MA22039: Probability theory
[Page last updated: 03 June 2024]
| Academic Year: | 2024/25 |
| Owning Department/School: | Department of Mathematical Sciences |
| Credits: | 10 [equivalent to 20 CATS credits] |
| Notional Study Hours: | 200 |
| Level: | Intermediate (FHEQ level 5) |
| Period: |
- Semester 2
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| Assessment Summary: | EXCB 100% |
| Assessment Detail: |
- Closed-book written examination (EXCB 100%)
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| Supplementary Assessment: |
- Like-for-like reassessment (where allowed by programme regulations)
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| Requisites: |
Before taking this module you must take MA22038
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| Learning Outcomes: |
On completing the unit, you will be able to:
- Formalize problems in a probabilistic framework;
- Understand and prove the convergence of random variables;
- Study standard branching processes;
- Study random walks in dimension one;
- Compute event probabilities for Poisson processes.
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| Synopsis: | In this unit, you will learn about the fundamentals of probability theory. These fundamentals allow you to formalize many problems that can be modelled using techniques from probability. Moreover, you will develop various mathematical tools to work with limits in a probabilistic setting. This unit gives you the toolkit necessary for the more advanced probability units.
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| Content: | Theoretical content: Kolmogorov axioms; measure theory essentials: discrete and continuous random variables, expectation of random variables and convergence theorems; modes of convergence of random variables; Borel-Cantelli lemmas; law of large numbers; central limit theorem and Lindeberg's proof; conditional expectation.
Main models used as illustration: one-dimensional random walks; branching process; Poisson processes.
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| Course availability: |
MA22039 is Optional on the following courses:
Department of Computer Science
- USCM-AFB32 : BSc(Hons) Computer Science and Mathematics (Year 2)
- USCM-AKB32 : BSc(Hons) Computer Science and Mathematics with professional placement (Year 2)
- USCM-AKB32 : BSc(Hons) Computer Science and Mathematics with study abroad (Year 2)
Department of Economics
- UHES-AFB12 : BSc(Hons) Economics and Mathematics (Year 2)
- UHES-AKB12 : BSc(Hons) Economics and Mathematics with professional placement (Year 2)
- UHES-AKB12 : BSc(Hons) Economics and Mathematics with professional placement and study abroad (Year 2)
- UHES-AKB12 : BSc(Hons) Economics and Mathematics with study abroad (Year 2)
Department of Mathematical Sciences
- USMA-AFB30 : BSc(Hons) Mathematics (Year 2)
- USMA-AFB32 : BSc(Hons) Mathematics and Statistics (Year 2)
- USMA-AKB32 : BSc(Hons) Mathematics and Statistics with professional placement (Year 2)
- USMA-AKB32 : BSc(Hons) Mathematics and Statistics with study abroad (Year 2)
- USMA-AFB33 : BSc(Hons) Mathematics, Statistics and Data Science (Year 2)
- USMA-AKB33 : BSc(Hons) Mathematics, Statistics and Data Science with professional placement (Year 2)
- USMA-AKB33 : BSc(Hons) Mathematics, Statistics and Data Science with study abroad (Year 2)
- USMA-AKB30 : BSc(Hons) Mathematics with professional placement (Year 2)
- USMA-AKB30 : BSc(Hons) Mathematics with study abroad (Year 2)
- USMA-AFM30 : MMath(Hons) Mathematics (Year 2)
- USMA-AKM30 : MMath(Hons) Mathematics with professional placement (Year 2)
- USMA-AKM31 : MMath(Hons) Mathematics with study abroad (Year 2)
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Notes: - This unit catalogue is applicable for the 2024/25 academic year only. Students continuing their studies into 2025/26 and beyond should not assume that this unit will be available in future years in the format displayed here for 2024/25.
- Courses and units are subject to change in accordance with normal University procedures.
- Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.
- Find out more about these and other important University terms and conditions here.
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