Module Description
Statistics provides methods for describing data, modelling uncertainty, and drawing conclusions from observations. The course begins with descriptive statistics and the graphical and numerical exploration of data. Probability theory and random variables are then introduced as the mathematical foundation for statistical modelling. Finally, limit theorems and methods of statistical inference—including estimation, confidence intervals, and hypothesis testing—provide the tools for drawing conclusions about populations from sample data.
Module Content
1. Descriptive Statistics
- Data, variables, and datasets
- Types and scales of data
- Tabular and graphical representation of data
- Summarizing distributions
- Empirical cumulative distribution function
- Measures of location
- Measures of dispersion
- Exploring relationships between variables
- Scatterplots, covariance, and descriptive correlation
2. Probability Models
- Probability as a measure of uncertainty
- Sample spaces, events, and probability measures
- Laws of probability
- Elementary combinatorics
- Conditional probability
- Bayes' theorem
- Independence
3. Random Variables and Probability Distributions
- Discrete and continuous random variables
- Probability mass functions, density functions, and cumulative distribution functions
- Expectation and variance
- Functions of random variables
- Joint distributions
- Marginal and conditional distributions
- Covariance and correlation
4. Convergence and Limit Theorems
- Sequences of random variables
- Weak and strong laws of large numbers
- Central limit theorem
- Statistical interpretation and relevance of limit theorems
5. Statistical Inference
- Populations, samples, parameters, and statistics
- Point estimation of parameters
- Properties of estimators
- Confidence intervals
- Principles of hypothesis testing
- Null and alternative hypotheses
- Test statistics, significance levels, and p-values
- Interpretation of statistical results