ST1126 Probability (Part B)
Introductory description
This module runs in Term 2 and follows on from ST111 Probability A and is an optional module which leads to numerous statistical, probabilistic, operational research and econometrics courses. You may be interested in this module if you wish to undertake further statistics modules.
Prerequisites: ST111 Probability A
Postrequisites: ST104 Statistical laboratory, ST202 Stochastic Processes, ST220 Introduction to Mathematical Statistics
This module is not available to students who have their home department in Statistics, who take an equivalent module. Students who are considering transferring to a course in Data Science, Mathematics & Statistics or MORSE at the end of their first year should take this module.
Module aims
To lay the foundation for all subsequent modules in probability and statistics, by introducing the key notions of mathematical probability and developing the techniques for calculating with probabilities and expectations.
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.
 The notion of a random variable and its distribution. Examples in both discrete and continuous settings. Probability mass functions and density functions. Cumulative distribution functions.
 Joint distributions. Independence of random variables.
 Expectation of random variables. Properties of expectation.
 Variance and Chebyshev's inequality. Covariance and the CauchySchwartz inequality.
 Addition of independent random variables: convolutions. Generating functions, Moment generating functions and their use to compute convolutions.
 Important families of distributions: Binomial, Poisson, negative Binomial, exponential, Gamma and Gaussian. Their properties, genesis and interrelationships.
 The law of large numbers and the Central limit theorem.
Learning outcomes
By the end of the module, students should be able to:
 Apply the theory of probability distributions, expectation, variance and covariance associated with random variables.
 Compute and apply generating functions for univariate random variables.
 Interpret problems and select appropriate distributions to create probability models.
 Apply the law of large numbers and the central limit theorem to probability models.
Indicative reading list
Durrett, Elementary Probability for Applications.
Grimmett and Walsh, Probability An Introduction.
Grimmett and Stirzaker, One Thousand Exercises in Probability
View reading list on Talis Aspire
Subject specific skills
TBC
Transferable skills
TBC
Study time
Type  Required  Optional 

Lectures  15 sessions of 1 hour (25%)  2 sessions of 1 hour 
Tutorials  2 sessions of 1 hour (3%)  
Private study  37 hours (62%)  
Assessment  6 hours (10%)  
Total  60 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.
Students can register for this module without taking any assessment.
Assessment group D3
Weighting  Study time  

Computer Based Assessment 1  5%  3 hours 
Multiple choice quiz which will take place during the term that the module is delivered. 

Computer Based Assessment 2  5%  3 hours 
Multiple choice quiz which will take place during the term that the module is delivered. 

1 hour examination (Summer)  90%  
The examination paper will contain three questions, of which the best marks of TWO questions will be used to calculate your grade. ~Platforms  Moodle

Assessment group R
Weighting  Study time  

1 hour examination (September)  100%  
The examination paper will contain three questions, of which the best marks of TWO questions will be used to calculate your grade. ~Platforms  Moodle

Feedback on assessment
Answers to problems sets will be marked and returned to students. Tutorials provide opportunities for students to discuss the problem sets.
Solutions and cohort level feedback will be provided for the examination.
Prerequisites
To take this module, you must have passed:
Antirequisite modules
If you take this module, you cannot also take:
 ST11512 Introduction to Probability
Courses
This module is Core for:
 Year 1 of UMAAGL11 Undergraduate Mathematics and Economics
 Year 1 of UECAGL12 Undergraduate Mathematics and Economics (with Intercalated Year)
This module is Optional for:
 Year 1 of UPXAFG33 Undergraduate Mathematics and Physics (BSc MMathPhys)
 Year 1 of UPXAGF13 Undergraduate Mathematics and Physics (BSc)
 Year 1 of UPXAFG31 Undergraduate Mathematics and Physics (MMathPhys)
This module is Option list A for:
 Year 1 of UCSAG4G1 Undergraduate Discrete Mathematics
 Year 1 of UCSAG4G3 Undergraduate Discrete Mathematics
 Year 1 of UMAAG100 Undergraduate Mathematics (BSc)
 Year 1 of UMAAG103 Undergraduate Mathematics (MMath)
 Year 1 of UMAAG106 Undergraduate Mathematics (MMath) with Study in Europe
 Year 1 of UMAAG1NC Undergraduate Mathematics and Business Studies
 Year 1 of UMAAG1N2 Undergraduate Mathematics and Business Studies (with Intercalated Year)
 Year 1 of UMAAGV17 Undergraduate Mathematics and Philosophy
 Year 1 of UMAAGV18 Undergraduate Mathematics and Philosophy with Intercalated Year
 Year 1 of UMAAG101 Undergraduate Mathematics with Intercalated Year
This module is Option list B for:
 Year 1 of UMAAGV17 Undergraduate Mathematics and Philosophy