Undergraduate Course: Elementary Probability and Statistics Semester 2 (MATH08086)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 8 (Year 2 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 20 |
ECTS Credits | 10 |
| Summary | The course introduces students to the fundamentals of probability theory and the principles of statistical methods by taking a mathematical representation of uncertainty. The outcome of many experiments can be challenging to predict as they result from uncertain or random processes. Examples include flipping a coin, calculating the chance of winning in a game of cards, assessing whether a new treatment is medically beneficial, etc. Such phenomena can be modelled using probabilistic methods and collected data can be statistically assessed to infer meaningful insights.
Topics covered in this course include: combinatorics, random variables, probability distributions, point and interval estimation, hypothesis testing, and simple linear regression. Students will learn how to use the R statistical software to perform probability calculations and conduct statistical assessments.
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| Course description |
This is an elementary course in probability and statistics, laying the foundation for further study of these subjects and demonstrating the strong links between them. A variety of random phenomena can be modelled with probabilistic methods, which possess a rich set of mathematical properties. Data, or observed measurements, are treated as realised values from a random process, allowing us to use probability theory as a basis for statistical methods to make appropriate inference about parameters and, potentially, to make predictions. Students are also provided with a wide range of opportunities to further develop their all-round mathematical skills. Additionally, the statistical package R will be introduced and used to perform a variety of computations.
Main topics will include:
- Basic R programming
- Combinatorics
- Fundamentals of mathematical probability and statistical concepts
- Random variables and associated concepts
- Probability distributions and their properties, including common distribution families
- Central limit theorem and its applications
- Point and interval estimation
- Hypothesis testing
- Simple linear regression
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | Due to limitations on class sizes, students will only be enrolled on this course if it is specifically referenced in their DPT. |
Information for Visiting Students
| Pre-requisites | Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling. |
Course Delivery Information
| Not being delivered |
Learning Outcomes
On completion of this course, the student will be able to:
- Demonstrate understanding of core probabilistic concepts such as random variables, independence, discrete and continuous distributions (multivariate distributions), expectation, variance, and covariance.
- Estimate parameters and confidence intervals from data and test statistical hypothesis.
- Demonstrate understanding of, and reason with, probabilistic and statistical statements in the presence of uncertainty.
- Demonstrate skills in probabilistic and statistical comprehension to extract relevant information into a rigorous mathematical framework
- Use the statistical computer package R to perform statistical analyses.
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Reading List
Blitzstein, Joseph K., and Hwang, J. (2019) Introduction to Probability. Chapman & Hall/CRC.
Devore, J. L., Berk, K. N., & Carlton, M. A. (2012). Modern Mathematical Statistics with Applications. Springer.
Speegle, D., and Clair, Bryan (2021) Probability, Statistics, and Data: A Fresh Approach Using R. Chapman & Hall/CRC.
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Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | Random variables,Probability distributions,central limit theorem,statistical models |
Contacts
| Course organiser | |
Course secretary | |
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