Course Introduction and Set Theory
Last modified — 23 May 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).
4 assignments, each worth 5%
Must be hand written (tablet or paper) and submitted digitally on Gradescope (linked on Canvas). No typed assignments unless you have accommodations.
Late policy: 5% deduction per hour late. No submissions after 24 hours (solutions will be posted). With the condensed term, we don’t have a lot of wiggle room. Sorry.
Must submit academic concession form at least 12 hours before due date for extenuating circumstances.
Midterm (Tuesday June 2nd): 30%
Final: 50%
All closed-book, but you can have a “cheat sheet”
Academic concessions:
The in-class exercises and weekly assignment problems are designed to prepare you for the kinds of questions we ask on exams (so… actually do them! They’re there to help you practice. Don’t rely on solutions you find online or AI assistance.)
This is a short term - we move fast!
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) | Tues/Wed, 12:00pm - 1:00pm | (This week only) ESB 1041* |
| Isaac | Tuesdays, 12:00pm - 1:00pm | (This week only) ESB 1041* |
| Mohammad | Thursdays, 4:00pm - 5:00pm | ESB 3174 |
| Nathan | Fridays, 3:00pm - 4:00pm | ESB 3174 |
*ESB 4192 after May 18
All content will be posted on this website
Canvas is currently down 💀
I have the same amount of information as you, and anticipate it to be back up next week.
Course communication will eventually be through Canvas announcements. Ensure your email notifications are on.
Until then, and Piazza and email will be used for announcements. Please ensure you’ve joined using the link I’ve emailed to you.
LATE ENTRANTS: please email me for access to Piazza and Gradescope!
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, and the summer term is face-paced. 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.
Keep this week’s Assignment due date on your radar (Wednesday May 20, 11:59pm)
Take care!
Stat 302 - Winter 2025/26