Coursework –tests 

2 - Set exercises - 15

3-hour examination

3 - Written exam - 70

Coursework -Computer-based assessment 

1 - Set exercises - 15

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This module will cover the following topics and more details about the specific content of individual lectures will be uploaded to Moodle as the module progresses. 
<ul><li>Univariate discrete and continuous distributions. </li><li>Independence, joint and conditional distributions, linear combinations of random variables. </li><li>Conditional expectation. Generating functions. </li><li>Limiting distributions. Central limit theorem. </li><li>Point estimation: method of moments and maximum likelihood. Properties of estimators. </li><li>Confidence intervals and hypothesis testing. </li><li>Bootstrap methods and permutation tests. </li><li>Simple and multiple linear regression. </li><li>Generalised linear models. </li><li>Bayesian statistics. </li><li>Applications in R (simulation of random variables, regression and applications, exploratory data analysis). </li></ul>

Feedback is provided in a number of ways throughout your module. This includes feedback you receive during teaching from both peers and lecturers and that provided for formative assessment. Following an assessment, you will be given your marks and feedback in line with the assessment regulations and policy. More information on the timing and type of feedback that will be provided for each assessment will be available from the module leader. <a href='https://www.citystgeorges.ac.uk/about/governance/policies/student-policies-and-regulations'>https://www.citystgeorges.ac.uk/about/governance/policies/student-policies-and-regulations</a>

This module will support the development of all the graduate attributes. Your module leader will provide you with information about how your learning, teaching and assessment activities support your development of these attributes. The graduate attributes are: - Always learning - Engaged in the world - Technical and digital - Connected Professional - Creating Impact

Self-directed - 

In-Person - 

Directed Asynchronous - 

Introduction to Probability and Statistics Using R

Probability and Statistics with R

Oxford, Elsevier/Academic Press. (Ebook available) 

Introduction to probability models

Introduction to mathematical statistics

Boca Raton, Chapman and Hall/CRC Press (Available online) 

An Introduction to Generalised Linear Models

Institute and Faculty of Actuaries Official Core Reading for Subject CS1

SMM047 - Probability and Mathematical Statistics (Subject CS1)

SMM047-PRD1-PER-ALV1

This module will be taught primarily through lectures and online lectures as well as the use of practical exercises.   
You will also be expected to spend a significant amount of time in self-directed study. 
Self-directed learning hours are for independent study and account for the minimum amount of time you should spend studying independently. For example, carrying out subject research, practising and reflecting on techniques learned in class, reading widely around the subject to develop a deeper understanding, carrying out activities using the VLE, attending induction and career development workshops, working in groups to complete assignments and presentations, and completing individual assignments and other homework.

Probability and Mathematical Statistics (Subject CS1)

Reflect on how statistics can be applied in actuarial work and understand the benefits and limitations of statistical models. 

Values and attitudes

Recognise the limitations of statistical conclusions and acknowledge the uncertainty. 

Apply and debate the principles of statistical inference. 

Knowledge

Test hypotheses and derive confidence intervals based on one or multiple samples. 

Skills

Define the concept of a random variable and show proficiency in its use over a broad range of applications. 

Explain and evaluate the theory underlying statistical techniques. 

Explain the fundamental concepts of Bayesian statistics and use them to compute Bayesian estimators. 

Solve problems involving more than one random variable. 

Derive and compute moments of distributions, either directly or using generating function techniques.

Summarise data using appropriate statistical analysis, descriptive statistics and graphical presentation. 

Consider how mathematical statistics can be used to measure the probability and risk of future events. 

Apply and interpret the results of the linear regression model and generalised linear regression models. 

Describe the essential features of statistical distributions. 