# ST220 - Introduction to Mathematical Statistics

• Module code: ST220
• Module name: Introduction to Mathematical Statistics
• Department: Statistics
• Credit: 12

## Module content and teaching

###### Principal aims

To introduce the main ideas of statistical inference, emphasising the use of likelihood for estimation and testing. These ideas are fundamental to the use of statistics in modern applications such as mathematical finance, telecommunications, bioinformatics as well as more traditional areas such as insurance, engineering and the social sciences.

###### Principal learning outcomes

1. Standard families of Probability distributions: Binomial, Geometric, Poisson, Exponential, Gamma, Gaussian. 2. The weak law of large numbers and central limit theorem. 3. The Multivariate Gaussian distribution. Orthogonality and Independence for jointly Gaussian random variables. Distributions derived from the Gaussian: Chi-squared, t and F. 4. The notion of a parametrized Statistical model, and examples. 5. Likelihood including maximum likelihood estimates and use of likelihood ratios to compare hypotheses. 6. The repeated sampling principle: bias and MSE, confidence intervals and p-values. 7. Fisher's theorem on Gaussian sampling, and its extension to linear regression.

###### Timetabled teaching activities

3 lectures a week, 5 hours of tutorials. This module runs in Term 1.

http://www2.warwick.ac.uk/fac/sci/statistics/modules/st2/st220

###### Other essential notes

This module is designed for students in the Mathematics department (and other non Statistics department students). It serves as a prerequisite, replacing ST218/219 Mathematical Statistics A&B for many of the 3rd year Statistics modules.

## Module assessment

Assessment group Assessment name Percentage
12 CATS (Module code: ST220-12)
B (Examination only) 2 hour examination (Summer) 100%

## Module availability

This module is available on the following courses:

N/A

N/A

###### Optional
• Undergraduate Mathematics (BSc) (G100) - Year 2
• Undergraduate Mathematics (BSc) (G100) - Year 3
• Undergraduate Mathematics with Intercalated Year (G101) - Year 2
• Undergraduate Mathematics with Intercalated Year (G101) - Year 4
• Undergraduate Mathematics (MMath) (G103) - Year 2
• Undergraduate Mathematics (MMath) (G103) - Year 3
• Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 2
• Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 3
• Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 4
• Undergraduate Mathematics (MMath) with Study in Europe (G106) - Year 2
• Undergraduate Mathematics (MMath) with Study in Europe (G106) - Year 3
• Undergraduate Mathematics and Business Studies (with Intercalated Year) (G1N2) - Year 2