Topic summary · Student revision
Mathematical Models in Statistics Topic Review summary
Self-review on statistical modelling assumptions and choosing distributions.
Files: Topic-Review-Mathematical-Models-in-Statistics.pdf · Topic-Review-Mathematical-Models-in-Statistics-Answers.pdf · free public downloads · diagrams in the PDFs
Key learning points
- A model simplifies reality — state assumptions explicitly.
- Discrete vs continuous choices depend on the variable measured.
- Independence and identical distribution assumptions underpin many tests.
- Comment on model quality when residuals or context disagree.
- Define the population and sampling method when surveys appear.
Worked example 1 — Assumption
Example assumption for a binomial model.
Working
BInomial checklist.
Worked example 2 — Critique
Why critique a model?
Working
Exams reward contextual comments.
Worked example 3 — A model simplifies reality — state assumpt
Apply this idea from the Topic Review: A model simplifies reality — state assumptions explicitly.
Working
Attempt without notes, then check the answers PDF.
Worked example 4 — Discrete vs continuous choices depend on t
Apply this idea from the Topic Review: Discrete vs continuous choices depend on the variable measured.
Working
Attempt without notes, then check the answers PDF.
Scaffolded Learning Sheet and answers (PDFs)
This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.