Course Introduction and Set Theory
Last modified — 13 Sep 2026
Topics (Broadly):
Set theory
Probability Rules
Random Variables and Distributions
Joint, Marginal, and Conditional Distributions
Expectation, Variance, Moment Generating Functions
Inequalities and Convergences
Be prepared to do lots of math (proofs, limits, derivatives, integration, maximization, minimization, transformations).
I am your instructor, Dr. Tompkins
Education: BSc Math (StFX), MMATH + PhD in Biostatistics (UWaterloo)
Hobbies: crafting, cozy gaming, travel
OR
(whichever gives you the highest mark!)
There are 7 In-class checkpoints throughout the term.
Based on weekly problems assigned for homework
~15 minutes each to solve one short problem in class
Each checkpoint is worth 10 points, and there are 70 points available to gain. Your score will be calculated as min(CP1 + CP2 + CP3 + CP4 + CP5 + CP6 + CP7, 50).
Can bring a cheat sheet (8.5 x 11 inches or smaller, HANDWRITTEN - no photocopies, no prints, not typed or written on tablets)
Can bring a non-graphing calculator
Friday Sept 25
Friday October 02
Friday October 09
Friday October 30
Friday November 06
Friday November 27
Friday December 04
NO CONCESSIONS. The grading scheme allows you to completely miss two checkpoints and still get full marks, though this is NOT recommended. Plan to write all checkpoints - save the “drops” for if you get sick.
Emails inquiring about dropping/reweighting checkpoints will be politely pointed to the syllabus.
Midterm 1: Friday October 16th
Midterm 2: Friday November 20
Final: TBD do not book travel until exam dates have been announced
All closed-book, but you can have a “cheat sheet” (see syllabus for rules)
Academic concessions:
Self-declared concessions can only be used for once throughout the course.
- For example, if a student already submitted a self-declared concession form for Midterm 1 and then requests a concession for Midterm 2, the case will be escalated to Science Advising. Office hours offer you an opportunity to get specific help from the teaching team to clarify concepts and work through practice problems.
When office hours are busy, they may run more like a tutorial where everyone can listen in on the questions being answered.
| Teaching Team Member | Times | Location |
|---|---|---|
| Grace (Instructor) | Thursdays, 2pm - 3pm | EST 3174 |
| Nathan | Mondays, 1pm - 2pm | ESB 3174 |
| Isaac | Wednesdays, 1pm - 2pm | ESB 3174 |
| Carlo | Wednesdays, 11am - 12pm | ESB 1041 |
All content will be posted on this website
Piazza is also enabled for peer discussion - this is not a place to ask TAs/me for help with problems. Help each other out!
To get help from me/the TAs, come to office hours 😁
This classroom has a zero tolerance policy for disrespectful behavior.
The content in this course can be challenging - help each other out! Be respectful and kind to your fellow students, TAs, and teaching team.
No recording/taking photos during lecture, please. Everything will be posted online for you.
This is more of a math course than a data science course. It uses calculus, proofs, and other mathematical skills that we expect at a 300-level statistics course.
The biggest barriers to success are leaving exam preparation to the last minute and doing insufficient practice.
We will be using many examples involving dice and cards. Unless otherwise stated, you can assume the following:
A standard die (plural is dice) 🎲:
Calculus and all of your other pre-requisites!
See Calculus Prep to get an idea of the expectations of this course.
After this lecture, students are anticipated to be able to:
Suppose \(A\), \(B\) are events (subsets of \(\Omega\)).
Union: \(A \cup B\)
\[ \omega \in A \cup B \Leftrightarrow \omega \in A \mbox{ or } \omega \in B \]
Intersection: \(A \cap B\) \[\omega \in A \cap B \Leftrightarrow \omega \in A \mbox{ and } \omega \in B\]
Complement: \(A^c\) \[\omega \in A^c\Leftrightarrow \omega \notin A\]
Symmetric difference: \(A \, \triangle \, B\) \[A \, \triangle \, B \, = \, \left( A \cap B^c \right) \, \cup \, \left( A^c \cap B \right)\]
Subset: \(A \subseteq B\) is read “A is a subset of B”.
This means every element in A appears in B. \[\forall a, a \in A \implies a \in B\]
Equality
Commutative:
\(A \cup B \ = \ B \cup A\)
\(A \cap B \ = \ B \cap A\)
Associative:
\(A\cup B\cup C \, = \, \left( A\cup B\right) \cup C=A\cup \left( B\cup C\right)\)
\(A\cap B\cap C \, = \, \left( A\cap B\right) \cap C=A\cap \left( B\cap C\right)\)
Distributive:
\(\left( A\cup B\right) \cap C \, = \, \left( A\cap C\right) \cup \left( B\cap C\right)\)
\(\left( A\cap B\right) \cup C \, = \, \left( A\cup C\right) \cap \left( B\cup C\right)\)
Hint: use the fact that \(B \cup B^c = \Omega\)
Hint: use the first rule above above to express \(B\) in terms of \(B\cap A\) and \(B\cap A^c\)
De Morgan’s Laws: For any two events (sets) \(A\) and \(B\), we have
\[ ( A\cup B ) ^{c} \, = \, A^{c}\cap B^{c} \]
To prove the theorem it is sufficient to show that
\[ ( A\cup B )^{c} \subseteq A^{c}\cap B^{c} \]
and that
\[ A^{c}\cap B^{c} \subseteq ( A\cup B ) ^{c} \]
Prove De Morgan’s Laws
The power set of \(\Omega\) (denoted \(2^\Omega\)) is the set of all possible subsets of \(\Omega\).
For example, if \(\Omega \ = \ \{ 1,2,3 \}\) then: \[2^{\Omega } \, = \Bigl\{ \varnothing , \{ 1\} , \{ 2 \} , \{ 3 \} , \{ 1,2 \} , \{ 1,3 \} , \{ 2,3 \}, \{ 1, 2, 3 \} \Bigr\}\]
\(\varnothing\) denotes the empty set: \(\varnothing = \{ \}\).
\(|\cdot|\) denotes the size of a set (number of elements).
If \(\Omega\) has \(n\) elements, what is \(|2^\Omega|\)?
Partition: A grouping of elements into non-empty, disjoint subsets such that every element in \(\Omega\) is in exactly one subset.
Stat 302 - Winter 2025/26