MAT-20023 - Probability
Coordinator: Jie Cheng Tel: +44 1782 7 33775
Lecture Time: See Timetable...
Level: Level 5
Credits: 15
Study Hours: 150
School Office: 01782 733075

Programme/Approved Electives for 2023/24

None

Available as a Free Standing Elective

No

Co-requisites

None

Prerequisites

MAT-10046 Calculus and MAT-10047 Algebra.

Barred Combinations

None

Description for 2023/24

Probability is the mathematics of uncertainty and randomness. The module begins with classical notions of probability associated with the analysis of games of chance using cards, dice, etc. It then moves to the treatment of the probability of random events. This leads to the definitions of statistical independence and conditional probability. The remainder of the module is concerned with a systematic study of discrete and continuous, univariate and bivariate, random variables, covering expectation, variance, covariance. The theory is applied to a wide range of theoretical and applied problems.

Aims
The aims of the module are to study:
(a) an axiomatic treatment of probability, motivated by classical notions of chance;
(b) the theory of univariate and bivariate random variables and their distributions;
(c) applications of the theory of univariate and bivariate random variables and their distributions.

Intended Learning Outcomes

prove and apply results that are consequences of the axioms of probability: 1,2,3
calculate and apply probability distributions, expectations and variances associated with univariate random variables: 1,2
calculate and apply probability distributions, expectations, variances and covariances associated with bivariate random variables: 1,2
solve problems involving the concepts of independence and conditioning: 1,2,3

Study hours

Lectures: 36 hours
Examples Classes: 12 hours
Continuous assessment preparation: 30 hours
Private study: 70 hours
Unseen examination: 2 hours

School Rules

None

Description of Module Assessment

1: Assignment weighted 15%
Take-home assessment
Continuous online assessment during the module will consist of written coursework, problem sheets, class tests, or any combination thereof.

2: Unseen Exam weighted 70%
Final examination
The examination paper will consist of no less than five and not more than eight questions all of which are compulsory.

3: Class Test weighted 15%
Class test
40 minutes class test covering mainly Chapter 1.