## Probability and Sampling Fundamentals (ODL) STATS5094

• School: School of Mathematics and Statistics
• Credits: 10
• Level: Level 5 (SCQF level 11)
• Typically Offered: Semester 1
• Available to Visiting Students: No
• Taught Wholly by Distance Learning: Yes

### Short Description

This course introduces students to key concepts from probability theory and provides an introduction to survey sampling with a focus on the underpinning probabilistic mechanisms.

### 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 (Level M)

Probability and Stochastic Models (ODL)

-/-

### Assessment

100% Continuous Assessment. The continuous assessment will typically be made up of six pieces of assessment, including four online quizzes (20%) and two class tests (30% and 50%). Full details are provided in the programme handbook.

### Course Aims

The course aims to introduce students to probability theory with a focus on understanding and being able to apply concepts, rather than deriving these concepts in a mathematically rigorous manner. Students will be introduced to key concepts in probability theory, univariate and multivariate random variables developing and moments. The course aims to prepare students to solve real-life problems using stochastic models.
Using the concepts from probability covered in the first part of the course, the course introduces students to sampling from a finite population. The course aims to equip students with an understanding of key concepts in sampling such as the difference between sampling with and without replacement, stratification and nonresponse.

### Intended Learning Outcomes of Course

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

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

■ compute moments in one or more dimensions (including the vector of expected values and the variance-covariance matrix) for given distributions and interpret them;

■ 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;

■ explain and apply key concepts in large sample theory;

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

■ explain the difference between different strategies for sampling in a probabilistic context and discuss advantages and disadvantages of these strategies in a context;

■ estimate parameters and their uncertainty in a finite population; and

■ 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.