# ST318 - Probability Theory

• Module code: ST318
• Module name: Probability Theory
• Department: Statistics
• Credit: 15

## Module content and teaching

###### Principal aims

This course aims to give the student a rigorous presentation of some fundamental results in measure theoretic probability and an introduction to the theory of discrete time martingales. In so doing it aims to provide a firm basis for advanced work on probability and its applications.

###### Principal learning outcomes

The objectives of the course are as follows: at the end of the course the student will:Understand the ideas relating to independence and zero-one laws and be able to apply these ideas in simple contexts; Understand the different modes of convergence for sequences of random variables (more generally random elements) and the relationship between these different modes; Be able to state and prove the Central Limit Theorem and understand how this result can be applied; Understand some basic results on discrete time martingales and how this theory can be used to prove Kolmogorovâ€™s Strong Law of Large Numbers.

###### Timetabled teaching activities

3 hours per week

http://www2.warwick.ac.uk/fac/sci/statistics/courses/modules/years3-4/st318

###### Other essential notes

Prerequisite(s): ST213 Mathematics of Random Events or MA359 Measure Theory (3rd year).

## Module assessment

Assessment group Assessment name Percentage
15 CATS (Module code: ST318-15)
B (Examination only) 2 hour examination (Summer) 100%

## Module availability

This module is available on the following courses:

###### Core
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30A) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30D) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30E) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30E) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30H) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30H) - Year 4
• Undergraduate Discrete Mathematics (G4G3) - Year 3
###### Optional Core
• Undergraduate Mathematics and Statistics (BSc MMathStat) (G1G3) - Year 3
###### Optional
• Undergraduate Mathematics (BSc) (G100) - Year 3
• Undergraduate Mathematics with Intercalated Year (G101) - Year 4
• Undergraduate Mathematics (MMath) (G103) - Year 3
• Undergraduate Mathematics (MMath) (G103) - Year 4
• Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 3
• Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 4
• Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 5
• Undergraduate Mathematics (MMath) with Study in Europe (G106) - Year 3
• Undergraduate Mathematics (MMath) with Study in Europe (G106) - Year 4
• Undergraduate Mathematics and Statistics (BSc MMathStat) (G1G3) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G300) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G300) - Year 4
• Undergraduate Data Science (G302) - Year 3
• Undergraduate Data Science (with Intercalated Year) (G303) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30A) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30A) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30A) - Year 5
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30B) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30B) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30B) - Year 5
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30C) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30C) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30C) - Year 5
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30D) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30D) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30D) - Year 5
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30E) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30E) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30E) - Year 5
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30F) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30F) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30F) - Year 5
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30G) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30G) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30G) - Year 5
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30H) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30H) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30H) - Year 5
• Undergraduate Discrete Mathematics (G4G1) - Year 3
• Undergraduate Discrete Mathematics with Intercalated Year (G4G2) - Year 4
• Undergraduate Mathematics and Physics (with Intercalated Year) (GF14) - Year 4
• Undergraduate Mathematics and Statistics (BSc) (GG14) - Year 3
• Undergraduate Mathematics and Statistics (with Intercalated Year) (GG17) - Year 4
• Undergraduate Mathematics,Operational Research,Statistics and Economics (Y602) - Year 3
• Undergraduate Mathematics,Operational Research,Statistics,Economics (with Intercalated Year) (Y603) - Year 4