)
    • 1.5 : Continuity of Probability Function 2007/09/17(¤@)(2)
    • 1.6 : Probabilities 0 and 1 2007/09/17(£¸)(2)
    • 1.7 : Random Selection of Points from Intervals 2007/09/17(¤@)(2), 2007/09/20(¥|)(1)

  • Ch2   : Combinatorial Methods
    • 2.1 : Introduction 2007/09/20(¥|)(1)
    • 2.2 : Counting principle 2007/09/20(¥|)(1), 2007/09/27(¥|)(1)
    • 2.3 : Permutations 2007/09/27(¥|)(1)
    • 2.4 : Combinations 2007/09/27(¥|)(1), 2007/10/01(£¸)(1)
    • 2.5 : Stirling's Formula 2007/10/01(£¸)(1)

  • Ch3   : Conditional Probability and Independence
    • 3.1 : Conditional Probability 2007/10/01(£¸)(2)
    • 3.2 : Law of Multiplication  2007/10/01(£¸)(2), 2007/10/04(¥|)(1)
    • 3.3 : Law of Total Probability 2007/10/04(¥|)(1), 2007/10/08(£¸)(1)
    • 3.4 : Bayes' Formula 2007/10/08(£¸)(1)
    • 3.5 : Independence  2007/10/08(£¸)(2),2007/10/11(¥|)(1)
    • 3.6 : Applications of Probability to Genetics 2007/10/15(£¸)(1), 2007/10/15(£¸)(2)
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  • Ch4   : Distribution Functions and Discrete Random Variables
    • 4.1 : Random Variables 2007/10/15(£¸)(2), 2007/10/18 (¥|)(1)
    • 4.2 : Distribution Functions 2007/10/18 (¥|)(1), 2007/10/22 (£¸) (1)
    • 4.3 : Discrete Random Variables  2007/10/22 (£¸) (1)
    • 4.4 : Expectations of Discrete Random Variables  2007/10/22 (£¸) (1), 2007/10/22 (£¸) (2), 2007/10/25 (¥|)(1)
    • 4.5 : Variances and Moments of Discrete Random Variables 2007/10/25 (¥|)(1), 2007/10/29 (£¸) (1)
    • 4.6 : Standardized Random Variables  2007/10/29 (£¸) (1)
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  • Ch5   : Special Discrete Distributions
    • 5.1 : Bernoulli and Binomial Random Variables 2007/10/29 (£¸) (1), 2007/10/29 (£¸) (2)
    • 5.2 : Poisson Random Variable  2007/10/29 (£¸) (2), 2007/11/01 (¥|)(1), 2007/11/05 (£¸) (1)
    • 5.3 : Other Discrete Random Variables 2007/11/05 (£¸) (1)(2)
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  • Ch6   : Continuous Random Variables
    • 6.1 : Probability Density Functions 2007/11/05 (£¸)(2), 2007/11/08 (¥|)(1)
    • 6.2 : Density Function of a Function of a Random Variable 2007/11/08(¥|)(1)
    • 6.3 : Expectations and Variances 2007/11/08 (¥|)(1), 2007/11/12 (£¸)(1)(2)
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  • Ch7   : Special Continuous Distributions
    • 7.1 : Uniform Random Variable  2007/11/12 (£¸)(2)
    • 7.2 : Normal Random Variable  2007/11/12 (£¸)(2), 2007/11/15 (¥|)(1)
    • 7.3 : Exponential Random Variables 2007/11/19 (£¸) (1)
    • 7.4 : Gamma Distribution 2007/11/19 (£¸)(1)(2)
    • 7.5 : Beta Distribution 2007/11/19 (£¸)(2)
    • 7.6 : Survival Analysis and Hazard Function 2007/11/19 (£¸)(2)
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  • Ch8   : Bivariate Distributions
    • 8.1 : Joint Distribution of Two Random Variables 2007/11/22 (¥|)(1), 2007/11/26 (£¸)(1)
    • 8.2 : Independent Random Variables 2007/11/26 (£¸) (1)(2)
    • 8.3 : Conditional Distributions  2007/11/26 (£¸)(2), 2007/11/29 (¥|)(1), 2007/12/03 (£¸)(1)
    • 8.4 : Transformations of Two Random Variables  2007/12/03 (£¸)(1)(2), 2007/12/06 (¥|)(1)
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  • Ch9   : Multivariate Distributions
    • 9.1 : Joint Distribution of n>2 Random Variables  2007/12/06 (¥|)(1) ,2007/12/10 (£¸)(1)
    • 9.2 : Order Statistics 2007/12/10 (£¸)(2)
    • 9.3 : Multinomial Distributions 2007/12/13 (¥|)(1)
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  • Ch10 : More Expectations and Variances
    • 10.1 : Expected Values of Sums of Random Variables  2007/12/13 (¥|)(1), 2007/12/17(£¸)(1)
    • 10.2 : Covariance 2007/12/17(£¸)(2)
    • 10.3 : Correlation 2007/12/20 (¥|)(1)
    • 10.4 : Conditioning on Random Variables 2007/12/20 (¥|)(1),2007/12/24(£¸)(1)(2)
    • 10.5 : Bivariate Normal Distribution 2007/12/27 (¥|)(1)
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  • Ch11 : Sums of Independent Random Variables and Limit Theorems
    • 11.1 : Moment-Generating Functions  2007/12/27 (¥|)(1)
    • 11.2 : Sums of Independent Random Variables 2007/12/31(£¸)(1)
    • 11.3 : Markov and Chebyshev Inequalities 2007/12/31(£¸)(1)(2)
    • 11.4 : Laws of Large Numbers 2007/12/31(£¸)(2), 2008/01/03 (¥|)(1)
    • 11.5 : Central Limit Theorem 2008/01/03 (¥|)(1)

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Lecture Recording

Probability

1. 2007/09/10 (¤@) (1) (2)

2. 2007/09/13 (¥|) (1)

3. 2007/09/17 (¤@) (1) (2)

4. 2007/09/20 (¥|) (1)

5. 2007/09/27 (¥|) (1)

6. 2007/10/01 (¤@) (1) (2)

7. 2007/10/04 (¥|) (1)

8. 2007/10/08 (¤@) (1) (2)

9. 2007/10/11 (¥|) (1)

10. 2007/10/15 (¤@) (1) (2)

11. 2007/10/18 (¥|) (1)

12. 2007/10/22 (¤@) (1) (2)

13. 2007/10/25 (¥|) (1)

14. 2007/10/29 (¤@) (1) (2)

15. 2007/11/01 (¥|) (1)

16. 2007/11/05 (¤@) (1) (2)

17. 2007/11/08 (¥|) (1)

18. 2007/11/12 (¤@) (1) (2)

19. 2007/11/15 (¥|) (1)

20. 2007/11/19 (¤@) (1) (2)

21. 2007/11/22 (¥|) (1)

22. 2007/11/26 (¤@) (1) (2)

23. 2007/11/29 (¥|) (1)

24. 2007/12/03 (¤@) (1) (2)

25. 2007/12/06 (¥|) (1)

26. 2007/12/10 (¤@) (1) (2)

27. 2007/12/13 (¥|) (1)

28. 2007/12/17 (¤@) (1) (2)

29. 2007/12/20 (¥|) (1)

30. 2007/12/24 (¤@) (1) (2)

31. 2007/12/27 (¥|) (1)

32. 2007/12/31 (¤@) (1) (2)

33. 2008/01/03 (¥|) (1)

34. 2008/01/14(¤@)(1)

 

 


Handout


Homework

Homework policy: This course allows and encourages discussion or collaboration on the homework. However, you are expected to write up your own solution and understand what you turn in. Please note that you are not allowed to look at the solution to previous homework solution. You will get zero point of your homework part 20% in this semester no matter how many problems you copy!! And please hand in your homework before 9:00pm on due date. No delay is allowed!!

¡P HW 1    Solution

o        section 1.2 problem  2

o        section 1.4 problem 12, 14, 21, 28

o        section 1.7 problem  3, 4, 7, 12

    Due date: 2007/10/04

¡P HW 2   Solution

o        section 2.2 problem 2, 7

o        section 2.3 problem 2, 3

o        section 2.4 problem 11, 17, 38

    Due date: 2007/10/15

¡P HW 3   Solution

o        section 3.1 problem 12, 13

o        section 3.2 problem 4

o        section 3.3 problem 9

o        section 3.4 problem 1

o        section 3.5 problem 14, 15

o        section 3.6 problem 1, 9

Due date: 2007/10/29

¡P HW 4   Solution

o        section 4.2 problem 9

o        section 4.3 problem 11

o        section 4.4 problem 3

o        section 4.5 problem 5, 7

Due date: 2007/11/08

¡P HW 5    Solution

o        section 5.1 problem 25

o        section 5.2 problem 22, 24

o        section 5.3 problem 9, 22

Due date: 2007/11/19 

¡P HW 6    Solution

o        section 6.1 problem 1

o        section 6.2 problem 2, 4

o        section 6.3 problem 4, 17

Due date: 2007/11/22

¡P HW 7   Solution

o        section 7.1 problem 14

o        section 7.2 problem 23

o        section 7.3 problem 15 Hint

o        section 7.4 problem 4

o        review        problem 8

Due date: 2007/12/04

¡P HW 8   Solution

o        section 8.1 problem 2

o        section 8.2 problem 13

o        section 8.3 problem 6

o        section 8.4 problem 1

Due date: 2007/12/17

¡P HW 9   Solution

o        section 9.1 problem 13, 15

o        section 9.2 problem 7

Due date: 2007/12/27

¡P HW 10  Solution

o        section 10.1 problem 10

o        section 10.2 problem 11

o        section 10.3 problem 6

o        section 10.4 problem 4

o        section 10.5 problem 7

Due date: 2008/01/06

 


Exams Solution

Midterm : 11/26 19:00¡ã21:00, chapter 1¡ã chapter 7, EECS R206¡B207

Final:       1/7  15:20¡ã17:10, ¡ã chapter 11.


Grading Grade

¡P 5%   Class participation

¡P 20% Homework

¡P 35% Midterm exam

¡P 40% Final exam

HOT!! Final Grades


                        Supplement

                       If you are interested in the following topics, you can see the related websites.

¡P Page 33, what is the "Axiom of Choice"?        http://www.math.vanderbilt.edu/~schectex/ccc/choice.html   

                                     You can also learn what "Banach-Tarski" Paradox is.                        

                                     Banach http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Banach.html

                                     Tarski    http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Tarski.html

¡P Page 91, Example 3.14 A simulation of Gambler's Ruin Problem

¡P Page 101, Theorem 3.5 Sequential analysis

¡P  English class

 


                              Useful link                 

                              MathWorld, Wikipedia

                                 Last update: 2008/01/18