Aims

The aim of the module is to extend your knowledge of statistical theory and its applications to introduce you to some of the basic methods of statistical inference and estimation, which are needed in data analysis. The aim will be achieved through a mixture of theory and practice.

Learning objectives

At the end of the module you should be able to...

1. be practised in the use and manipulation of standard density and distribution functions of both discrete and continuous random variables;
2. be acquainted with the concepts of joint and conditional distributions and the distribution of functions of random variables.
3. understand the use of moment generating functions and their use in proving the Central Limit Theorem, and to see this in use with, for example, Poisson and exponential random variables;
4. comprehend the usefulness of the normal distribution in aiding the calculation of the distribution of certain functions of the data, for instance sample means and variances, and the t-ratio;
5. understand the most basic concepts of statistical inference;
6. know about convergence in probability and convergence in distribution;
7. be able to perform basic statistical inference on the parameters of standard distribution functions, including estimation of parameters using several methods, construction of confidence intervals (with a brief mention of hypothesis tests).  

Syllabus

• An Introductory Lecture
• Discrete Random Variables
• Continuous Random Variables
• The Bivariate Normal Distribution
• Nature of Statistical Methods
• Random Sampling
• Convergence of Random Variables
• Central Limit Theorem
• Further Distribution Theory
• Likelihood

Recommended texts

• P G Hoel Introduction to Mathematical Statistics (5th edn), Wiley (SF HOE).
• A Rice, Mathematical Statistics and Data Analysis (2nd edn), Wadsworth and Brooks/Cole (SF RIC).
• G Cassella and R L Berger, Statistical Inference (2nd edn), Duxbury Press. (SF 2 CAS)
• W Mendenhall, R L Scheaffer, and D D Wackerly, Mathematical Statistics with applications (4th edn), Duxbury Press. (SF MEN)
• R V Hogg, J W McKean and A T Craig, Introduction to Mathematical Statistics (6th edn), Prentice-Hall (SF HOG).
  In addition students should obtain copies of the following tables:
• H R Neave, Statistics Tables for mathematicians, engineers, economists and the behavioural and management sciences, Routledge (paperback) (SF 0.83 NEA and REF SF 0.83 NEA).

Teaching

• Autumn Term
• 2 lectures per week
• 1 seminar per week

Assessment

One and a half hour closed examination in week 1 Spring Term (90%); Coursework: (10%). Note that coursework submitted after the advertised deadlines will be given a mark of zero.

Elective information

Introduction to distributions arising in inference from normally distributed samples (and some others). Central limit theorem. Sample mean and variance.

Please check prerequisites carefully before asking to take this module as an elective.

Prerequisites

• Probability Theory I (0590032)