Unit information: Probability 3 in 2012/13

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Unit name Probability 3
Unit code MATH35700
Credit points 10
Level of study H/6
Teaching block(s) Teaching Block 1B (weeks 7 - 12)
Unit director Dr. Leslie
Open unit status Not open
Pre-requisites

MATH11340
Co-requisites

None
School/department School of Mathematics
Faculty Faculty of Science

Description including Unit Aims

This unit develops the rigorous theoretical background to much of the probabilistic (and partly statistical) methodology covered in probability/statistics units at levels 1, 2 and 3. It deals with various modes of convergence of random variables and the connections between them, weak laws and strong laws of large numbers, and a range of theorums including Central Limit Theorums, and local limit theorums.

Aims

To outline, discuss, and prove some of the key results in probability theory and their applications to statistics.

Syllabus

  • Properties of conditional expectations.
  • Modes of convergence of random variables.
  • Borel-Cantelli lemmas, 0-1 laws.
  • Weak and Strong law of large numbers.
  • Characteristic functions.
  • Central Limit Theorems and related topics.

Relation to Other Units

This unit develops the rigorous theoretical background to much of probabilistic (and partly statistical) methodology covered in probability/statistics units at levels 1, 2, and 3.

Intended Learning Outcomes

To gain a (better) understanding of:

  1. Conditional expectations;
  2. Types of convergence of random variables;
  3. Strong and Weak laws and Central Limit Theorems;
  4. The ways to establish the above results rigorously.

Transferable Skills:

Self-assessment by working examples sheets and using solutions provided.

Teaching Information

Lectures, exercises to be done by students.

Assessment Information

The assessment mark for Probability 3 is calculated from a 1½-hour written examination in April consisting of THREE questions. A candidate's best TWO answers will be used for assessment. Calculators are NOT permitted for this examination.

Reading and References

Each of the following texts will be useful:

  1. R. Durrett, Probability: Theory and Examples, 2nd edition, Duxbury Press.
  2. S.R.S. Varadhan, Probability Theory, AMS
  3. G.R. Grimmett and D.R. Stirzaker, Probability and Random Processes, Oxford Univ. Press.

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