School of Computing and Mathematics

Faculty of Natural Sciences

For academic year: 2023/24 Last Updated: 13 February 2024

MAT-20023 - Probability

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MAT-10046 Calculus and MAT-10047 Algebra.

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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.

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.

(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.

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

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

Lectures: 36 hours

Examples Classes: 12 hours

Continuous assessment preparation: 30 hours

Private study: 70 hours

Unseen examination: 2 hours

Examples Classes: 12 hours

Continuous assessment preparation: 30 hours

Private study: 70 hours

Unseen examination: 2 hours

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Take-home assessment

Continuous online assessment during the module will consist of written coursework, problem sheets, class tests, or any combination thereof.

Final examination

The examination paper will consist of no less than five and not more than eight questions all of which are compulsory.

Class test

40 minutes class test covering mainly Chapter 1.