Probability and Statistics 2
| Code | School | Level | Credits | Semesters |
| MATH2108 | Mathematical Sciences | 2 | 20 | Autumn UK |
- Code
- MATH2108
- School
- Mathematical Sciences
- Level
- 2
- Credits
- 20
- Semesters
- Autumn UK
Summary
In this module, the ideas of probability and statistics introduced in MATH1102 are extended to provide a more rigorous introduction to the theory of probability and random variables, with particular attention being paid to continuous random variables and statistical models and methods of estimation and inference.
Topics include:
- Evaluation of probabilities and expectations using multivariate, marginal, and conditional probability mass and density functions, including the multivariate normal distribution.
- Analysis of transformations of one or more random variables.
- Generating functions, distributions of sums of random variables, and the Central Limit theorem.
- Important inequalities and convergence (e.g., Markov and Chebyshev’s inequalities; the Law of Large Numbers).
- Statistical models for data, and likelihood functions.
- Frequentist and Bayesian methods for estimation of parameters in standard statistical models, construction of exact and approximate confidence and credible intervals for parameters, and hypothesis testing.
- Practical data analysis using statistical computing software.
Target Students
Single Honours and Joint Honours students from the School of Mathematical Sciences.
Classes
- Eleven 1-hour lectures each week for 2 weeks
- Eleven 2-hour lectures each week for 2 weeks
Teaching will be through a variety of methods, with delivery tailored to the material on a week-by-week basis.
Assessment
- 40% Coursework: Summative assessment based on tasks distributed through the semester.
- 60% Exam (2-hour): Written examination – Autumn
Assessed by end of autumn semester
Educational Aims
The purpose of this module is to provide a thorough grounding in a broad range of techniques required in the analysis of probabilistic and statistical models, and to introduce a wide range of statistical concepts and methods fundamental to applications of statistics.Learning Outcomes
A student who completes this module successfully will be able to:
L1 – Select and apply suitable mathematical techniques to solve routine and novel problems in probability and statistics.
L2 – Reason logically and work analytically to develop and justify theoretical probability and statistical models, then relate them to real-world problems, extracting relevant information and identifying gaps and where more information is required.
L3 – Summarise complex ideas clearly and concisely, defining the essence of a real-world problem and creating a plan to solve it using appropriate probabilistic and statistical methods.
L4 – Present conclusions, verbally or in writing, using structured and mathematically rigorous arguments and contextually appropriate language, defending their arguments, results, choices or assumptions against query and criticism.
L5 – Make effective use of a statistical software package to conduct computations, analyse data, and visualise results for a range of audiences.
Conveners
- Dr Aidan O'Keeffe
- Dr Christopher Fallaize
- Prof Frank Ball