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Course Outline


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Instructor

Xiaoting Li (
xiaoting.li@stat.ubc.ca
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)

Course Description

STAT 302 is an undergraduate-level probability course designed to provide a comprehensive understanding of fundamental probability theory. Topics covered include probability rules, random variables, expectation and conditional expectation, as well as discrete and continuous probability distributions, and limit theorems.

Prerequisites

One of MATH 200, 217, 226, 253 or 254.
Note: STAT 302 is equivalent to MATH 302. Unlike 200-level STAT courses, this course is primarily a MATH course. Mathematical proofs or derivations is an essential component of this course.

References

Lecture slides or notes will serve as the primary references for the course, and no specific textbook is required. However, if you are seeking more detailed explanations and additional practice problems, the following two textbooks may be useful:
A First Course in Probability by Sheldon Ross.
Mathematical Statistics with Applications by Dennis D. Wackerly.

List of topics

Module 1: Probability Rules
Basic Definitions related to probability
Combination and Permutations
Conditional Probability and Bayes’ Rule
Module 2: Univariate Distribution
Basic Definitions of Random Variables
Special discrete distributions
Special continuous distributions
Module 3: Multivariate Distribution(*)
Joint Distribution, Marginal Distribution, Conditional Distribution
Total laws on conditional expectation/variance
Covariance and Correlation
Independent random variables
Module 4: Transformations of Random Variables(if time permits)
Univariate Transformation
Bivariate Transformation
Sums of independent random variables (convolution and moment generating function)
Module 5: Large Sample Theory
Probability inequalities.
Law of large numbers
Central Limit Theorem

Some advice:

The modules in this course vary in difficulty levels. While some may be relatively straightforward, others can be significantly more challenging. It's important to anticipate these changes and plan your time accordingly.
The pace of the summer course is notably faster compared to regular term courses. I would recommend you only take one course in summer term. Treat it as a full-time job.
Probability is the theoretical foundation of statistics. This course will help you build the understanding of the fundamental probability concepts, which is necessary in higher-level statistics courses.

Assessment

Category
Scheme 1
Scheme 2
1
Written Assignments
20%
20%
2
WebWork
5%
5%
3
Midterm Exam
25%
10%
4
Final Exam
50%
65%
There are no rows in this table
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There are two grading schemes, and the final grade will be based on the higher one.
Here's a brief description of each component:
Written Assignments: There will be four written assignments. Each assignment contributes 5% to your overall grade. The purpose of the written assignments are to inspire/deepen your thinking about the concepts and provide feedback on how to properly show your work in solving the questions.
Webwork: There will be roughly five Webworks, accounting for 5% of the final grade. There is no limit on the number of attempts, and the questions are intended to help you familiarize yourself with new concepts. Treat them as learning resources, and make sure that you understand each step of the solution.
Exams: There will be an in-class midterm on June 4th Tuesday in ESB 1012. There will be no makeup test for the midterm; if missed for a valid reason, the weight will be shifted to the final exam. The final exam is scheduled during the exam period from June 24 to 28. To pass the course, typically a minimum of 50% of the marks on the final exam is required.
Two review sessions will be conducted by TAs the week before each exam to assist in preparation.

Links to UBC academic policies

UBC policies for Academic concessions
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https://www.calendar.ubc.ca/vancouver/index.cfm?tree=3,329,0,0
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UBC policies related to exam issues ​
https://science.ubc.ca/students/advising/exams
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UBC policy with regards to Academic Misconduct:
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https://www.calendar.ubc.ca/vancouver/index.cfm?tree=3,54,111,0
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We acknowledge that UBC Vancouver is located on the traditional, ancestral, and unceded territory of the Musqueam people.
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