Midterm examination
Duration: 120 minutes. Total: 100 marks. Coverage: Lectures 1–6.
Section A — Probability and distributions (25)
Define probability spaces, derive moments, conditional expectation, covariance properties, and a transformation density.
Section B — Asymptotic theory (25)
Apply LLN/CLT, Slutsky, and delta method. Distinguish convergence in probability and distribution.
Section C — Estimation and inference (30)
Derive a likelihood estimator; construct a confidence interval; formulate a test and interpret its size, power, and p-value.
Section D — Bayesian inference (20)
Derive a conjugate posterior and compare posterior credible intervals with frequentist confidence intervals.
Final examination
Duration: 180 minutes. Total: 100 marks. Coverage: Entire course.
Section A — Experimental design and ANOVA (25)
Analyze a randomized-block or factorial design, specify the model, derive degrees of freedom, and define planned contrasts.
Section B — Regression and GLM (25)
Interpret logistic or Poisson regression output, calculate marginal effects, and assess model diagnostics.
Section C — Advanced methods (25)
Answer problems on nonparametric inference, power, mixed models, or PCA. State the inferential target and assumptions.
Section D — Applied statistical design (25)
Develop a statistical analysis plan with sampling design, estimand, model, multiplicity strategy, power justification, diagnostics, and reproducibility protocol.
Standards
- Define symbols, parameters, and dimensions.
- State assumptions before applying a theorem or test.
- Distinguish model-based and design-based inference.
- Interpret effect sizes and uncertainty, not only p-values.
- Explain what diagnostics can and cannot establish.
- Provide reproducible code and package versions for computational submissions.