Unit name | Probability 34 |
---|---|
Unit code | MATHM0700 |
Credit points | 10 |
Level of study | M/7 |
Teaching block(s) |
Teaching Block 1B (weeks 7 - 12) |
Unit director | Dr. Leslie |
Open unit status | Not open |
Pre-requisites |
None |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
This course deals with various modes of convergence of random variables (almost surely, weak, in probability, and in Lp) and the connections between them. We also discuss and prove weak laws and strong laws of large numbers, prove the Borel-Cantelli lemmas, the Kolmogorov 0-1 law, and the three series theorem. We study the properties and applications of characteristic functions. Central Limit Theorems, Lindeberg conditions, Local limit theorems, Barry-Essen inequality will proved / discussed.
Aims
To outline, discuss, and prove some of the key results in probability theory and their applications to statistics.
Syllabus
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, 3, and M.
To gain a (better) understanding of:
Transferable Skills:
Self-assessment by working examples sheets and using solutions provided.
Lectures, assignments, and exercises to be done by students.
20% of the assessment mark for Probability 34 is based on the assignment done during the course.
80% of the assessment mark 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.
Each of the following texts will be useful: