Important: This module is for students from the Statistics department only. Students from other departments should take ST220 Introduction to Mathematical Statistics.
Prerequisite(s): ST115 Introduction to Probability.
Commitment: 3 lectures/week, 1 tutorial/fortnight. This module runs in Term 1.
Aims: To build the necessary probability background for mathematical statistics.
- Discrete and continuous multivariate distributions. Marginal distributions.
- Jacobian transformation formula.
- Conditional distributions, conditional expectation and properties.
- Moment generating functions for multivariate random variables.
- Multivariate Gaussian distribution and properties.
- Distributions related to Gaussian distribution: the Chi-squared, Student's and Fisher distributions.
- Convergence in distribution, convergence in probability and almost sure convergence. Examples.
- Laws of large numbers.
- Central limit theorem.
- A. Gut: An Intermediate Course in Probability
- Casella and Berger: Statistical Inference
- Suhov and Kelbert: Probability and Statistics by Example: Basic Probability and Statistics
- J. Pitman: Probability
Assessment: 90% by 2 hour examination in January, 10% by coursework.
Examination Period: January
Deadlines: Assignment 1: week 3, Assignment 2: week 5, Assignment 3: week 7 and Assignment 4: week 9.
Feedback: You will hand in answers to selected questions on the fortnightly exercise sheets. Your work will be marked and returned to you in the tutorial taking place the following week when you will have the opportunity to discuss it. The results of the January examination will be available in week 10 of term 2.