Quantiles and Functions of Random Variables

This lecture covers the definition of quantiles for a function, including the 0.5th quantile known as the median. It explains how to calculate quantiles for different distributions and discusses the uniqueness of quantiles for most continuous random variables. The lecture also delves into conditional densities, probability density functions, and distribution functions of random variables, both discrete and continuous. The concept of functions of random variables is explored, along with examples of calculating mass functions and expectations. The Jacobian matrix in variable transformations is introduced, along with a theorem summarizing results on scalar variable transformations.