This lecture by the instructor covers the basics of statistical modelling, including the explanatory and generative frameworks, the role of probability in data analysis, and the concepts of parametric and non-parametric problems. It also delves into the fundamentals of probability, conditional probability, and independence, providing insights into random variables, joint distributions, and probability mass functions. The lecture emphasizes the importance of understanding the joint distribution of random vectors and how to model outcomes of experiments using probability theory.