Probability - MAST4009

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Module delivery information

Location Term Level1 Credits (ECTS)2 Current Convenor3 2024 to 2025
Canterbury
Autumn Term 4 15 (7.5) Jian Zhang

Overview

Introduction to Probability. Concepts of events and sample space. Set theoretic description of probability, axioms of probability, interpretations of probability (objective and subjective probability).
Theory for unstructured sample spaces. Addition law for mutually exclusive events. Conditional probability. Independence. Law of total probability. Bayes' theorem. Permutations and combinations. Inclusion-Exclusion formula.
Discrete random variables. Concept of random variable (r.v.) and their distribution. Discrete r.v.: Probability function (p.f.). (Cumulative) distribution function (c.d.f.). Mean and variance of a discrete r.v. Examples: Binomial, Poisson, Geometric.
Continuous random variables. Probability density function; mean and variance; exponential, uniform and normal distributions; normal approximations: standardisation of the normal and use of tables. Transformation of a single r.v.
Joint distributions. Discrete r.v.'s; independent random variables; expectation and its application.
Generating functions. Idea of generating functions. Probability generating functions (pgfs) and moment generating functions (mgfs). Finding moments from pgfs and mgfs. Sums of independent random variables.
Laws of Large Numbers. Weak law of large numbers. Central Limit Theorem.

Details

Contact hours

Total contact hours: 47
Private study hours: 103
Total study hours: 150

Method of assessment

Assessment 1 Exercises, requiring on average between 10 and 15 hours to complete 15%
Assessment 2 Exercises, requiring on average between 10 and 15 hours to complete 15%
Examination 2 hours 70%
The coursework mark alone will not be sufficient to demonstrate the student's level of achievement on the module.

S. Ross, A First Course in Probability (9th ed.), Pearson, 2012.
J.H.McColl, Probability, Butterworth-Heinmann, 1995.

See the library reading list for this module (Canterbury)

Learning outcomes

The intended subject specific learning outcomes.
On successfully completing the module students will be able to:
1 demonstrate knowledge of the underlying concepts and principles associated with probability
2 demonstrate the capability to make sound judgements in accordance with the basic theories and concepts in the following areas, whilst demonstrating a reasonable level
of skill in calculation and manipulation of the material: set theoretic description of probability, axioms of probability, random variables, examples of discrete and continuous
distributions, generating functions, weak law of large numbers.
3 apply the underlying concepts and principles associated with probability in several well-defined contexts, showing an ability to evaluate the appropriateness of different
approaches to solving problems in this area.

Notes

1. Credit level 4. Certificate level module usually taken in the first stage of an undergraduate degree.
2. ECTS credits are recognised throughout the EU and allow you to transfer credit easily from one university to another.
3. The named convenor is the convenor for the current academic session.