# Probability and Stochastic Models (ODL) STATS5077

**Academic Session:**2019-20**School:**School of Mathematics and Statistics**Credits:**10**Level:**Level 5 (SCQF level 11)**Typically Offered:**Semester 1**Available to Visiting Students:**No**Available to Erasmus Students:**No**Taught Wholly by Distance Learning:**Yes

#### Short Description

This course provides a structured development of probability theory and its use to construct stochastic models. The pace of the course is brisk, as it begins from the assumption that students have little prior exposure to probability yet reaches advanced concepts by the end. The course aims both at developing a theoretical understanding as well as equipping students with the skills to use stochastic models in an applied context.

#### Timetable

The course mostly consists of asynchronous teaching material.

#### Requirements of Entry

The course is only available to online-distance learning students on the PGCert/PGDip/MSc in Data Analytics and Data Analytics for Government.

#### Excluded Courses

Statistics 2R: Probability

Statistics 2X: Probability II

Probability

Probability (Level M)

#### Co-requisites

-/-

#### Assessment

30% Continuous Assessment

70% Final exam (can be taken at test centres)

The continuous assessment typically consists of five homework exercises. Full details are provided in the programme handbook.

**Main Assessment In:** April/May

#### Course Aims

The aims of this course are:

■ to provide a structured development of probability theory, with an emphasis on the theory of random variables and random vectors;

■ to prepare students to solve real-life problems using stochastic models

#### Intended Learning Outcomes of Course

By the end of this course students will be able to:

■ state the Axioms of Probability and use them to prove basic propositions in probability theory;

■ use probability mass functions and probability density functions in one or more dimensions to compute probabilities and percentiles in particular cases;

■ write down general definitions of moments in one or more dimensions (including the vector of expected values and the variance-covariance matrix), derive general properties from these definitions, and compute moments in particular cases;

■ recognise some of the standard discrete and continuous probability distributions in a context, and use them to obtain probabilities, percentiles and moments;

■ use the joint distribution of a random vector to derive marginal or conditional distributions of one or more of the component variables;

■ determine whether two or more random vectors are independent;

■ write down general definitions of the moment generating function in one or more dimensions, derive general properties from these definitions, and compute the functions in particular cases;

■ find the distribution of functions of random variables in one or more dimensions;

■ state and use the laws of large numbers and the central limit theorem;

■ state and use properties of the multinomial and Multivariate Normal (MVN) distribution;

■ integrate their knowledge of topics in the course to solve realistic problems.

#### Minimum Requirement for Award of Credits

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.