Course overview
This course covers the foundational mathematical methods and probability distribution concept necessary for an in depth understanding of biostatistical methods. The course commences with an introduction to mathematical expressions, followed by the fundamental calculus techniques of differentiation and integration, and essential elements of mixed algebra. The concepts and rules of probability are then introduced , followed by the application of the calculus methods covered earlier in the course to calculate fundamental quantities of probability distributions, such as mean and variance. Random variables, their meaning and use in biostatistical applications is presented, together with the role of numerical simulation as a tool to demonstrate the properties of random variables.
Course learning outcomes
- Manipulate general mathematical expressions and inequalities
- Understand and apply the essential elements of calculus, including differentiation and integration
- Manipulate and evaluate matrix expressions and calculate inverses of matrices
- Demonstrate an understanding of the meaning and laws of probability
- Recognise common probability distributions and their properties
- Apply calculus-based tools to derive key features of a probability distribution and properties of random variables, such as mean and variance
- Demonstrate skills in simulation of random variables to illustrate and explain statistical concepts