Ping-Chun Hsieh
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515512 Probability (機率)

  • Instructor: Ping-Chun Hsieh

  • Email: pinghsieh [AT] nycu [DOT] edu [DOT] tw

  • Textbook:

    • [Gha] Saeed Ghahramani, Fundamentals of Probability with Stochastic Processes, 4th edition, CRC Press, 2018.

  • References:

    • [Ber-Tsi] Dimitri P. Bertsekas and John N. Tsitsiklis, Introduction to Probability, 2nd edition, Athena Scientic, 2002.

    • [Res] Sidney I. Resnick, A Probability Path, Springer Science & Business Media, 2013.

    • [Bis] Christopher M. Bishop, Pattern Recognition and Machine Learning, Springer, 2006.

    • [Ras-Wil] Carl Edward Rasmussen and Christopher K. I. Williams, Gaussian Processes in Machine Learning, MIT Press, 2006.

  • Grading

    • Homework: 45%

    • Midterm: 25%

    • Final exam: 30%

  • Course Schedule:

Week Lecture Date Topics References Lecture Slides
1 1 9/4 Probability Model and Set Operations [Gha Ch. 1.1-1.4] Lec1 annotated
1 2 9/6 Probability Axioms [Gha Ch. 1.3-1.5] Lec2 annotated
2 3 9/11 Continuity of Probability Functions and Conditional Probability [Gha Ch.1.5-1.6 and 3.1-3.4] Lec3 annotated
2 4 9/13 Conditional Probability [Gha Ch. 2, 3.5, and 4.1-4.3] Lec4 annotated
3 5 9/18 Conditional Probability, Combinatorics, and Random Variables [Gha Ch. 3.5, 4.1, and 4.3] Lec annotated
4 6 9/25 Random variables [Gha Ch.4.1-4.3] Lec6 annotated
4 7 9/27 Discrete Random variables [Gha Ch. 5.1-5.3] Lec7 annotated
5 8 10/4 Discrete Random Variables, Entropy, and Expected Value [Gha Ch. 5.1-5.3] Lec8 annotated
6 9 10/9 Discrete Random Variables, Entropy, and Expected Value [Gha Ch. 5.1-5.3] Lec9 annotated
6 10 10/11 Expected Value and Moments [Gha Ch. 5.1-5.3] Lec10 annotated
7 11 10/16 Moments and Continuous Random Variables [Gha Ch. 4.4-4.5 and 6.1] Lec11 annotated
7 12 10/18 Continuous Random Variables [Gha Ch. 6.1 and 7.1-7.3] Lec12 annotated
8 13 10/23 Continuous Random Variables, Expectation, and Joint Distributions [Gha Ch. 6.3 and 7.3] Lec13 annotated
9 10/30 Midterm
9 14 11/1 Joint Distributions [Gha Ch. 7.3] Lec14 annotated
10 15 11/6 Joint Distributions and Sum of Independent Random Variables [Gha Ch. 8.1-8.2 and 11.1-11.2] Lec15 annotated
10 16 11/8 Moment Generating Functions [Gha Ch. 8.1-8.2 and 11.1-11.2] Lec16 annotated
11 17 11/13 Concentration Inequalities [Gha Ch. 11.2-11.3] Lec17 annotated
11 18 11/15 Concentration Inequalities [Gha Ch. 11.2-11.3] Lec18 annotated
12 19 11/22 Weak Law of Large Numbers [Gha Ch. 11.4-11.5] Lec19 annotated
13 20 11/27 Weak and Strong Laws of Large Numbers [Gha Ch. 11.4-11.5] Lec20 annotated
13 21 11/29 Laws of Large Numbers and Central Limit Theorem [Gha Ch. 11.4-11.5] Lec21 annotated
14 22 12/4 Central Limit Theorem and Conditional Distributions [Gha Ch. 11.5 and 8.3] Lec22 annotated
14 23 12/6 Conditional Distributions [Gha Ch. 11.5 and 8.3] Lec23 annotated
15 24 12/13 Bivariate Normal [Gha Ch. 10.5 and 8.4] Lec24 annotated
16 12/18 Final Exam