### Math 180AIntroduction to Probability

##### Fall 2021, Lecture C00

Instructor: Gwen McKinley (gmckinley@ucsd.edu)

Lectures: 5-5:50pm on MWF, in Center Hall 216
Discussion sections: Tuesday evenings in AP&M 6402

Office hours:

• Gwen McKinley: M. 11am-12pm and F. 1-3pm in AP&M 6333
• Eva Loeser: Th. 4:30-6:30pm in in AP&M 7218
• Nicholas Sieger: M. 3-4pm on Zoom (link posted on Canvas)

#### Course information

For information on grading, textbook, acommodations, and more: see the Course Syllabus.

Due dates: here is a master calendar of all homework due dates and exam dates.

Exams/Quizzes: There will be four in-person quizzes held in class on the following dates:

• Quiz 1: Wed, Oct 6
• Quiz 2: Wed, Oct 20
• Quiz 3: Wed, Nov 3
• Quiz 4: Wed, Nov 17

The final exam will be held in person on Saturday, Dec 4, from 7-10pm, location TBA.

#### Homework

Weekly homework assignments are posted here. Homework is due by 11:59pm on the posted date (generally Monday), through Gradescope. These dates are also listed on the master calendar of assignments.
Note: there may be some slight changes to the assigments posted below (e.g., shifting a problem to a later homework), but each assgnment will be finalized no later than one week before its due date.

#### Lecture schedule

Here is a tentative schedule of what will be covered in each lecture, together with the relevant section(s) of the textboox (Introduction to Probability by Anderson, Seppäläinen, and Valkó). This is subject to change; there will be some give and take between lectures.

Week Date Topic ASV Sections
0 9/24 Definition of Probability, Course Logistics 1.1
1 9/27 Properties of Probability Appendix B, 1.2, 1.4
9/29 Combinatorial Probability (review videos on counting) Appendix C, 1.2, 1.4
10/1 Conditional Probability 2.1
2 10/4 Bayes' Formula 2.2
10/6 Quiz 1 (quiz), (solutions), (review slides from Lecture B00)
10/8 Independent Events 2.3
3 10/11 Discrete Random Variables (PMF and CDF plot for sum of two dice) 1.5, 3.2
10/13 Expectation of Discrete Random Variables 3.3, 8.1
10/15 Variance of Discrete Random Variables (examples with expectation 0) 3.4
4 10/18 Binomial and Geometric Distributions (examples from class) 2.4, 3.3-3.4
10/20 Quiz 2 (quiz), (solutions)
10/22 Poisson Distribution, Part 1 4.4
5 10/25 Poisson Distribution, Part 2 (graphs), (examples), (V-1 example) 4.4
10/27 Continuous Random Variables (follow-up note) 3.1-3.4, 5.2
10/29 Normal Distribution (warm-up problem), (normal PDF and CDF graphs) 3.5
6 11/1 Exponential Distribution (example from class) 4.5
11/3 Quiz 3 (quiz), (solutions)
11/5 Joint Distributions of Random Variables (warm-up problem) 6.1-6.2
7 11/8 Independence of Random Variables 6.3, 8.2
11/10 Sums of Independent Random Variables (warm-up),
(continuous example, alternate solution)
7.1
11/12 Covariance and Correlation (sum of normals), (spurious correlations),
(sharks!), (correlation graphs), (game!)
8.4
8 11/15 Moment Generating Functions, Part 1 (warm-up), (skewness and kurtosis) 5.1
11/17 Quiz 4 (quiz), (solutions)
11/19 Moment Generating Functions, Part 2 (differentiating integrals) 5.1, 8.3
9 11/22 Markov and Chebyshev Inequalities 9.1
11/24 Law of Large Numbers (warm-up) 9.2, 9.5
11/26 No Class (Black Friday)
10 11/29 Central Limit Theorem, Part 1 (graphs) 9.3
12/1 Central Limit Theorem, Part 2 9.3
12/3 REVIEW
12/4 Final Exam (Saturday, 7-10pm)