ST21812 Mathematical Statistics Part A
Introductory description
This module runs in Term 1 and is core for students with their home department in Statistics and not available for students from other departments.
Prerequisite: ST115 Introduction to Probability.
Module aims
To develop more advanced probabilistic methods that are used in Statistics.
The module builds the necessary probability background for mathematical statistics. It covers topics such as multivariate probability distributions, conditional probability distributions and conditional expectation, multivariate normal distribution, convergence of sequences of random variables.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
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 Chisquared, Student's and Fisher distributions.
Convergence in distribution, convergence in probability and almost sure convergence. Examples.
Laws of large numbers.
Central limit theorem.
Learning outcomes
By the end of the module, students should be able to:
 Understand more advance notions of probability needed in mathematical statistics including properties of multivariate Gaussian distributions, the law of large numbers, and the central limit theorem.
 Be able to calculate probabilities and expected values in more complex and sometimes multidimensional contexts.
 To be able to manipulate mathematical statements regarding the limiting behaviour of random sequences.
Indicative reading list
View reading list on Talis Aspire
Subject specific skills
Mathematical, analytical, problem solving
Transferable skills
Analytical, problem solving, investigative skills, communication, good working habits
Study time
Type  Required 

Lectures  30 sessions of 1 hour (25%) 
Tutorials  5 sessions of 1 hour (4%) 
Private study  61 hours (51%) 
Assessment  24 hours (20%) 
Total  120 hours 
Private study description
Weekly revision of lecture notes and materials, wider reading and practice exercises, working on problem sets and preparing for examination.
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Assessment group D1
Weighting  Study time  

Written assignment  10%  12 hours 
The assignment will contain a number of questions for which solutions and / or written responses will be required. The preparation and completion time noted below refers to the amount of time in hours that a wellprepared student who has attended lectures and carried out an appropriate amount of independent study on the material could expect to spend on this assignment. You will write your answers on paper and submit it as instructed. 

Multiple Choice Quizzes  10%  12 hours 
A number of multiple choice quizzes which will take place during the term that the module is delivered. 

Examination  80%  
Full marks may be obtained by correctly answering Question 1 from Part I and two complete questions from ~Platforms  Moodle

Assessment group R
Weighting  Study time  

Online Examination  Resit  100%  
Full marks may be obtained by correctly answering Question 1 from Part I and two complete questions from ~Platforms  Moodle

Feedback on assessment
Answers to problems sets will be marked and returned to you in a tutorial or seminar taking place the following week when you will have the opportunity to discuss it.
Solutions and cohort level feedback will be provided. The results of the January examination and cohort level examination feedback will be available in week 10 of term 2.
Postrequisite modules
If you pass this module, you can take:
 ST40915 Medical Statistics with Advanced Topics
 ST33215 Medical Statistics
 EC30615 Econometrics 2: Time Series
 EC33815 Econometrics 2: Microeconometrics
Antirequisite modules
If you take this module, you cannot also take:
 ST22012 Introduction to Mathematical Statistics
Courses
This module is Core for:

USTAG302 Undergraduate Data Science
 Year 2 of G302 Data Science
 Year 2 of G302 Data Science
 Year 2 of USTAG304 Undergraduate Data Science (MSci)
 Year 2 of USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 2 of USTAG1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)

USTAGG14 Undergraduate Mathematics and Statistics (BSc)
 Year 2 of GG14 Mathematics and Statistics
 Year 2 of GG14 Mathematics and Statistics

USTAY602 Undergraduate Mathematics,Operational Research,Statistics and Economics
 Year 2 of Y602 Mathematics,Operational Research,Stats,Economics
 Year 2 of Y602 Mathematics,Operational Research,Stats,Economics
This module is Optional for:
 Year 3 of UMAAGL11 Undergraduate Mathematics and Economics
 Year 4 of UECAGL12 Undergraduate Mathematics and Economics (with Intercalated Year)
This module is Option list B for:

UCSAG4G1 Undergraduate Discrete Mathematics
 Year 2 of G4G1 Discrete Mathematics
 Year 2 of G4G1 Discrete Mathematics
 Year 2 of UCSAG4G3 Undergraduate Discrete Mathematics