Aims and Fit of Module

This module aims to cement a solid foundation in the theoretical teaching of different statistical distributions and their applications. It provides an unusually comprehensive depth and breadth of coverage and reflects the latest in statistical thinking and current practices. This is a required module for students in a variety of fields in finance, economics, financial mathematics, natural sciences and engineering, etc. The designer/instructor of this module believes it is helpful for students to spend some time learning how the mathematical ideas of statistics carry over into the world of practical applications.

Learning outcomes

A. Understand probability distributions, probability densities and multivariate distributions.


B. Calculate the expectation of a random variable.


C. Use moment generating functions to calculate the moments of a random variable.


D. Work with transformations of random variables, find the probability distribution of a function of random variables.


E. Understand sampling distributions and the Central Limit Theorem.


F. Understand maximum likelihood estimation, including its asymptotical properties. Apply related techniques with nonlinear models.


G. Understand hypothesis testing and its related topics.


H. Understand multivariate linear regression, including its geometric interpretation, classical finite sample and asymptotical properties and inference on the estimators

Method of teaching and learning

This module will be delivered by a combination of formal lectures and tutorials.