0: Preface

These are my notes for STA238H1: Probability, Statistics and Data Analysis II at the University of Toronto.

Course Overview

An introduction to statistical inference and practice:

• Statistical models and parameters
• Estimators of parameters and their statistical properties
• Methods of estimation
• Confidence intervals
• Hypothesis testing
• Likelihood function
• The linear model

The Articles

Part I: Foundations

1. Probability Review — Random variables, distributions, expectation, variance
2. Statistical Models — Parameters, families of distributions, sufficient statistics

Part II: Estimation

3. Estimators & Properties — Bias, variance, MSE, consistency, efficiency
4. Method of Moments — Matching sample and population moments
5. Maximum Likelihood Estimation — Likelihood function, MLE properties, Fisher information

Part III: Inference

6. Confidence Intervals — Pivotal quantities, interval estimation, interpretation
7. Hypothesis Testing — Null/alternative, test statistics, p-values, power
8. Likelihood Ratio Tests — Neyman-Pearson, generalized LRT

Part IV: Regression

9. The Linear Model — OLS, assumptions, Gauss-Markov theorem
10. Inference for Linear Models — t-tests, F-tests, prediction intervals

Coming Winter 2026.