## Comprehensive Exam Requirements

All Ph.D. students must pass a Comprehensive Exam, which consists of two parts. Part I consists of two written exams. Part II consists of preparing a written report and completing an oral exam. Further details about Parts I and II are given below. Students must pass Part I before Part II can be attempted. All Ph.D. students must complete Comprehensive Part I and Part II within the first two years of study in the program.

## Comprehensive Exam Part I

Comprehensive Part I exam consists of two written exams covering basic underrgraduate material. Students must pass both exams.

### Exam A (Introductory Probability, Mathematical Statistics )

Based on material from STATS 2D03 and STATS 3D03. Sample topics:

- Probability, conditional probability, Bayes theorem, random variable and their distributions, moment generating function, univariate and bivariate transformations.
- Convergence in probability and in distribution, weak law of large numbers, central limit theorem.
- Point estimators and properties, interval estimation, hypothesis testing, Cramer-Rao lower bound.

### Exam B (Statistical Methods and Regression)

Based on material from STATS 2MB3 and STATS 3A03. Sample topics:

- Method of moments, multivariate distributions, maximum likelihood estimation, central limit theorem and applications, confidence intervals and hypothesis tests in one sample, two-sample inference based on the normal distribution.
- Simple linear regression and correlation, multiple linear regression, one-way and two-way ANOVA.

### Sample Exams

- Statistics Comprehensive Exam A – January 2022
- Statistics Comprehensive Exam B – January 2022
- Statistics Comprehensive Exam A – May 2022
- Statistics Comprehensive Exam A – 2021/08
- Statistics Comprehensive Exam B – 2021/08
- Statistics Comprehensive Exam A – 2019/09
- Statistics Comprehensive Exam B – 2019/08

Students who do not pass both written exams on their first attempt are permitted a second attempt at the exam(s) not passed.

## Comprehensive Exam Part II

Comprehensive Part II involves preparing a written report and taking an oral examination on subject matter related to the proposed research area.

### Purpose of the Exam

This exam is intended to check that the student has sufficient knowledge of the general area of their proposed research to undertake original research and produce publishable results.

### Examining Committee

The exam committee consists of the supervisor and two additional faculty members. One of the additional faculty members will serve as the chair of the exam committee.

### Written Report

At least two weeks before the exam, the student must submit a document (15-20 pages, prepared in LaTeX) to the exam committee that contains a literature review and research proposal.

### Oral Exam Format

The oral exam begins with a presentation from the student (15-20 mins) summarizing the contents of the written report with more focus on the research proposal part, and less on the literature review part. The student will then answer examiners’ questions about the contents of the report and the presentation. Usually, the questioning is in two rounds, with up to 10 mins per examiner per round.