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MA2010: PROBABILITY (2018-2019)

Last modified: 22 May 2019 17:07


Course Overview

Probability theory is concerned with the analysis of random phenomena by providing an abstract mathematical framework to study them within the language of set theory. This is done by the concepts of "probability spaces" and "random variables". The theory began in the 16th century in attempts to analyze games of chance; In 1812 Pierre Simon Laplace wrote: "It is remarkable that a science which began with the consideration of games of chance should have become the most important object of human knowledge."

The course is recommended to anyone interested in the foundations and applications of mathematics.




Course Details

Study Type Undergraduate Level 2
Session First Sub Session Credit Points 15 credits (7.5 ECTS credits)
Campus None. Sustained Study No
Co-ordinators
  • Professor Vassili Gorbunov

Qualification Prerequisites

  • Programme Level 2

What courses & programmes must have been taken before this course?

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

No

Course Description

  • Sample spaces and the probability function.
  • Application of conditional probability and the partition theorem.
  • Random variables and distribution functions.
  • Expectation and variance.
  • Limit theorems and their application.
  • Generating functions and their uses.
  • Branching processes.
  • Markov Chains.

Syllabus

  • Sample spaces and (discrete) probability spaces.
  • Conditional probability and the partition theorem.
  • Random variables and distribution functions.
  • Expectation and variance of random variables. Linearity of the expectation. The covariance.
  • Independent random variables.
  • Frequently used distributions: Bernoulli, binomial, geometric, hypergeometric, Poisson.
  • Limit theorems (Chebyshef's inequality, the weak law of large numbers, the central limit theorem).
  • Branching processes (if time permits).

Further Information & Notes

Course Aims
To provide an introduction to \probability theory", namely the mathematical framework used to study events involving randomness. Applications range from game theory to financial mathematics.

 

Learning Objectives
_Understand the basic concepts of probability:
_ Sample spaces and the probability function.
_ Application of \conditional probability" and the partition theorem.
_ Random variables and distribution functions.
_ Expectation and variance.
_ Limit theorems and their application.
_ Generating functions and their uses.
_ Branching processes and Markov chains.

In light of Covid-19 this information is indicative and may be subject to change.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

  • 2 Lectures during University weeks 7 - 17
  • 1 Tutorial during University weeks 7 - 17

More Information about Week Numbers


In light of Covid-19 and the move to blended learning delivery the assessment information advertised for second half-session courses may be subject to change. All updates for second-half session courses will be actioned in advance of the second half-session teaching starting. Please check back regularly for updates.

Summative Assessments

1st Attempt: 1 two-hour written examination (80%), in-course assessment (20%).

Resit: 1 two-hour written examination paper, maximum resit (100%) and resit (80%) with (20%) in-course assessment (20%).

Formative Assessment

Informal assessment of weekly homework through discussions in tutorials.

Feedback

In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact the Course Coordinator for feedback on the final examination.

Course Learning Outcomes

None.

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