Lectures: M, TU, W, TH, 9:00 am - 10:29 am; Jun 17, 2024 - Aug 09, 2024.
Location: North Gate 105
Lecturer: Ziran Liu, office hour (TBA).
GSI: TBA (tba@berkeley.edu). S/He will run recitation sections in {location} on {Day of the Week, time}.
Reader: TBA
Course description: An introduction to probability, emphasizing concepts and applications. Conditional expectation, independence, laws of large numbers. Discrete and continuous random variables. Central limit theorem. Selected topics include the Poisson process, Markov chains, and characteristic functions.
Prerequisites: This course is intended for math/stat majors and other students strongly interested in this subject. It requires fluency in topics such as multi-variable integration and the basics of real analysis.
Textbook: Our reference text will be Probability by Jim Pitman.
Homework: They will be posted on this page every Thursday during the same week of lectures. (You should hand in your HW to your GSI during the recitation session the following week.)
Grading: problem sets (35%), quizzes (10%), midterm (20%), and a final exam (35%).
A tentative schedule for this course is:
Jan. 24.
Introduction, some combinatorics. Reading: Sections 1.1, 1.2, 1.3, and 1.4
(Permutations and Combinations in the 6th century B.C., A conversation between Fermat and Pascal)
Jan. 26.
More combinatorics. Sample space and events. Reading: Sections 1.5, 2.1, and 2.2
(Kolmogorov's foundations of probability theory)
Jan. 31.
Axioms of probability. Reading: Sections 2.3 and 2.4
Feb. 2.
Some probability distributions on finite sets, Inclusion-exclusion. Reading: Sections 2.4 and 2.5.
Feb. 7.
Conditional probability. Reading: Sections 3.1, 3.2 and 3.5.
Sometimes conditioning changes it all, sometimes conditioning does not matter: keep the order of magnitude in mind.
Feb. 9.
Bayes' formula (Example). Reading: Section 3.3.
Feb. 14.
Independence (as explained by Marc Kac). Reading: Section 3.4
Feb. 16.
Discrete random variables. Reading: Sections 4.1 and 4.2.
Feb. 21.
Expectation, variance. Reading: Sections 4.3, 4.4 and 4.5.
Feb. 23.
Some discrete distributions I. Reading: Section 4.6
Feb. 28.
Some discrete distributions II. Reading: Section 4.7.
Mar. 2.
Some discrete distributions III. Reading: Section 4.8.
Mar. 7.
Review
Mar. 9.
Midterm exam
Mar. 14.
Spring Break
Mar. 16.
Spring Break
Mar. 21.
Review of midterm exam and multivariate calculus.
Mar. 23.
Continuous random variables, distribution and density. Reading: Section 5.1.
Mar. 28.
Expectation, variance, transformation and Jacobian. Reading: Section 5.2.
Mar. 30.
Some continuous distributions. Reading: Sections 5.3, 5.4, 5.5.
Apr. 4.
Jointly distributed random variables. Reading: Section 6.1.
Apr. 6.
Expectation, covariance, transformation and Jacobian. Reading: Sections 6.3, 6.7, 7.2, 7.3, 7.4
Apr 11.
Conditional probability. Reading: Sections 6.4, 6.5, 7.5
Apr. 13.
Independence. Reading: Section 6.2.
Apr. 18.
Moment generating functions. Reading: Section 7.7.
Apr. 20.
Law of large numbers I. Reading: Section 8.2.
Apr. 25.
Law of large numbers II. Reading: Section 8.4.
Apr 27.
Central limit theorem I. Reading: Section 8.3.
May 2.
Central limit theorem II. Reading: Section 8.3.
May 4.
Markov Chains.
May 10 to 16.
Final exam.
Problem sets.