Introduction to Mathematical Statistics
This course provides a precise and accurate treatment of probability, distribution theory and statistical
inference at the introductory level.
- Data visualisation and descriptive statistics
- Probability theory
- Random variables
- Common distributions of random variables
- Multivariate random variables
- Sampling distributions of statistics
- Point estimation
- Interval estimation
- Hypothesis testing
- Analysis of variance
- Linear regression
At the end of this course, and having completed the Recommended reading and activities, students
should be able to:
- Compute probabilities of events, including for univariate and multivariate random variables.
- Apply and be competent users of standard statistical operators and be able to recall a variety of well-known probability distributions and their respective moments.
- Derive estimators of unknown parameters using method of moments, least squares and maximum likelihood estimation techniques, and analyse the statistical properties of estimators.
- Explain the fundamentals of statistical inference and develop the ability to formulate the hypothesis of interest, derive the necessary tools to test this hypothesis and interpret the results in a number of different settings.
- Be familiar with the fundamental concepts of statistical modelling, with an emphasis on analysis of variance and linear regression models.
All essential reading is provided within the course materials. A recommended textbook for additional exposition and practice problems is:
- Larsen, R.J. and M.J. Marx (2017) An Introduction to Mathematical Statistics and Its
Applications, Pearson Education, 6th edition.
