ST11910 Probability 2
Introductory description
This module follows Probability 1 developing the theory of probability distributions, conditional expectation, modelling and other fundamental concepts. This module aims to develop students’ ability to create probabilistic arguments and models.
This module is core for students with their home department in Statistics and is not available to students from other departments. Students from other departments should consider ST120 Introduction to Probability.
Module aims
The aims of the modules are
 to introduce students to the nature of mathematics as an academic discipline;
 to develop mathematical comprehension and reasoning skills in a concepts and prooforiented setting;
 to develop communication skills in mathematics including proof writing;
 to develop systematic problemsolving skills;
 to lay the foundation for concurrent and subsequent modules in probability and statistics by introducing the key notions of mathematical probability;
 to introduce the techniques for calculating with probabilities and expectations.
 to build a foundation for independent learning including selfregulation and assessment literacy.
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.
This module covers the following: common families of probability distributions, conditional expectation, probabilistic modelling, moment generating functions and the central limit theorem
Learning outcomes
By the end of the module, students should be able to:
 interpret key ideas of probability and calculate associated probabilities and expectations of random variables
 interpret concepts relating to the theory of probability distributions
 describe the role of randomness in mathematical modelling of real world situations
Indicative reading list
Ross, S. (2014). A first course in probability. Pearson;
Pitman, J. (1999). Probability, Springer texts in Statistics;
Suhov and Kelbert, Probability and Statistics by Example: Basic Probability and Statistics.
View reading list on Talis Aspire
Subject specific skills

Demonstrate facility with advanced mathematical and probabilistic methods.

Select and apply appropriate mathematical and/or statistical techniques.

Demonstrate knowledge of key mathematical and statistical concepts, both explicitly and by applying them to the solution of mathematical problems.

Create structured and coherent arguments communicating them in written form.

Construct and develop logical mathematical arguments with clear identification of assumptions and conclusions.

Reason critically, carefully, and logically and derive (prove) mathematical results.
Transferable skills
 Problem solving: Use rational and logical reasoning to deduce appropriate and wellreasoned conclusions. Retain an open mind, optimistic of finding solutions, thinking laterally and creatively to look beyond the obvious. Know how to learn from failure.
 Self awareness: Reflect on learning, seeking feedback on and evaluating personal practices, strengths and opportunities for personal growth.
 Communication: Written: Present arguments, knowledge and ideas, in a range of formats.
 Professionalism: Prepared to operate autonomously. Aware of how to be efficient and resilient. Manage priorities and time. Selfmotivated, setting and achieving goals, prioritising tasks.
Study time
Type  Required  Optional 

Lectures  20 sessions of 1 hour (16%)  2 sessions of 1 hour 
Seminars  5 sessions of 1 hour (4%)  
Private study  73 hours (59%)  
Assessment  26 hours (21%)  
Total  124 hours 
Private study description
Weekly revision of lecture notes and materials, wider reading and practice exercises working on problem sets and preparing for the examination.
Costs
No further costs have been identified for this module.
You must pass all assessment components to pass the module.
Assessment group D
Weighting  Study time  

Termtime assignments  20%  24 hours 
There will be approximately weekly problem sets. Each problem set will contain a number of individual questions based on the material delivered in the lectures. Problem sheets are supported by seminars, including both analytical and computational tasks. 

Inperson Examination  80%  2 hours 
You will be required to answer all questions on this examination paper.

Assessment group R1
Weighting  Study time  

Inperson Examination  Resit  100%  
You will be required to answer all questions on this examination paper.

Feedback on assessment
Individual feedback will be provided on formative problem sheets by class tutors. A cohortlevel feedback will be available for the examination. Students are actively encouraged to make use of office hours to build up their understanding, and to view all their interactions with lecturers and class tutors as feedback.
Courses
This module is Core for:

USTAG302 Undergraduate Data Science
 Year 1 of G302 Data Science
 Year 1 of G302 Data Science
 Year 1 of USTAG304 Undergraduate Data Science (MSci)
 Year 1 of USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 1 of USTAG1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)

USTAGG14 Undergraduate Mathematics and Statistics (BSc)
 Year 1 of GG14 Mathematics and Statistics
 Year 1 of GG14 Mathematics and Statistics

USTAY602 Undergraduate Mathematics,Operational Research,Statistics and Economics
 Year 1 of Y602 Mathematics,Operational Research,Stats,Economics
 Year 1 of Y602 Mathematics,Operational Research,Stats,Economics