Statistics (Double Degree with the University of Bologna) BSc/LSc
Statistics 2X: Probability II STATS2005
- Academic Session: 2026-27
- School: School of Mathematics and Statistics
- Credits: 10
- Level: Level 2 (SCQF level 8)
- Typically Offered: Semester 2
- Available to Visiting Students: Yes
- Collaborative Online International Learning: No
- Curriculum For Life: No
Short Description
This course introduces students to multivariate probability distributions and basic concepts in large sample theory;
Timetable
Lectures: Monday and Wednesday at 9.00 am.
Workshops and drop-in help-rooms arranged via MyCampus (several groups available).
Co-requisites
Statistics 2R: Probability
Mathematics 2A
Mathematics 2B
Assessment
End-of-course examination (80%); coursework (20%).
Reassessment will, generally, not be available for the coursework.
Main Assessment In: April/May
Course Aims
The aims of this course are:
■ to introduce students to multivariate probability distributions;
■ to introduce students to methods for obtaining the distribution of a sum or mean of a sequence of independent random variables;
■ to equip students to apply probability to solve problems from a wide range of disciplines;
■ to promote an interest in Probability and Statistics and hence encourage students to study more advanced courses.
Intended Learning Outcomes of Course
By the end of this course students will be able to:
■ explain the terms joint distribution and independent random variables;
■ derive marginal and conditional distributions and their moments, and the covariance and correlation between random variables (both discrete and continuous);
■ find the distribution of functions of more than one random variable;
■ use standard methods to derive the distribution of the sum of a sequence of random variables;
■ use and derive links between different discrete and continuous distributions;
■ define and use the multivariate normal distribution and use and derive core properties such as the marginal and conditional distributions
■ state, use and derive probability inequalities such as the Chebyshev inequality;
■ state, explain and use the laws of large numbers and the central limit theorem.