# ST119-10 Probability 2

22/23
Department
Statistics
Level
Saul Jacka
Credit value
10
Module duration
10 weeks
Assessment
Multiple
Study location
University of Warwick main campus, Coventry

##### 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 proof-oriented setting;
• to develop communication skills in mathematics including proof writing;
• to develop systematic problem-solving 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 self-regulation 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.

##### 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 well-reasoned 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. Self-motivated, setting and achieving goals, prioritising tasks.

## Study time

Type Required Optional
Lectures 20 sessions of 1 hour (20%) 2 sessions of 1 hour
Seminars 5 sessions of 1 hour (5%)
Private study 73 hours (73%)
Assessment 2 hours (2%)
Total 100 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 B
Weighting Study time
In-person Examination 100% 2 hours

You will be required to answer all questions on this examination paper.

• Answerbook Pink (12 page)
##### Assessment group R
Weighting Study time
In-person Examination - Resit 100%

You will be required to answer all questions on this examination paper.

• Answerbook Pink (12 page)
• Students may use a calculator
• Cambridge Statistical Tables (blue)
##### Feedback on assessment

Individual feedback will be provided on formative problem sheets by class tutors. A cohort-level 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:

• USTA-G302 Undergraduate Data Science
• Year 1 of G302 Data Science
• Year 1 of G302 Data Science
• Year 1 of USTA-G304 Undergraduate Data Science (MSci)
• Year 1 of USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
• Year 1 of USTA-G1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
• USTA-GG14 Undergraduate Mathematics and Statistics (BSc)
• Year 1 of GG14 Mathematics and Statistics
• Year 1 of GG14 Mathematics and Statistics
• USTA-Y602 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

Assessments dates for Statistics modules, including coursework and examinations, can be found in the Statistics Assessment Handbook.