# Mathematical Statistics module (MA52007)

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Credits

15

Module code

MA52007

### About the module

Mathematical Statistics is an important area, providing useful connections to other areas of Mathematics, and having applications across the sciences, business, government and more.

In this module you will engage with and extend the fundamentals of Mathematical Statistics including Distribution Theory, Statistical Inference, and Models, with Applications in R.

This module is aimed at level 5 students. This module may be taken in combination with other Level 4 and 5 modules by Level 5 students. If you have questions about this module or the possible combinations, please contact your Advisor of Studies.

### Prerequisites

Students taking this module must have achieved a pass mark in the module MA22004 or equivalent.

### Indicative Content

• Descriptive Statistics and R
• Review the basics of the R system
• Graphical display of data. Charts, tables and grouped data.
• Probability and Distributions
• Probability Review. Combinatorics, Events, Discrete and Continuous Random Variables, Expected Values.
• Theory of Discrete Distributions: (including) Binomial, Geometric, Hypergeometric, and Poisson
• Theory of Continuous Distributions: (including) Uniform, Normal, Exponential, Gamma, Chi-squared.
• Transforming Random Variables. Transformations and Computations.
• Statistical Models and Estimation
• Sampling Distributions. Random Sampling. The Central Limit Theorem.
• Point estimation. Cramer-Rao. Moments. Maximum Likelihood.
• Confidence Intervals. One sample and two sample. Large samples. Bootstrap methods. Hypothesis testing.
• Regression, Correlation and Analysis of Variance
• Simple Linear Regression and Forms of Correlation.
• ANOVA
• Multiple Regression and Linear Models
• Goodness of Fit Tests and Categorical Data Analysis

### Delivery and Assessment

The module is delivered in the form of lectures and computer workshops/tutorials and assessed via an exam (60%) and coursework (40%). Coursework will include short written tests and computer lab reports. Students on MA52007 will do additional more advanced level assignments that will not form part of the assessment for MA42008.

### Credit Rating

This module is a Scottish Higher Education Level 5 or SCQF level 11 module and is rated as 15 SCOTCAT credits or 7.5 ECTS credits.