This second course builds on the introductory statistics course, further exploring key statistical problems and their solution methods.

Lectures-Tutorials-Practicals-Credits: 4-0-0-4

Week 1: Multiple random variables - joint, marginal, conditional PMFs; Conditioning and examples.

Week 2: Independence of random variables; Functions and visualisation (one and two variables); Sum, minimum and maximum; Examples.

Week 3: Expectation (properties, simulation); Variance and standard deviation; Covariance and correlation; Probability bounds.

Week 4: Continuous random variables - CDF, PDF; Discrete vs continuous; Approximation; Common distributions; Colab illustrations.

Week 5: Continuous random variables - functions and expectations; Joint distributions (discrete and continuous); Motivation.

Week 6: Jointly continuous random variables; Marginal and conditional densities; Independence; From data to distributions; 1D/2D histograms (Colab).

Week 7: Statistics from i.i.d. samples; Empirical distribution and descriptive statistics; Sum of independent random variables; Data illustrations.

Week 8: Moment generating functions; Central Limit Theorem; Distributions and properties; Descriptive statistics of normal samples.

Week 9: Parameter estimation; Error, bias, variance and risk; Method of moments and maximum likelihood estimation; Evaluation of ML estimators; Real-life statistical problems.

Week 10: Bayesian estimation; Choice of priors; Estimation problems; Model estimation.

Week 11: Hypothesis testing - introduction and types; Size and power of tests; z-test and p-value; Problem solving and data-based inference.

Week 12: t-test (mean, unknown variance); Chi-squared test (variance); Two-sample tests (z/F); Tests for normal samples; Problem solving.