Probability
This section is a probability study archive. It contains lecture notes, distribution summaries, convergence guides, prelim solutions, and proof-recognition notes.
The emphasis is practical review: identify the object, recognize the theorem shape, and write a clean argument under constraints.
Start Here
- Probability Prelim: past preliminary exam writeups and exam-oriented notes.
- Pre-Prelim Checklist: notes on triage, theorem recognition, partial solutions, and exam execution.
- Convergence: modes of convergence and related proof techniques.
- Distributions: distribution facts, transformations, Bayesian roles, and recognition notes.
- Distribution Toolkit: common distribution manipulations, MGFs, characteristic functions, transformations, and order statistics.
Course Notes
- STT 881: Probability I lecture notes.
- STT 882: Probability II lecture notes.
- STT 996: additional probability/statistics notes.
- STT 997: homework, definitions, and lecture notes.
- MTH 868: smooth manifold notes that connect to proof-writing and formalization interests.
Topic References
- Martingales
- Inequalities
- Characteristic Functions
- Asymptotics
- Real Analysis
- Useful Trigonometry for Probability
- High-Dimensional Probability
How To Use These Notes
For prelim work, start with the checklist and then move into the specific problem archive. For conceptual review, use the convergence and distribution pages as hubs. For course context, use the lecture-note folders as chronological records.
Many pages are written for retrieval and exam readiness rather than textbook completeness. The goal is not to replace a course text; it is to keep recurring proof moves easier to find.
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